![Alignment between SS block and channel RBs (see section 4.3.14 of [5])](https://www.researchgate.net/publication/342221540/figure/fig2/AS:11431281127533654@1679051121861/Alignment-between-SS-block-and-channel-RBs-see-section-4314-of-5_Q320.jpg)
![A typical non-coherent PRACH receiver processing chain [37].](https://www.researchgate.net/publication/342221540/figure/fig5/AS:11431281127533655@1679051122191/A-typical-non-coherent-PRACH-receiver-processing-chain-37_Q320.jpg)
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VOLUME XX, 2020 1
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, 2020
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THIS WORK IN OTHER WORKS
VOLUME XX, 2020 1
Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier xx.xxxx/ACCESS.2020.Doi Number
On the design details of SS/PBCH, Signal
Generation and PRACH in 5G-NR
Arvind Chakrapani1, Member, IEEE
1Qualcomm Technologies, Inc, Bridgewater, NJ 08807 USA
Corresponding author: (e-mail: achakrap@ qti.qualcomm.com).
ABSTRACT The 3rd Generation Partnership Project (3GPP) specification of the fifth generation (5G) New
Radio (NR) allows for a highly scalable and flexible radio access technology to cater to network operators
with different requirements. Such scalability and flexibilities in network configurations inevitably translate
to complications in the design and implementation of 5G-NR systems. Radio access in 5G-NR is much more
complex and involved than its predecessor, 4G long term evolution (LTE) and LTE-Advanced technology.
Therefore, the 5G-NR specifications turn out to be quite dense. Specifically, the specifications are concise,
design motivations rarely explained, and the information can be convoluted or distributed across several
documents. Moreover, there are several key design details associated with the access layer procedures for
any given physical layer channel, which are often omitted in the specifications. For example, design
motivation aspects of initial access channels or signal generation can be quite difficult to follow or understand
in 5G-NR. In this paper, all the design details associated with initial access channels and signal generation in
5G-NR specifications are laid out. The contributions of the paper are three folds. First, the design details and
justifications associated with both downlink and uplink access channels are presented along with signal
generation details. Secondly, receiver design aspects of NR PRACH short formats are discussed. Lastly,
PRACH receiver implementation aspects and performance reports from different network operators are
presented and compared with 3GPP specified Radio Performance and Protocol aspect requirements1 for
millimeter wave (mmW) access. The work in this paper is of significant value to researchers and system
engineers looking to design and build initial access algorithms as part of 5G NR systems.
INDEX TERMS 3GPP, 5G-NR, 4G, LTE, OFDM
I. INTRODUCTION
With innumerous and radically diverse deployment
scenarios in 5G-NR, the NR cell architecture should offer
scalability and flexibility across an extreme variation in
connectivity requirements[1]. Very high throughput (1 Gbps
or more), ultra-low latency (order of 0.5ms in some cases),
ultra-high reliability and mobility with low energy
consumption are the key driving factors of 5G-NR. Towards
this end, all the physical layers channels can be configured
flexibly to cater for different scenarios. Such flexibility has
led to a dense and complex specifications for physical layer
procedures in 5G-NR. For example, for initial downlink
access, the synchronization block (SS/PBCH) can be
transmitted with a sub-carrier spacing (SCS) different than
the carrier SCS for faster synchronization; different time
1 Radio Performance and Protocol aspect requirements are specified by the 3GPP Radio Access Network working group 4, also known as RAN4.
placement pattern of SS/PBCH can be adopted (only for
30kHz SCS) to accommodate NR-LTE coexistence;
different patterns can be configured for the time/frequency
placement of SS/PBCH and remaining system information
(RMSI) blocks and so on. Further, SS/PBCH can be placed
on a different sync raster than the regular channel raster (only
option in LTE), for faster downlink synchronization by
making synchronization blocks sparser in frequency (i.e.,
SS/PBCH placement at only given frequency locations).
This facility requires calculations on the sync raster entries
based on bandwidth configuration, SS/PBCH resource size,
etc. For uplink initial access/synchronization, the random
access (PRACH) channel supports several long and short
formats for different coverages and combinations of formats
(short) with configurable time/frequency placements. A
PRACH preamble can have varying number of sequence
VOLUME XX, 2020 3
repetitions depending on the format to provide different
coverage range. There could also be several preambles
within a slot to cater for multiple random access occasions.
Support of formats with large repetitions or multiple PRACH
occasions within a slot, increases the receiver processing
load at a 5G next generation-base-station (gNB) and
therefore the gNB feature support capabilities should be
carefully determined. Further, to help towards beam
correspondence, different SS/PBCH to PRACH mapping are
defined so that single/multiple SS/PBCH map to
multiple/single PRACH occasions along with the regular
one-to-one mapping. These mapping options have
implications on the SS/PBCH and PRACH receiver
processing complexity at the gNB. Also, if a common digital
front end (DFE) chain is to be used for data and random
access reception in the same slot, the PRACH receiver at
gNB will be required to perform additional phase corrections
due to cyclic prefix (CP) removal on the data channel.
As 5G-NR specification allows for different SCS which can
be configured for initial access and data channels; provides
flexibility of placing the resources on separate bandwidth
parts (BWPs2), and therefore there are several frequency
offsets parameters defined in the 3GPP physical layer
procedures specification with complicated equations. These
offsets are necessary for correct placements of resources and
for correct OFDM signal generation and reception in 5G-NR.
To understand all the details on design goals and motivations
for SS/PBCH, PRACH channels and OFDM signal
generation in 5G-NR, one must go through several 3GPP
specifications and contributions. This could prove be a very
difficult task for anyone not familiar with 3GPP
standardization process and documentation. Moreover,
information is scattered across a vast number of documents
with nested references, making the task of connecting the
dots a very tedious process.
The objective of this paper is to unwind all the
design details associated with the initial access channels and
illustrate them with examples wherever possible to help
understanding better the overall design. Specifically, the
following contributions are made in this paper. First, all the
design details associated with downlink access channels and
OFDM signal generation in 5G-NR are presented with
examples. Secondly, design details of PRACH channel
along with important receiver design aspects are presented.
Finally, PRACH receiver implementation aspects and
performance from different network operators are presented
and compared with RAN4 recommended minimum
requirements for millimeter wave (mmW) access. Rest of the
document is organized as follows. In section 2, SSS/PBCH
channel design details are provided with illustrations and
examples. Section 3, details of the OFDM signal generation
and phase pre-compensation at the transmitter are presented.
2 In 5G-NR, gNB can fragment the carrier bandwidth into smaller BWPs
with similar or different subcarrier spacing [4]. This flexibility allows users
Section 4 focuses on all the PRACH channel design aspects
and details. Lastly, important aspects of the PRACH
receiver design along with RAN4 performance from
different network operators is presented and discussed.
II. SS/PBCH DESIGN
SS/PBCH block transmission allows UEs to synchronize or
lock to a cell. In NR, synchronization signal blocks constitute
of a primary synchronization signal (PSS), a secondary
synchronization signal (SSS), and a physical broadcast
channel (PBCH). Unlike LTE, which has PSS/SSS
transmitted every 5ms and PBCH transmitted every 10ms,
the three SS/PBCH components in NR are always transmit-
Figure 2-1: Synchronization signal structure in 4G-LTE and 5G-
NR .
-ted together (i.e., they all have the same periodicity). As
illustrated in Figure 2-1, a given SS/PBCH is repeated within
a set of SS/PBCH transmissions, which can be used for gNB
beam-sweeping transmission [2]. One or multiple SS/PBCHs
compose an SS/PBCH set as indicated in Fig 2.1. The
SS/PBCH set is confined to a 5 ms window and transmitted
periodically. For initial cell selection, the user equipment
(UE) assumes a default SS/PBCH set periodicity of 20 ms,
but subsequently this periodicity can be configured to be
5/10/40/80/160 ms depending on need to make SS/PBCH
with different bandwidth and device capabilities to operate within a smaller
bandwidth part (BWP) compared to the carrier bandwidth.
VOLUME XX, 2020 4
more frequent or sparser. Synchronization during initial
access is a two-step identification process (via PSS and SSS)
to provide for both timing (only symbol and slot) and
frequency synchronization. PBCH demodulation will reveal
system frame number and enable reception of control/data
channels (PDCCH/PDSCH). Detection of RMSI
(transmitted over regular PDCCH/PDSCH) may be
necessary during initial access for UE to perform random
access (via PRACH). However, transmission of RMSI itself
is optional to gNB (for non-standalone or NSA mode) and
the presence or absence of RMSI is indicated in the PBCH
block. Note that SS/PBCH transmission can also be used for
signal measurement purposes at the user equipment (UE) and
only those SS/PBCH associated with an RMSI are referred
to as a Cell-Defining SS Block (CD-SSB) (see section 5.2.4
of [4]). PSS/SSS/PBCH can be transmitted with SCS of
15/30kHz for frequency range 1 (i.e., FR1 or sub-6 bands)
and with SCS of 120/240kHz for frequency range 2 (i.e., FR2
or mmW bands). However, RMSI is defined only for SCS of
15/30kHz for FR1 and SCS of 60/120kHz for FR2 [2]. This
is mainly to cater for different channel conditions and
different coverages with different frequency ranges. The
SS/PBCH set contents, including the maximum number of
SS/PBCHs within an SS/PBCH set, SS/PBCH mapping
pattern, and SS/PBCH set mapping to slots in a radio frame
is also carrier-frequency-dependent.
Regardless of the SS/PBCH set composition, the
transmission of SS/PBCHs within an SS/PBCH set is
confined to a 5 ms window. The maximum number of
SS/PBCHs within an SS/PBCH set (i.e., within 5ms period)
is specified to be 4 for frequency ranges up to 3 GHz, 8 for 3
to 6 GHz, or 64 for 6 to 52.6 GHz in order to achieve a trade-
off between coverage and resource overhead. Furthermore,
the number of actual transmitted SS/PBCHs is configurable
and could be less than the maximum number. This option is
particularly useful towards reducing processing burden at the
gNB, especially in the case of requiring transmission of
multiple SS/PBCHs on multiple carriers within a slot.
Within a broadcast channel (BCH) transmission time
interval (TTI) period of 80 ms, there are 16 possible positions
of an SS/ PBCH set if we consider the minimum period for
an SS/PBCH set is 5 ms. The 16 possible positions of an
SS/PBCH set could be identified by the 3 least significant
bits (LSB) of the System Frame Number (SFN) and 1-bit half
radio frame number index. The SS/PBCHs are repeated
within an SS/PBCH set and when the UE detects an
SS/PBCH, it can acquire the timing information from its
PBCH, from which the UE can identify the radio frame
number, the slot index in a radio frame, and the orthogonal
frequency-division multiplexing (OFDM) symbol index in a
slot. The timing information contains additional 6 bits for
SFN, 1 bit for half radio frame index, and 2, 3, or 6 bits for
SS/PBCH time index for frequency ranges up to 3 GHz, 3 to
6 GHz, and greater than 6 GHz, respectively. Within the
SS/PBCH indices, two or three LSBs are carried by changing
the demodulation reference signal (DMRS) sequence of
PBCH. Thus, for the frequency ranges below 6 GHz, the UE
can acquire the SS/PBCH index without decoding the PBCH.
It also facilitates PBCH soft combining over multiple
SS/PBCHs as these SS/PBCHs with different indices carry
the same content of PBCH payload. SS/PBCH can be placed
(in frequency) on channel raster (as in LTE) or the newly
defined sync channel raster in 5G-NR.
A. Sync Channel Raster
Synchronization (or sync) channel raster identifies the set
of possible frequency locations of the SS/PBCH, consisting
the synchronization channels PSS/SSS and the PBCH.
Unlike LTE, the SS/PBCH block in NR need not be in a fixed
position within the configured bandwidth of the RF carrier
but can be placed anywhere on the RF carrier bandwidth.
This enables a sync channel raster that is sparser than the RF
channel raster [5]. The advantage of having a sparser sync
channel raster is a reduced search time for the initial access
(less hypothesis to work with at the UE receiver). It relies on
the SS/PBCH block bandwidth (i.e., PBCH bandwidth)
being smaller than full channel bandwidth of the RF carrier
transmitted from the gNB and that it is not in a fixed position
within the configured bandwidth. The PBCH bandwidth of
240 subcarriers corresponding to 20 resource blocks (RBs)
defines the flexibility of placing the sync channel. A primary
cell (PCell) is always associated to a CD-SSB located on the
synchronization raster. Note that in 5G-NR the definition of
a physical resource block (PRB) is the same as LTE with 12
subcarriers constituting an RB, but the bandwidth of a PRB
varies with the numerology or SCS being used.
The relation between the RF channel raster and sync
channel raster is demonstrated with an example in Figure 2-
2. In the example, two carrier positions 1 and 2 are shown
leading to two different placements of the PBCH. The PBCH
(and the SS) can be placed on a raster that is sparser than the
RF carrier raster and those sync channel raster positions are
denoted by 𝐹,. Position 1 is the highest (rightmost)
SS/PBCH
Configured
Bandwidth (BW)
Channel Data SS/PBCH
Sync channel
raster spacing
PBCH BW
Δ
𝐹
𝐶𝐻
,
𝑅𝑎𝑠𝑡𝑒𝑟
Δ
𝐹
𝑆𝐶
,
𝑅𝑎𝑠𝑡𝑒𝑟
𝐹
𝑆𝐶
,
1
𝐹
𝑆𝐶
,
2
Channel Data
Figure 2-2:Sync and channel raster
VOLUME XX, 2020 5
position of the configured bandwidth on the RF channel
raster where the PBCH can be related to the sync channel
position 𝐹,, thus the PBCH occurs as far left as possible
on the carrier. Position 2 is the next position on the RF
channel raster, thus offset by Δ𝐹, + Δ𝐹, from
Position 1. The sync channel raster spacing Δ𝐹, will
be limited by the following equation:
Δ𝐹, ≤𝐵𝑊−𝐵𝑊+𝐹,
where 𝐵𝑊 is the configured transmission bandwidth,
𝐵𝑊 is the PBCH and Δ𝐹, is the channel raster
spacing.
Sync raster is defined such that there is a minimum
number of entries for each band [5] and raster entries are
defined for each band (see section 4.3.1 of [5]). Sync raster
entries will be defined for initial system acquisition, but
SS/PBCH blocks can be transmitted by gNB in other
frequency locations if the position is signaled to the UE
explicitly3 using the parameter 𝑘SSB , which is derived from
the frequency difference between the SS/PBCH block and
Common Resource Block (CRB), also referred to as Point A
in [3] ( see section 7.4.3.1 of [3] and section 13 of [7]). The
SS/PBCH block is not RB aligned with the data RBs in the
channel as shown in Figure 2-3. Instead, there is an arbitrary
offset between the edge of the SS/PBCH block RBs and the
edge of the data RBs in the channel and this offset can be up
to 11 Resource Elements (REs) for mmW. Such placement
enables multiple radio channels (with different NR-Absolute
radio-frequency channel numbers or NR-ARFCN) that are
subcarrier grid aligned but not RB grid aligned to use the
same SS/PBCH block location. Hence, radio channels with
different NR-ARFCNs that are offset by up to 11 REs in
frequency can re-use the same SS/PBCH block frequency
location.
The gNB places the SS/PBCH block at 𝑆𝑆 (one of the
synchronization raster’s). This is indicated by the red-line at
3 This is handled by gNB by setting the Master Information Block (MIB)
parameter ssb-SubcarrierOffset (or the PHY parameter 𝑘SSB) as 𝑘SSB >11
for FR2 or 𝑘SSB >23 for FR1 (see section 4.1 of [7]).
the center of SS/PBCH block in Figure 2-3. The gNB also
signals the offset (in number of subcarriers) between
SS/PBCH block and the channel data RBs to help determine
the control resource set for Type0-PDCCH common. This
serves as an indirection for RMSI. Following parameters are
signaled in RMSI for each supported SCS (each SCS is
usually a different component carrier).
1. Absolute frequency of Point A -
absoluteFrequencyPointA in FrequencyInfoDL,
signaled as ARFCN NR
2. Offset in PRB units from Point A to the first usable
PRB - offsetToCarrier in SCS-SpecificCarrier
3. Carrier bandwidth in PRB units - carrierBandwidth
in SCS-SpecificCarrier
4. Sub-carrier spacing to determine the size of PRB -
subcarrierSpacing in SCS-SpecificCarrier
Note that point A is RE#0 of RB#0 used to generate
sequences for reference signals and scrambling. From
section 7.4.3.1 of [3], the quantity 𝑘 is the subcarrier
offset from subcarrier 0 in common resource block 𝑁
to
subcarrier 0 of the SS/PBCH block, where the 4 least
significant bits of 𝑘 are given by the higher-layer
parameter ssb-SubcarrierOffset and for SS/PBCH block type
A the most significant bit of 𝑘 is given by 𝑎 in the
PBCH payload as defined in subclause 7.1.1 of [3] (also see
section 4, TS 38.212). The value 𝑘 ∈{0,⋯,11} for FR2
and 𝑘 ∈{0,⋯,23} for FR1. For FR2, or when 𝜇∈{2, 3},
the quantities 𝑘SSB, and 𝑁CRB
SSB are expressed in units of
resource blocks assuming 60 kHz subcarrier spacing. For
FR1, or when 𝜇∈{0, 1}, the quantities 𝑘SSB , and 𝑁CRB
SSB are
expressed in units of resource blocks assuming 15 kHz
subcarrier spacing (see section 4.2.2.2 of [3]). Figure 2-4
shows the computation of subcarrier offset 𝑘 for different
numerologies of SS/PBCH and RMSI in FR1 and why
𝑘 ∈{0,⋯,23} for FR1. The parameter 𝑘 ∈{0,⋯,11}
Figure 2-3: Alignment between SS block and channel RBs (see section 4.3.14 of [5])
𝑁
CRB
SSB
𝑘
SSB
𝑆
𝑆
𝑟𝑒𝑓
VOLUME XX, 2020 6
for FR2, since SS/PBCH is defined only for 120/240kHz and
RMSI is defined only for 60/120kHz and that the
configuration of SS/PBCH at 60kHz and RMSI at 120kHz is
not valid (and hence 12 values for 𝑘 suffice).
B. CRB to SS/PBCH offset examples
The common resource block and sub-carrier offsets to
SS/PBCH should be computed in terms of subcarrier spacing
of SS/PBCH for correct placement of the resources in
frequency. In [3] however, for FR2, or when 𝜇∈{2, 3}, the
quantities 𝑘SSB , and 𝑁CRB
SSB are expressed in units of resource
blocks assuming 60 kHz subcarrier spacing. Let,
𝑆𝑆𝐵
represent the offset from point A to the closest
common resource block before SS/PBCH. Let, 𝑆𝑆𝐵
be
the subcarrier offset from subcarrier 0 in common resource
block 𝑆𝑆𝐵
to subcarrier 0 of the SS/PBCH block
assuming sub-carrier spacing of SS/PBCH. The SSB CRB
offset (𝑆𝑆𝐵
) and subcarrier offset (𝑆𝑆𝐵
) are
illustrated for FR2 in Figure 2-5. For FR2, SS/PBCH can
only use either 120kHz or 240kHz subcarrier spacing. The
first tone of SS/PBCH block (or the PBCH tone) can only
begin at the center (or peak) of a 120kHz/204kHz subcarrier.
This means that 𝑘 ∈{0,…,11} can only take values
which are multiples of 2 when SS/PBCH subcarrier spacing
is 120kHz and values which are multiples of 4 when
SS/PBCH subcarrier spacing is 240kHz. Computing of
𝑆𝑆𝐵
and 𝑆𝑆𝐵
using 𝑘SSB, and 𝑁CRB
SSB can be done
as, 𝑆𝑆𝐵
=⌊∗
⌋ and 𝑆𝑆𝐵
=
∗
+𝑚𝑜𝑑∗
∗𝑁
,𝑁
, where Δ𝑓
and Δ𝑓 are SCS of carrier and SS/PBCH respectively.
Note, unequal tone amplitudes between different SCS are
illustrated in Figure 2-5 only to avoid clutter and need not be
the case in practice.
𝑁
CRB
SSB
𝑁
CRB
SSB
𝑁
CRB
SSB
𝑁
CRB
SSB
𝑺𝑺
𝑩
𝒔𝒄
𝒐𝒇𝒇𝒔𝒆𝒕
𝑺𝑺
𝑩
𝑪𝑹𝑩
𝒐𝒇𝒇𝒔𝒆𝒕
𝒌
𝒔𝒔𝒃
𝒌
𝒔𝒔𝒃
𝒌
𝒔𝒔𝒃
Figure 2-5:CRB and subcarrier offset with different numerology in FR2.
0 1 … 11 0 1 … 11 0 1 2 ... 11 ... 23
SSB RE
RMSI RE
SS/PBCH &
RMSI at
15kHz
SS/PBCH at
30kHz & RMSI
at 15kHz.
Scenarios
SS/PBCH at 15kHz &
RMSI at 30kHz.
.
.
.
.
12
1
SSB RE
RMSI RE
𝒌
𝒔𝒔𝒃
Figure 2-4: : Subcarrier offset
𝑘
in FR1.
VOLUME XX, 2020 7
C. SS/PBCH block
In order to provide enough deployment flexibility for NR,
the number of NR physical-layer cell identities (PCIDs) is
extended to 1008 (504 in LTE). Each NR-cell ID can be
jointly represented by a PSS/SSS. The SS/PBCH block
arrangement is shown in Figure 2-6. The PSSs consist of
three frequency-domain-based binary phase shift keying
(BPSK) m-sequences with length-127, and the SSSs
correspond to m-sequences of length-127 picked from 336
m-sequences. Both PSS and SSS signals are mapped onto
127 contiguous subcarriers. With very good cross-
correlation properties of m-sequences, NR SSs significantly
outperform LTE SSs in terms of both PCID detection
probability and false detection probability in the cases of
initial and non-initial acquisition, respectively, as shown in
[11]. For each SS/PBCH block, the PSS, SSS, and PBCH
share the same single antenna port. It should be noted that
the physical beams applied to an SS/PBCH block are
transparent to the UE since the latter only sees the equivalent
SSs and PBCH signal after potential precoding and/or
beamforming operations that are up to the network
implementation. The unique physical-layer cell ID is given
by (see section 7.4.2 of [3]),
𝑁
=3𝑁
()+𝑁
(),
where N
() ∈ {0,1,….,335} and N
() ∈ {0,1,2}. 𝑁
() is
carried by PSS, whereas 𝑁
() is carried by SSS. PSS is a
frequency domain-based pure BPSK M-sequence with 1
generator polynomial (g(x)= x+ x+ 1) and 3 cyclic
shifts in frequency domain (43𝑁
()={0,43,86}). The SSS
sequence is generated using two generator polynomials with
cyclic shifts according to cell IDs 𝑁
() and 𝑁
(). For more
details (for implementation) on PSS/SSS sequence
generation refer to section 7.4.2.2.1 and 7.4.2.3.1 of [3]
respectively. The PBCH REs maps to 240 subcarriers in
frequency and in time spans over 2 full symbols and an
additional 8 RBs on the SSS symbol. PBCH contains PBCH
data REs and PBCH DMRS REs. Energy Per Resource
Element (EPRE) between PBCH-DMRS and PBCH-data
shall be equal [3]. PBCH DMRS mapping will be frequency-
first, time-second in increasing frequency order. Also,
physical-layer cell ID based frequency shift is used for
PBCH-DMRS RE locations (see table 7.4.3.1-1 of [3]). The
3 bits of SS block index are carried by changing DMRS
sequence within each 5ms period, half-frame information is
also provided for max 𝐿=4, with the remaining bits of the
timing information carried explicitly in the PBCH payload.
Note that the REs that are not used for SS/PBCH block in
any data RB that partially or fully contain SS/PBCH block
REs are transmitted with zero power and other PHY channels
are rate matched around such PRBs. On the PDSCH carrying
RMSI and the corresponding PDCCH CORESET, no
SS/PBCH block is transmitted in the allocated resources.
When the SS/PBCH and PDSCH are scheduled in the same
symbols, DMRS of data and SS/PBCH can be in the same
symbol, provided DMRS of data and SS/PBCH are not
overlapping in the frequency domain, spatially quasi co-
located (QCL’d) and have the same SCS (see section 10.1 of
[3] and section 5.1.6.2 of [9]).
D. PBCH Payload
The PBCH payload size is 32 bits and is contained within
the SS/PBCH command. The PBCH payload consists of
three parts, CHOICE bit (1bit), MIB payload or the MIB
information element (IE) consisting of 23 bits (shown below
in red font) defined in [S4] and the extra 8 bits related to
additional timing information (see section 7.1.1 of [3]). The
CHOICE bit along with the MIB payload is also known as
the BCH payload. Note that the “CHOICE Bit” (see section
A.3.2 of [S4]) is not part of the MIB but is part of the BCH
message which includes the CHOICE bit and the MIB
payload.
MIB ::= SEQUENCE {
systemFrameNumber BIT STRING (SIZE (6)), 6 bits
subCarrierSpacingCommon ENUMERATED {scs15or60, scs30or120}, 1
bit
ssb-SubcarrierOffset INTEGER (0..15), 4 bits
dmrs-TypeA-Position ENUMERATED {pos2, pos3}, 1 bit
pdcch-ConfigSIB1 PDCCH-ConfigSIB1, 8 bits
cellBarred ENUMERATED {barred, notBarred}, 1 bit
intraFreqReselection ENUMERATED {allowed, notAllowed}, 1
bit
spare BIT STRING (SIZE (1)) 1 bit
}
Note that the PBCH payload bits (denoted below with the
same notation as in section 7.1.1 of [3])
a
⏞
a,a,a,...,a
a
,a
,a
,a
,…,a
239
192
182
56
47
0
n
n+1
n+2
n+3
OF DM
Sym bo ls
48 ton es 127 ton es 48 tones
8 to ne s wi th
com ple x valu e s et
to 0 s
9 to ne s wi th
com ple x valu e s et
to 0 s
20 Reso urce Blocks o r 240 to nes. Ban dwidth = 24 0*∆f
PSS
SSS
Ti m e
PBCH
PBCH PBCH
PBCH
PBCH
data
PBCH
DMRS :
Frequency
locat ion
computed as,
v
=𝑁
mod 4
Figure 2-6 SS/PBCH block resource arrangement
VOLUME XX, 2020 8
must be interleaved as defined in section 7.1.1 of [3], using
the interleaver pattern defined in Table 7.1.1-1 of [3]. PBCH
payload is scrambled (1st scrambling) before polar encoding
as per the method defined in section 7.1.2 of [3]. Note that
the scrambling depends on fields that are already sent in the
PBCH command (N
, ssbIndex) and header (SFN). The
scrambling sequence for the additional timing bits is 0. Note
that after the interleaving process, the position of the
additional timing bits will change according to the
interleaver pattern and care should to be taken to set only the
scrambling bits to zero which correspond to the additional
timing bits.
III. OFDM SIGNAL GENERATION
In Figure 2-2, the spectrum allocation available for a given
carrier for various subcarrier spacings with respect to
reference Point A was shown. The common RB numbering
in Figure 2-2 (denoted as CRB in [3]) is for the whole carrier.
The first subcarrier of the common RB of different
numerologies coincide at a reference point called Point A
(see section 4.4.4.2 of [3]). Different bandwidth parts (either
for uplink or downlink) can be defined by the network using
different sub-carrier spacings (i.e., with Δ𝑓,2Δf, etc.).
Irrespective of the different bandwidth parts the OFDM
signal generation equation remains essentially common
(with appropriate subcarrier-based scaling for parameters
involved) for a given carrier center frequency. For successful
demodulation on any bandwidth part, a phase pre-
compensation is applied for all channels (except PRACH).
The OFDM signal generation is described below. The
baseband OFDM signal (dropping antenna port 𝑝 notation
for convenience) in given by (section 5.3 of [3])
𝑠(𝑡)
= 𝛼,𝑒
,
,
,
(1)
,
with 𝑇,
=𝑁,
𝑇 being the duration of CP, 𝑡,
≤
𝑡<𝑡,
+𝑁+𝑁,
𝑇 is the transmission time range
of symbol 𝑙, with 𝑁 and 𝑁,
being the symbol and CP sizes
respectively; 𝑡,
is the symbol start time, as defined in
[3]; Δ𝑓 and 𝜇 are the subcarrier spacing and subcarrier
spacing configuration respectively, defined in section 4.2 of
[3]; 𝛼, is the 𝑙 transmitted data symbol on subcarrier
index 𝑘; 𝑘
is a term that enables single carrier frequency
for all numerologies
𝑘
=𝑁
,+𝑁
, 2
⁄𝑁
−𝑁
,+𝑁
,2
⁄𝑁
2 (2)
In [3], 𝜇 is the largest 𝜇 value among the subcarrier
spacing configurations provided to the UE for this carrier.
A. Phase reset at symbol boundaries: Downlink
reception of SS-PBCH/RMSI/BWP
During initial access UE will not know the downlink
center frequency and it may not be the same as the center
frequency of SS/PBCH block and RMSI. Similarly, when the
UE is configured to receive on a bandwidth part (BWP),
there could mismatch in frequencies used at gNB and UE.
The mismatch in center frequencies at transmitter and
receiver during initial access is illustrated in Figure 3-1. This
is handled at the gNB transmitter/UE receiver by resetting
phase at OFDM symbol boundaries at the RF center
frequency. This phase reset at the beginning of every symbol
is described in the up-conversion related parts of the
specifications (section 5.4 for [3]). The implementation is
easier to perform at the baseband rather than RF. To
understand this, consider the baseband OFDM signal
(dropping antenna port 𝑝 notation for convenience) in
section 5.3 of [3].
𝑠(𝑡)
= 𝛼,𝑒
,
,
,
(3)
,
with 𝑇,
=𝑁,
𝑇 being the duration of CP, 𝑡,
≤𝑡<
𝑡,
+𝑁+𝑁,
𝑇 is the transmission time range of
symbol 𝑙, with 𝑁 and 𝑁,
being the symbol and CP sizes
respectively; 𝑇 is the basic unit of sample duration; 𝑡,
is the symbol start time, as defined in [3]; Δ𝑓 and 𝜇 are the
subcarrier spacing and subcarrier spacing configuration
respectively, defined in section 4.2 of [3]; 𝛼, is the 𝑙
transmitted data symbol on subcarrier index 𝑘; 𝑘
is a term
𝑓
0
𝑔𝑁𝐵
𝑁
𝑔𝑟𝑖𝑑
𝑠𝑖𝑧𝑒
,
𝜇
𝑁
𝑆𝐶
𝑅𝐵
Δ
𝑓
𝑓
0
𝑈𝐸
𝑓
0
𝑔𝑁𝐵
𝑓
0
𝑈𝐸
𝑓
0
𝑔𝑁𝐵
𝑓
0
𝑈𝐸
Figure 3
-1: Center frequency mismatches at gNB and UE.
VOLUME XX, 2020 9
that enables use of a single carrier frequency for all
numerologies (see following sections). Assuming the center
frequency of the gNB to be 𝑓, the transmitted signal is,
𝑥(𝑡)=𝑒 𝑠(𝑡)
Assuming the UE center frequency as 𝑓, the received
signal can be written as, 𝑦(𝑡)=𝑒 𝑥(𝑡).
Expanding,
𝑦𝑡+𝑡,
=𝑒,
,
𝑒,
,
×
ℎ,𝑎,𝑒
,
,
,
(4)
where Δ𝑘=
+𝑘
−
,
. Note that the
center frequency offset (i.e., 𝑓 −𝑓) is always an
integer number of subcarriers. Also, Δ𝑘 is independent of 𝑙
and hence will not impact reception. Therefore, the impact
of this center frequency offset is only the per-symbol phase
rotation caused by gNB center frequency as the UE phase
part in Eq. (4 ) can be corrected as 𝑓 is known at the UE.
The gNB part of the residual phase on every symbol can be
compensated in the baseband (at gNB) by multiplying with
the conjugate of the gNB part of the residual phase at the
transmitter. This is,
𝑠(𝑡)𝑒(,
,
) , (5)
which will result in the received signal not having terms
dependent on gNB center frequency. The phase
compensation can also be done at the up-conversion step (as
described in the spec [3]) as follows –
𝑅𝑒𝑠(𝑡)𝑒∗𝑒,
,
= 𝑅𝑒 𝑠(𝑡)𝑒 ,
,
(6)
This essentially implies the phase of the RF signal is reset
at symbol boundaries. This is difficult to implement in RF
analog domain. The baseband signal can be pre-compensated
so that there is no need for phase reset in RF. Note that, only
for PRACH signal transmission, there is no common phase
correction applied during the up-conversion at the
transmitter (see section 5.4 of [3]) as accurate phase
information may not be necessary for PRACH
demodulation. Common phase correction can be
implemented in the IFFT/FFT modules of
transmitter/receiver respectively. This phase reset works
only when the difference in the transmission and reception
frequencies is a multiple of subcarrier spacing. 𝑓 is a
multiple of 1 kHz and hence the phase terms
𝑒(,
,
) will repeat every 1 ms (see [26]). So,
it is enough to pre-compute phase terms for 2×14
symbols. The subcarriers in the range
𝑁
,−𝑁
,𝑁
,𝑁
,−𝑁
,𝑁
+
𝑁
,𝑁
− 1 is of interest, where 𝑁
, and 𝑁
,
are starting CRB of BWP and carrier grid with sub-carrier
spacing 𝜇 respectively (see Figure 3-2). So, a smaller FFT
around 𝑁
,−𝑁
,𝑁
+𝑁
,𝑁
/2 −1
should be sufficient. Note that the pre-compensation and
IFFT operations are interchangeable. The phase reset at
symbol boundaries is useful to do the following with only the
knowledge of the corresponding BWP parameters. 1) UE can
receive SS-PBCH, RMSI or data on a BWP 2) UE can
transmit on any BWP. After downlink synchronization, the
center frequencies of gNB and UE will be the same, i.e.,
𝑓 =𝑓 =𝑓 and a single 𝑓 is used to transmit and
receive on a given BWP. Users within a given BWP can
center their FFT at the middle of their configured BWP, and
while upconverting use a frequency offset to the carrier
center frequency 𝑓. The frequency 𝑓 to be used during
up-conversion is given by
𝑓 =𝑓−𝑁
,𝑁
2
⁄−𝑁
,𝑁
−𝑁
,𝑁
2
⁄+𝑁
,𝑁
Δ𝑓.
At the gNB receiver, a corresponding phase reset must be
applied at symbol boundaries in RF. Again, this is easier to
do in the baseband (just like in the transmitter). The per-
symbol phase correction to be applied at the receiver for
OFDM symbol index 𝑙 is given by 𝑒, where 𝜃 =
2𝜋𝑓𝑡start,
+𝑇CP,
, where 𝑓 is the receiver center
frequency in Hz. If the receiver center frequency is a multiple
of 1 kHz, it can be shown that the phase correction factors 𝜃
defined above are periodic with a periodicity of 1ms (i.e. at
most 28 unique values for 𝜇=1, see [26]). If the receiver
center frequency includes a 7.5 kHz shift when UL is shared
with LTE, the periodicity is 2ms (i.e. at most 56 unique
values for 𝜇=1 [26]).
B. Frequency offset parameter
The locations of the RB grids of all numerologies are
indicated to the UE using RRC parameters 𝑁,
, and
𝑁,
, [8]. The parameter 𝑘
is the subcarrier offset from
the middle subcarrier of numerology 𝜇 (i.e. the 𝑁,
,𝑁
/
2+1‘th subcarrier in the 𝑁,
,𝑁
subcarriers) to 𝑓, as
illustrated in Figure 3-2. From Figure 3-2, one can write,
𝑓−𝑓 =𝑁,
,𝑁
∆𝑓+𝑁,
,𝑁
2×
⁄∆𝑓
−𝑘
∆𝑓 (7)
Therefore, for any two numerologies 𝜇 and 𝜇:
𝑁,
,𝑁
+𝑁,
,𝑁
2
⁄−𝑘
×2
=𝑁,
, 𝑁
+𝑁,
,𝑁
2
⁄−𝑘
×2 (8).
Rewriting the above equation for 𝑘
, we have,
𝑘
=𝑁,
,𝑁
+𝑁,
,𝑁
2
⁄+𝑘
−
𝑁,
,𝑁
−𝑁,
,𝑁
2
⁄×2 (9).
VOLUME XX, 2020 10
Note that 𝑓 does
A
f
0
f
fNN
RB
sc
startxgrid
,
,
fNN RB
sc
size
xgrid
,
,
2
,
,
fNN
RB
sc
size xgrid
fk
0
Figure 3-2:Relationship between 𝑘
,𝑓 and other parameters.
not have to be on the channel raster nor the center of the RF
filter. The channel raster or the RF implementations do not
impose any restriction to the value of 𝑘
. Therefore, the
value of 𝑘
can be predefined and is set to 0 i.e., 𝑘
=0.
Accordingly, 𝑘
can be derived using:
𝑘
=𝑁
,+𝑁
, 2
⁄𝑁
−𝑁
,+
𝑁
,2
⁄𝑁
2 (10).
IV. PRACH DESIGN
In this section we will discuss PRACH channel and its
design principles in 5G-NR. Two preamble formats are
defined in NR, long and short preamble formats of sequence
length 839 and 139 respectively. Long formats can be
configured only for sub-6GHz frequency range (FR1),
whereas short formats can be configured for both sub-6
(FR1) and mmW (FR2) frequency range. Long formats
option is mainly aimed towards catering for LTE re-farming
and large cell scenarios [2]. In this paper, we will consider
only the short preamble formats. The PRACH preamble
consists of a cyclic prefix of duration 𝑇CP (𝑁
samples) and
sequence part of duration 𝑇SEQ (𝑁 samples and with or
without repetitions depending on the PRACH format) and
guard duration of 𝑇. Figure 4-1 shows the various PRACH
preamble formats associated with short-sequence length,
with sizes of cyclic prefix (CP), PRACH sequence, Guard
duration (if any) in number of samples for the configured
parameters (i.e., 𝜇,𝑓 and starting symbol shown on the right
side of Figure 4-1) and the bandwidth of each format. For
PRACH formats with no guard duration, the CP is
aggregated for the number of repetitions of the sequence(s)
and appended at the beginning of the PRACH sequence(s).
For PRACH formats with guard duration, the guard duration
𝑇GP extends from the end of the preamble to the next symbol
boundary. The preambles for all formats always start and end
at symbol boundaries within a slot (see Figure 4-4 in section
IV-B). Also shown is the length of each preamble sequence
in micro-seconds. The CP length, sequence length and total
preamble length (in samples) can be calculated for short
sequence length preambles using the Table 6.3.3.1-2 of [3].
The time duration of different preamble components
(sequence, CP, guard etc) for different preamble formats
shown in Figure 4-1 are with subcarrier spacing of Δ𝑓 =
120kHz (𝜇 =3). Bandwidth for a frequency domain
occasion with short sequence and SCS of 120kHz can be
calculated as 𝐵𝑊 =
× 12 tones× 120kHz=
17.28MHz.
A formats starting at S ymbol = 0 C formats starting at Symbol = 0
A3 C2
A2 C0
A1
B formats starting at Symbol = 0
B4
Config Parameters (change as required)
B3
mu fs PRACH Start
OFDM symbol #
3 1.23E+08 0
B2 Note: All size s shown in # of samples at fs
B1
CP
208 SEQ
1024
SEQ
1024
CP
1088 SEQ
1024 GT
1458
SEQ
1024 SEQ
1024 SEQ
1024
CP
684 SEQ
1024 GT
548
CP
496
SEQ
1024 SEQ
1024 SEQ
1024 SEQ
1024 SEQ
1024 SEQ
1024
CP
532
SEQ
1024 GT
396
SEQ
1024
SEQ
1024
SEQ
1024
SEQ
1024
SEQ
1024
SEQ
1024
SEQ
1024
SEQ
1024
SEQ
1024
SEQ
1024
SEQ
1024
CP
316 SEQ
1024
GT
180
SEQ
1024 SEQ
1024 SEQ
1024 SEQ
1024 SEQ
1024
CP
244 SEQ
1024
GT
108
SEQ
1024 SEQ
1024 SEQ
1024
CP
172
SEQ
1024
GT
36
SEQ
1024
CP
352 SEQ
1024 SEQ
1024 SEQ
1024 SEQ
1024
54.04 us
36.2 us
18.36 us
107.55 us
54.04 us
36.2 us
18.36 us
54.05 us
18.36
17.28MHz
17.28MHz
17.28MHz
Figure 4-1:PRACH preamble for different formats with short-sequence length.
VOLUME XX, 2020 11
A. PRACH time/frequency structure
Within a cell, preamble transmission can take place within a
configurable subset of slots (denoted as the PRACH slots)
that repeats every PRACH configuration period as shown in
Figure 4-2. The PRACH configuration period is given by the
parameter 𝑥 in Table 6.3.3.2-4 of [3] for FR2. PRACH
periodicity can be configured to range from 10 ms up to 160
ms. A configurable set of PRACH slots are present within
the PRACH period. For a given SFN, a PRACH slot can be
present only when 𝑛𝑚𝑜𝑑 𝑥=𝑦. Further, for a given
SFN, where PRACH slots can be present (i.e., when
𝑛𝑚𝑜𝑑 𝑥=𝑦), PRACH can be only be on slots given by
‘Slot Number’ column in Table 6.3.3.2-4 of [3] for FR2. As
an example, let SFN = 1 (i.e., 2nd frame) and let PRACH
config index = 14 (see Table 1). Then, for PRACH config
index = 14, the parameters 𝑥=1 and 𝑦=0 (using Table
6.3.3.2-4 of [3] of FR2), shown below. PRACH slots are on
slot numbers 24,29,34,39 (using Table 6.3.3.2-4 of [3] of
FR2), from the snippet shown in Table 1. Section 2 of [24]
has more information on PRACH slot in a frame based on
subcarrier spacing. Within any given PRACH slot (see
Figure 4-2), multiple PRACH occasions can exist
consecutively in time and frequency. Utilization of multiple
time & frequency resources is towards yielding NR-PRACH
capacity as large as LTE [29]. This is because PRACH
capacity would be limited compared to LTE with large
subcarrier spacing and short sequence lengths.
Details on time domain occasions within a PRACH slot is
Table 1: PRACH configuration for Frequency Range 2 (FR2).
PRACH
Config.
Index
Preamble
format
Slot
number
Starting
symbol
Number
of
PRACH
slots
within a
60 kHz
slot
𝑁
,
number
of time-domain
PRACH
occasions within
a PRACH slot
𝑁
PRACH
duration
14 A1 1 0 24,29,34,39 7 1 3 2
yxn
mod
SFN
x
y
Figure 4-2: PRACH time frequency structure.
K*M
RBs
KK
K
𝑵
𝒕
𝑹
𝑨
𝒔𝒍𝒐𝒕
𝑛
𝑆𝐹𝑁
mod
𝑥
=
𝑦
VOLUME XX, 2020 12
shown in Figure 4-2. There can be multiple frequency
domain PRACH occasions jointly covering 𝐾∗
𝑀 consecutive resource blocks, where 𝐾 is the preamble
bandwidth measured in number of resource blocks and 𝑀 is
the number of frequency-domain PRACH occasions defined
by the higher layer parameter msg1-FDM with 𝑀∈
{1,⋯,8}. PRACH configuration can be different across
frequency domain occasions, but within a given a frequency
domain occasion, the PRACH configuration will same
across all time-domain occasions.
B. Definition of PRACH Slot Number
Column ‘Slot Number’ in Table 6.3.3.2-4 of [3] is defined in
terms of 60kHz SCS for FR2. Essentially, the number of
PRACH slots is defined as the number of PRACH slots within
a subframe for FR1 (𝜇=15,30 kHz) and the number of
PRACH slots within a 60kHz slot for FR2 (𝜇=60,120kHz)
as shown in Figure 4-3. Therefore, the column ‘Slot Number’
in Table 6.3.3.2-4 of [3] is always between 0 to 39 for FR2.
For a given PRACH config, when the number of PRACH slots
within a 60kHz is specified as 1 in Table 6.3.3.2-4 of [3] and
when PRACH subcarrier spacing is 120kHz (with 2 slots in a
60kHz), PRACH is always transmitted on the 2nd slot of
120kHz SCS (see section 5.3.2 of [3]). For the example
PRACH configuration in Table 1, within the allowable slots
numbers 24,29,34 and 39 (or slots {48,49}, {58,59},
{68,69}and {78,79} in terms of 120kHz SCS), PRACH can
be transmitted only in the 2nd slot corresponding to 120kHz
numerology, i.e., slots 49, 59, 69 and 79 slots of 120kHz. For
a given preamble type, corresponding to a certain preamble
bandwidth, the overall available time/frequency PRACH
resource within a cell can now be described as follows (see
illustration in Figure 4-2). Within a given frequency domain
PRACH occasion, there can be multiple TD occasions defined
by the parameter 𝑁 given in Table 6.3.3.2-4 in [3]. The
duration of each TD occasion is given by the parameter 𝑁
and is in terms of PUSCH symbols. Within each TD occasion
the configured PRACH preamble is present, including CP,
sequence(s) and guard (if any) of durations 𝑇,𝑇 and 𝑇
respectively, as shown in Figure 4-2. Note that all TD
occasions are continuous in time (i.e., no gaps between TD
occasions). Alignment of PRACH symbols for different
formats with OFDM symbol boundaries is shown in Figure 4-
4. For a given PRACH format/configuration, the time domain
occasion can start at different symbols as specified by the
“starting symbol” (or 𝑙 in section 5.3.2 of [3]) column of
Table 6.3.3.2-4 in [3]. Symbol start period of 2 was chosen to
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
CP RACH RACH RAC H RACH
CP RACH
CP RACH RACH R ACH RACH RACH RACH RACH RACH RACH R ACH RACH RACH GP
CP RACH RACH RACH RACH RACH RACH
CP
RACH RACH RACH RACH
CP
RACH RACH
CP RACH RACH RACH RACH RACH R ACH
CP RACH RACH RACH RACH
CP
RACH RACH
Figure 4-4:Short preamble format timelines in 5G NR.
Figure 4-3:PRACH slot definitions for different μ.
VOLUME XX, 2020 13
accommodate PDCCH on first two symbols (see section 2.1
of [25]). Start symbol 6 and 8 was chosen to avoid DL to UL
interference. A significant concern was the transmission point
(TRP) to TRP, or DL-to-UL interference between PRACH
and a preceding PDCCH transmitted in a gap at the beginning
of the slot [32]. If the preamble format specified in Tables
6.3.3.2-2 to 6.3.3.2-4 of [3] is A1/B1, A2/B2 or A3/B3, then
only the last TD occasion will have the preamble format of B1,
B2 or B3 respectively (see section 5.3.2 of [3]). Note that,
formats B2 and B3 are only supported in combination with A2
and A3 respectively, i.e., B2 and B3 cannot be configured by
themselves. Also, with Ax/Bx format, supporting Bx seems
mandatory(see [30]), although the 3GPP specification doesn’t
explicitly state this. Here, Ax/Bx corresponds to A1/B1,
A2/B2 or B3/B3 short format pairs.
For preamble format A, guard duration is not explicitly
defined. Since Ax doesn’t have a guard band, Bx (which has a
guard band) was appended to Ax, when Ax/Bx is configured.
But again, having no Bx would have acted as a guard band for
the last time domain occasion of Ax, but Bx was chosen
instead [31] of defining a guard period for the last time domain
occasion of Ax. The CP sizes of Ax are larger than Bx. Given
this, for example, consider a scenario where, UE-1 is
configured to use A2 format and UE-2 is configured to use B2
format. Then if UE1 propagation delay is greater than B2 CP,
then it may interfere with UE-2s PRACH (if UE-2 is close to
gNB). The medium access control (MAC) scheduler should
take care to avoid this scenario. Further, PRACH is supposed
to work at low SNR during interference, so UE-2 performance
may not be significantly impacted (see [30]). One benefit of
having PRACH preamble start and end at the user data OFDM
symbols (as shown in Figure 4-4) is the negligible inter-carrier
interference (that too for the first and the last OFDM symbols)
if the preamble is delayed. Note that format C2 has the largest
guard period and CP size across all formats as it was intended
for larger cell coverage (see cell dimensioning in section
4.C.2. Also, RAN4 performance evaluations will be only for
formats are A1, A2, A3, B4, C0 and C2, see [6] and [23].
Coverages shown in Table 2 of section 4.C, shows that support
of formats A1, A2, A3 and A3/B3 may suffice for small cells.
Support of mixed format of format A and format B was
agreed, in order to avoid the inter-symbol interference to the
following uplink/downlink data receiving/transmitting at
gNB/UE due to the zero-guard time of preamble format A (see
[31]) and may need to be supported for a small cell scenario.
C. PRACH Channel Design
As discussed in section 2.2.2.1, NR PRACH short
sequence formats are defined with different CP durations,
and sequence repetitions to cater for different size cells and
PRACH capacity. In this section, brief details are provided
on PRACH preamble generation/properties and cell
sizes/cyclic-shift dimensioning. Understanding PRACH
preambles generation/properties will be useful towards
understanding the PRACH receiver detection/estimation.
Understanding cell sizes/cyclic-shift dimensioning for all
PRACH formats will be useful towards analysing receiver
processing complexity for any given PRACH format and
defining gNB requirements.
The basic PRACH preamble sequences (of duration
𝑇 and number of tones 𝐿) are Zadoff-Chu (ZC)
sequences generated using a given root sequence and a given
cyclic shift. A gNB configures the set of preamble sequences
(with a maximum of up to 64 preambles) the UE can use, and
UE will select one preamble (randomly out of the 64
preambles) for transmitting msg1 (or PRACH preamble).
A PRACH receiver objective is to detect the transmitted
preamble at the correct root sequence and cyclic shift and
estimate the timing offset (propagation delay) for the given
UE. The generation and transmission of preamble is briefly
described below. A ZC sequence can be generated in time-
domain (TD), using a physical root sequence 𝑢 as 𝑥(𝑛)=
e ()
,𝑛=0,1,…,L−1, where 𝐿 is the sequence
length with 𝑢∈{0,1, …, 𝐿−1}. For short sequence
preamble formats 𝐿 =139. The gNB configures the UE
to use a start logical root sequence 𝑖 (higher layer parameter
prach-RootSequenceIndex), which is used to derive the start
physical root sequence 𝑢, using Table 6.3.3.1-4 of [3] for
FR2. A cyclic shifted version (with cyclic shift value of 𝐶)
of the ZC-TD signal can be obtained as 𝑥,(𝑛)=
𝑥(𝑛+𝐶)mod 𝐿. For unrestricted set (i.e., with low or
no Doppler), the cyclic shift is given by,
𝐶=𝑣𝑁 𝑣=0,1,…,𝐿
𝑁−1,𝑁 ≠0
0 𝑁 =0 (11)
The parameter 𝑁 is configured by the gNB which is
derived from the higher layer parameter
zeroCorrelationZoneConfig using Table 6.3.3.1-7 of [3] for
Figure 4
-5:
Generating preambles from a single root sequence for
𝐿
= 139 (short sequence).
t
0
u
1
2
1
C S
R A
N
L
x
𝑵
𝒄𝒔
𝑵
𝒄𝒔
𝑳
𝑹𝑨
𝑵
𝑪𝑺
≥
𝟔
VOLUME XX, 2020 14
FR2. The 𝑁 parameter specifies how many cyclic shifts
can be used within a given root sequence. Using the start
physical root sequence and 𝑁, the UE generates 64 ZC
sequences (or preambles) for each time-frequency PRACH
occasion, enumerated in first increasing order of cyclic shifts
𝐶 of a logical root sequence, and then in increasing order of
the logical root sequence index (section 6.3.3.1 of [3]). A
frequency domain (FD) version of the sequence is generated
as 𝑦,(𝑛)=∑𝑥,(𝑚)⋅𝑒
RA
RA
. All 64 preambles
can be generated using a single root sequence or using
multiple root sequences depending on the sequence length
𝐿 and the cyclic shift parameter 𝑁. An example for each
scenario is illustrated in Figure 4-5 and Figure 4-6 for 𝐿 =
139 (short sequence).
1) ZC properties for Preamble detection:
Specifically, two properties of the ZC sequences (see
chapter 7 of [20] for all properties of ZC sequences) are
useful at the receiver for detection and timing estimation (for
unrestricted sets). First, the normalized cross-correlation
between two unique ZC sequences (i.e., ZC sequences
generated with two different root sequences) will be low and
equal to
. Second property is that the cyclic shifts of a
ZC sequence (i.e., generated with a given root sequence) are
orthogonal (i.e., zero cross-correlation) to each other. Note
that the orthogonality between cyclic shifts is retained at the
receiver side only if the relative cyclic shift between two
sequences is larger than any difference in their respective
received timing. Therefore, in practice only a subset of the
cyclic shifts can be used to generate orthogonal preambles,
where the number of available shifts depends on the
maximum timing uncertainty to be considered (depends on
cell size). In general, for small cell sizes a relatively large
number of cyclic shifts are available compared to larger cell
sizes. Table 2 shows the maximum cell radius for different
formats of both long and short-sequence length PRACH
preambles for all values of 𝜇. The supported cell size is
determined by the minimum of the zero-correlation zone
length 𝑁CS and the guard period length 𝑁. For low Doppler
scenarios, all possible cyclic shifts are allowed and are
labelled as Unrestricted Sets. In the case of high Doppler
scenarios, some of the cyclic shifts are not allowed. This is
because of a property of ZC sequences according to which
energy transmitted on a given cyclic shift will appear at other
cyclic shifts depending upon the root sequence and the
sequence length. These cyclic shifts are not considered in
forming the preamble sets and are labelled as “Restricted
Sets”. For detection of preambles from restricted sets, the
correlation energy of these “co-cyclic shifts” will also need
to be accumulated. Restricted sets are not applicable for
frequency range 2, i.e., FR2 in 5G-NR.
The parameter 𝑁 indicates the width of the “zero-
correlation zone”, thus providing larger or smaller “zones”
in terms of timing error for which orthogonality (i.e., zero
correlation) is retained. The set of cyclic shifts for a sequence
are partitioned into groups of 𝑁 shifts per preamble index.
Essentially, the gNB receiver looks for a strong correlation
with one of the root sequences. Location of the spike (i.e.,
which cyclic shift) determines the preamble index (within
which 𝑁 group it shows up in) and the timing (where in the
𝑁 group is shows up). Note that the gNB is aware of the
start root sequence and number of root sequences used
(depending on the parameter 𝑁 gNB has configured) and
hence needs to do sequence matching (or correlation) for
only the configured roots sequences. At the receiver, the
received signal is sequence matched with a set of ZC-
sequences starting from the starting root (and up to number
of roots required) and typically filtered using an IFFT for
preamble detection and timing estimation (see section 5 and
64 preambles can be from different root sequences u if is large i.e., if
u
0
1
2
Eg: Unrestricted set zeroCorrelationZoneConfig = 10 and
0
6
2
1
u
8
u
0
0
1
2
6
Cyclic
shift 0
Cyclic
shift 7
Cyclic
shift 63 Unused root can be used by gNB for
noise estimation
Preamble
index 0
Preamble
index 63
Timing offset
t
Correlation
spike location
x
= Start root sequence index =
Lookup Table 6.3.3.1-4
(i = prach-RootSequenceIndex)
𝑵
𝑪𝑺
=
𝟏𝟗
𝑳
𝑹𝑨
𝑵
𝑪𝑺
<
𝟔𝟒
𝑵
𝑪𝑺
Figure 4-6:Generating preambles from different root sequences for
𝐿
=
139
(short sequence).
VOLUME XX, 2020 15
Figure 5.1 for more details). The IFFT filtering operation
will cover for all the cyclic shifts used within the given root
sequence, i.e., preamble transmitted with a given root
sequence and any cyclic shift within can be detected with a
single IFFT. Therefore, the receiver complexity scales only
with the number of root sequences used. The details on
receiver complexity is provided in section 6.A.
2) Cell dimensioning:
The cell radius, number of cyclic shifts and number of root
sequences required to generate 64 preambles can be
computed as below. Parameters 𝑇 , 𝑇 and path profile
values (in samples) in Table 2 are assuming 15kHz SCS (see
Table 6.3.3.1-2 of [3]) and scaled accordingly for different
SCS. Maximum radius in Table 2 for different SCS is
computed as follows. First, compute 𝑁 as follows. Step 1:
First compute N
=
()×𝐿 . Using 𝑁
, find the
quantized value of 𝑁 using Table 6.3.3.1-7 of [3] for FR2.
E.g., for A1 format, 𝑁
will be (288/2048)*139 = 19.54,
which will be quantized to 19. Step 2: Compute number of
cyclic shifts required as 𝐶=
. E.g., for A1 format, this
will be 𝐶=
=7.
Step 3: Compute the number of root sequences required to
generate 64 preambles as,
. E.g., for A1 format, this will
be
= 10. Step 4: The cell radius (see [20]) can be
calculated as Cell Radius =
−
×
(in meters).
Here, 𝜏 is the delay spread equal to the PUSCH CP size
(144𝑇 or 4.69 𝜇𝑠 @15kHz).
The maximum cell radius, number of cyclic shifts and root
sequences required for all NR PRACH formats are shown in
Table 2 when un-restricted sets are used. Preamble indices
not used for Contention based Random Access (CBRA) in a
PRACH occasion can be reserved for Contention Free
Random Access (CFRA) as in LTE, so the overall preambles
to be processed during a PRACH occasion could be less than
the maximum indicated in Table 2. Also, the quantized 𝑁
values used with restricted sets are different (see [3]) and
therefore the maximum radius achievable for different
PRACH formats will be different for restricted sets
compared to the ones indicated in Table 2. The timing offset
estimate error tolerance is related to the SCS configured for
the PRACH channel [36]. While selecting the proper
PRACH format and 𝑁, the maximum timing offset
allowable should be considered. The largest time offset Δ𝜏,
2
,
0
RB
sc
size
grid
NN
k
2
,
0
RB
sc
size
grid
NN
k
0
k
RB
sc
start
grid
NN
,
RB
sc
start
grid
startiBWP
NNN )(
,
,
RB
sc
start
RA
Nn
RB
sc
RA
RBRA
NNn
1
k
𝑛
𝑅𝐴
Figure 4-7:Location of PRACH transmission occasion within the resource grid.
PRACH
format
Number of
reps. Tcp Tseq TGP Path profile
(Ts)
Path profile
(us) Use case Upper
bound on
Quantized
less than
CP
Number
of cylic
shifts
Number
of root
sequences
Maximum
radius (m)
for 15 kHz
SCS
Maximum
radius (m)
for 30 kHz
SCS
Maximum
radius (m)
for 60 kHz
SCS
Maximum
radius (m)
for 120 kHz
SCS
A1 2 288 4096 0 96 3.13 Small cell 19.54688 19 7 10 939 448.703237 224.35162 112.175809
A2 4 576 8192 0 144 4.69 Normal cell 39.09375 34 4 16 2110 871.271583 435.63579 217.817896
A3 6 864 12288 0 144 4.69 Normal cell 58.64063 46 3 22 3517 1302.92626 651.46313 3 25.731565
B1 2 216 4096 72 96 3.13 Small cell 14.66016 13 10 7 586 232.875899 116.43795 58.2189748
B2 4 360 8192 216 144 4.69 Normal cell 24.43359 23 6 11 1055 475.588129 237.79406 118.897032
B3 6 504 12288 360 144 4.69 Normal cell 34.20703 34 4 16 1758 871.271583 435.63579 217.817896
B4 12 936 24576 792 144 4.69 Normal cell 63.52734 46 3 22 3869 1302.92626 651.46313 325.731565
C0 1 1240 2048 1096 144 4.69 Normal cell 84.16016 69 2 32 5354 2130.26439 1065.1322 532.566097
C2 4 2048 8192 2916 144 4.69 Normal cell 139 139 1 64 9301 4648.25 2324.125 1162.0625
0 1 3168 24576 2976 192 6.25 LTE ref arming 108.1523 93 9 8
1 2 21024 49152 21904 512 16.67 La rge cell
(<100km) 717.7383 419 2 32
2 4 4688 98304 4528 192 6.5 Co verage
enh.
160.0436 167 5 13
5 kHz
SCS 3 4 3168 24576 2976 192 6.25 High speed
case 432.6094 439 1 64
1.25k
Hz
SCS
12364.04946
57427.98629
22910.57807
Short
Sequence
14759.75864
Long
Sequence
Maximum radius (m) for Long Formats
𝑵
𝑪𝑺
𝑵
𝑪𝑺
Table 2:NR PRACH Cell dimensioning.
VOLUME XX, 2020 16
due to propagation delay cannot be larger than the length of
the detection window corresponding to the given 𝑣 and 𝑁
(see [36]). That is,
Δ𝜏<min𝑇
,−1
2𝑇 ,1
2∙𝑇−𝜏
where 𝑇 =
∗ 2048 ∗ 𝜅 ∗ 2∗𝑇. The timing offset
ranges for different formats can be then be calculated.
D. Resource mapping for PRACH
The time-continuous signal 𝑠(,)(𝑡) on antenna port 𝑝 for
PRACH is defined (see [3]) by,
𝑠(,)(𝑡)
= 𝑎
(,RA)𝑒(
)CP,
RA start
RA
RA
(12)
The terms in the above equations are defined in section 5.3.2
of [3]. The PRACH resource mapping parameters of interest
are 𝑘 and 𝑘
. The factor 𝐾=
, is required as 𝑘 is
defined in multiples of Δ𝑓. In this section we will discuss
only the relevant terms used in PRACH signal resource
mapping, which are required for correct tone extraction at
gNB receiver.
E. Details on the sub-carrier offset 𝒌𝟏
The term 𝑘 (is in multiples of Δ𝑓) is used to locate the
lowest subcarrier of the lowest PRB of the PRACH
transmission occasion in frequency domain (𝑛) with
respect to the start of the corresponding resource grid, as
illustrated in Figure 4-7 (also see [15]). 𝑘 is given by
(section 5.3.2 of [3]), 𝑘=𝑘
+(𝑁,
−𝑁
,)𝑁
+
𝑛RA
start𝑁sc
RB +𝑛RA 𝑁RB
RA𝑁sc
RB −grid
size,sc
RB
. The parameter 𝑘
is
the subcarrier offset from the middle subcarrier of
numerology 𝜇 to the carrier center frequency 𝑓 and as
described in section III-B. Here, the term 𝑘
−𝑁
,𝑁
/
2 represents the start of the resource grid; the term 𝑛
𝑁
represents the start of the lowest PRACH transmission as a
frequency offset with respect to the start of the active uplink
BWP; the term 𝑛𝑁
𝑁
represents the start of the
current (or target) PRACH transmission, and is the frequency
offset from the start of the lowest (or first) PRACH
transmission; and the term 𝑁,
𝑁
is the frequency offset
between Point A and the start of the active uplink bandwidth.
Here, (𝑁,
− 𝑁
,)𝑁
is the frequency offset
between resource grid and active uplink bandwidth part.
Note that Δ𝑓 is the subcarrier spacing of the initial active
uplink bandwidth part during initial access (for CBRA).
Otherwise (for CFRA), Δ𝑓 is the subcarrier spacing of the
active uplink bandwidth part. Also, 𝑛
cannot point to
PRACH resources outside of the active BW (see [33]).
F. Details on the sub-carrier offset 𝒌
𝑘
(defined in table 6.3.3.2-1 of [3]) is the subcarrier offset
(in multiples of Δ𝑓) from PUSCH RB corresponding to the
PRACH frequency domain occasion index 𝑛 to the actual
random-access subcarrier. This is illustrated in Figure 4-8
(see [16]) with an example. The details of the below example
(in Figure 4-8) are as follows, 𝐿 =839 with Δ𝑓 =
1.25kHz and Δ𝑓=15kHz. PRACH bandwidth is then
839×Δ𝑓 =1048750 𝐻𝑧 . 6 RBs at Δ𝑓 = 6×12×Δ𝑓=
1.08𝑀𝐻𝑧. Unused bandwidth is then 31250Hz (or 25 tones
@Δ𝑓). Note that the PRACH resource offset 𝑘
starts from
the middle of the PUSCH subcarrier (i.e.,
) as in LTE.
Table 3: Subcarrier offset for PRACH resources.
𝑳
𝑹𝑨
𝚫
𝒇
𝑹𝑨
for
PRACH
in kHz
𝚫
𝒇
for
PUSCH
in kHz
𝑵
𝐑𝐁
𝐑𝐀
(allocation
expressed in
number of
PUSCH RBs)
k
839 1.25 15 6 7
. …… …. … ..
. …… …. … ..
139 120 120 12 2
Figure 4-8:
𝒌
is offset to RA subcarrier from PUSCH subcarrier.
Δ
𝑓
𝑅𝐴
=
1
.
25
kHz
Δ
𝑓
=
15
kHz
𝒌
=
𝟕
𝒏
𝑹𝑨
Δ
𝑓
2
𝒏
𝑹𝑨
+6
VOLUME XX, 2020 17
Therefore, 7.5kHz should be subtracted from 31250Hz on
either side, which leaves 13 unused tones @Δ𝑓 ( =
16.25kHz). Out of these 7 tones are not used at the start,
which is represented by the parameter 𝑘
and 6 tones are not
used at the end as shown in Figure 4-8. PRACH resource
referencing is from the mid of the PUSCH subcarrier (i.e.,
from 𝚫𝒇
𝟐 ) as in LTE (see [20]). Calculations for short
preamble (i.e., 𝐿 =139) with Δ𝑓 =120kHz and Δ𝑓=
120𝑘𝐻𝑧 (see Table 3 above) are as follows. PRACH
bandwidth is 𝐿×Δ𝑓 = 139 × 120× 10=
16.68𝑀𝐻𝑧. In terms of PUSCH RBs (12 RBs from Table 3)
this is 𝑁
×Δ𝑓×12=17.28𝑀𝐻𝑧. Guard tones =
600kHz, which is 5 tones @120kHz. With 𝑘
=2 for this
case, 2 zero tones are in the beginning to PRACH start (i.e.,
with 𝑘
=2 in the Figure 4-8) and 2 zero tones are at the end
of PRACH (with
guard, there will be 2 tones at
Δ𝑓 =120kHz).
V. IMPORTANT ASPECTS OF PRACH RECEIVER
DESIGN
In this section, all important aspects of PRACH receiver
design will be discussed. Specifically, aspects which need to
be addressed while designing a PRACH receiver in 5G-NR
are presented along with some real system use cases.
A. PRACH Receiver flow.
A typical non-coherent PRACH receiver processing chain
is shown in Figure 5-1 The data CP is removed from the
received time domain signal and 𝑁 point FFT is taken to
obtain the frequency domain (FD) samples. The FD samples
are correlated with the configured root sequences. Since the
UE’s would have used random preamble indices for
transmission, several hypotheses, starting from the start root
sequence and up to number of root sequences configured
will be used for detection purposes at gNB. Note that
correlation in FD corresponds to complex multiplication of
received FD samples with the root sequences. Cross
correlation is followed by a time domain energy analysis
(using an IFFT) to detect correlation peaks and their exact
location within the detection window. With a non-coherent
PRACH detector, for each of the received antennas and
symbols, the received preamble can be processed
independently, and time domain energies can be combined
before peak detection. However, the performance and
complexity of the non-coherent detector may not be
desirable for PRACH formats with higher repetitions which
are expected to operate in low SNR regimes. The complexity
here is due to use of an IFFT being used per
root/symbol/antenna/TD/FD occasion which could prove to
be a bottleneck for most systems. Coherent detection offers
lower complexity and better detection gains but will require
combining of the received PRACH symbols (and/or
antennas) before correlation and time domain analysis.
Coherent combining of PRACH symbols will require a few
additional processing steps before correlation and time
domain analysis can be performed. Specifically, two
additional steps will be required before coherently
combining the received PRACH symbols. First, the common
phase correction which is typically applied in the DFE for
data channels, must be undone for PRACH processing.
Second, the timing offset introduced due to data CP removal
must be compensated before combining. The details
associated with these processing steps are defined in the
following sections.
Figure 5-1: A typical non-coherent PRACH receiver processing chain [37].
VOLUME XX, 2020 18
B. Tone extraction.
The first step though is to extract the required PRACH
tones for processing, using all the sub-carrier offsets used in
the OFDM signal generation. Consider the case when
Δ𝑓 =Δ𝑓 and where a common wideband FFT is used.
The first starting tone index for the 𝑛RA
frequency occasion
is given by (see Figure 4-8),
𝑁
=
−𝑘
+
𝑁,
−𝑁
,𝑁
+𝑛RA
start𝑁sc
RB +𝑛RA 𝑁RB
RA𝑁sc
RB
. +
𝑘
(13).
Simplifying we get (see derivation of 𝑘 and 𝑘
in section IV-
E and IV-F), 𝑁
=
+K𝑘+ 𝑘
, where
𝐾,𝑘and 𝑘
are defined in sections IV-E and IV-F and 𝑁
is the wideband FFT size. Here, the factor 𝐾 is required
because 𝑘 will be in units of Δ𝑓 (see section IV-E). Starting
from 𝑁
, 𝐿 number of tones can be extracted for
PRACH receiver processing.
C. Undo common phase correction.
During the up-conversion to the carrier frequency 𝑓 (or
𝑓, see section III-B), there is no common phase
correction term applied at the UE for PRACH transmission
(see section 5.4 of [3]). However, due to the use of common
DFE chain between PRACH and data channels, common
phase correction which is done for data channels (typically
within DFE) should be undone for PRACH processing if a
coherent detector is being used. This phase per-symbol for
OFDM symbol index 𝑙 is given by 𝑒, where, 𝑖= √−1,
𝜃=2𝜋𝑓𝑡start,
+𝑇CP,
, where 𝑓 is the receiver
center frequency of the gNB in Hz. The phase offset for
PRACH signal due to the common phase correction should
be undone before coherent combining of the PRACH
symbols (repetitions). The phase de-rotation term can be
computed as follows. Let the PRACH start symbol (column
6 of Table 6.3.3.2-4 in [3]) be denoted as 𝑝 ∈{0,…14}
and the number of PRACH repetitions as 𝑁
=
⋅ (with 𝑁 defined in Table 6.3.3.1-2 of [3]). For the
PRACH symbol 𝑝∈{𝑝,..,𝑝+𝑁
−1}, the
accumulated phase is 𝑡
, from the reference symbol (i.e.,
symbol 0 of slot with mod𝑛
,2==0)) to symbol 𝑝 for
slot 𝑠= mod𝑛
,2. In slot 𝑠, for the 𝑗th FFT output and
PRACH symbol 𝑝, the phase de-rotation term will be
𝑒 = 𝑒
, . Since the phase term repeats
every 1ms (see derivation in [26]), 𝑡start,
will repeat every 2
or 8 slots. The reference data symbol for phase compensation
will be symbol 0 of the slots where phase term repeats, i.e.,
data symbol 0 of slots with mod𝑛
,2==0. Adding slot
notation to 𝑡start,
as 𝑡start,
, to denote the accumulated phase
in slot 𝑠, the accumulated phase 𝑡
, from the reference
symbol to symbol 𝑙 for slot 𝑠= mod𝑛
,2, is given by,
𝑡
,
= 𝑡
,+𝑇(𝑁,
, + (𝑙 − 1) × (𝑁+𝑁,
)), 𝑙>0
𝑡
,+𝑇𝑁,
,, 𝑙=0 (14)
with 𝑡,
, =0 for slots with 𝑠=0 𝑎𝑛𝑑 𝑙=0. Here, 𝑁,
is the number of samples in data CP for data symbol 𝑙. Note
that 𝑁,
will be longer by 16𝜅, for slots 𝑠 =0 or 2 .
D. Timing compensation (due to Data CP removal)
One of the design items discussed in 3GPP during the
PRACH preamble design in NR was to enable the use of the
common wideband FFT (at gNB) for all uplink channels (see
[18] [34] and [35]) when the sub-carrier spacing between
data and access channels is same as shown in Figure 5-2.
This has a consequence on the PRACH receiver, which may
have to account for the data CP removal before the common
wideband FFT, especially when a coherent combining of
symbols is being considered. The signal within each FFT is
Figure 5-2:Common wideband FFT for PRACH with A1 short format and Data.
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
CP RACH RACH RACH RACH
CP RACH RACH R AC H RACH
FFT
FFT
FFT FFT
VOLUME XX, 2020 19
a cyclic shifted version of the PRACH preamble sequence
and can be easily rotated. However, in case of long formats,
a separate DFE chain needs to be present (to cater to 1.25kHz
and 5kHz subcarrier spacing) and a common wideband FFT
cannot be used. The removal of data CP time samples results
in a phase ramp on the frequency domain samples of PRACH
and needs to be compensated for in the PRACH receiver if
coherent combining across symbols is required. For a
PRACH preamble with CP and sequence being repeated
several times, each OFDM symbol acts as a cyclic prefix for
the next OFDM symbol. However, the OFDM symbols
which is repeated has much smaller length as compared to
LTE PRACH and equals the same length as adjacent user
data OFDM symbols. The received signal within each FFT
window will then act on a cyclic shifted version of the
PRACH preamble sequence [18].
With the use of wideband FFT for PRACH, we see that
each extracted PRACH symbol consists of two parts of
samples coming from adjacent two repetitions (see Figure 5-
2). The timing offset compensation due to this operation
needs to be done for proper PRACH detection/timing
estimation. The timing offset in the time domain is
equivalent to the phase ramping in the frequency domain.
After tone extraction, the phase ramping will be
implemented for each of the symbols. After tone extraction,
denote the frequency domain tone as 𝑋[𝑘],0≤𝑘≤L−
1,0≤𝑙≤𝑁 for each symbol 𝑙, and each received antenna
𝑟={1,⋯𝑁}. Here, 𝑁 is the number of repetitions of a
PRACH sequence for a given PRACH format and given by
𝑁=
⋅ . Denote the phase ramping factor as 𝜌 for the
𝑗 FFT tick. The phase ramping should start from the tone 0
of 1024 tones since coherent combing will be done
subsequently. Since PRACH is not located in the tone 0, the
initial phase offset needs to take the initial PRACH tone
location into account. The initial phase is 𝑒
. The phase
ramping is 𝑋[n] = 𝑋[n]𝑒()
, where 𝑘=𝐾𝑘+
𝑘
+
with 𝐾 ,𝑘
and 𝑘 defined earlier. The phase
ramping factor can be computed as,
𝜌=𝑚𝑜𝑑𝑁
−𝑁,
−(𝑗−1)
∗𝑁,
, 𝑁.(15)
Note that for formats Bx, which have guard bands at the end
of the PRACH preamble, some of the PRACH symbols will
be aligned to left of the PUSCH symbol boundaries and some
symbols are aligned to the right of the PUSCH symbol
boundaries (see Figure 4-4). The PRACH symbols which are
aligned to the left of the PUSCH symbol will result in
𝑁
−𝑁,
−(𝑗−1)∗𝑁,
<0 and the phase
ramping factor will need to be circularly shifted by 𝑁 for
coherent combining of symbols. Due to the possible
frequency offset, it might not be possible to coherently
combine all the repetitions without degrading performance.
Let 𝜉 is the residual frequency offset between receiver and
transmitter, i.e., residual frequency offset is the remaining
frequency offset after the downlink synchronization has
happened at the UE. In [23], for FR2, 𝜉=4000𝐻𝑧 was
assumed during simulations and the phase rotation over 1
PRACH symbol will be 2𝜋×𝜉×𝑇×𝑁=6°. This
angular rotation seems small enough to combined adjacent
symbols.
E. Timing offset Estimation.
The IFFT size (≥𝐿 ) determines the timing offset
resolution of the PRACH receiver. There will be
samples in time domain to analyse for a peak per root. The
number of windows to analyse will be
. For Δ𝑓 =
120kHz and 𝐿 =139, the timing resolution with 𝑁 =
144 will be
≈57.87𝑛s. This has to converted to some
multiple of minimum resolution of timing advancement,
therefore the peak detection index should be appropriately
quantized. From section 4.2 of [7], the initial time alignment
value 𝑁TA =𝑇⋅16×64×𝑇2
⁄, with index values of 𝑇
= 0, 1, 2, ..., 3846. The lowest resolution (with 𝑇 = 1) for
𝜇 = 3 is then 1×16×
×
∗∗≈ 65𝑛𝑠, which
is basically .
in terms of LTE resolution. Note that the
detection metric must be normalized with noise and
compared with a threshold for a correct detection. The
detection threshold for each format and 𝑁 can be
determined by using the method described in [42]. Noise
estimation can be based on unused roots or cyclic shifts. It
can also be made based on the IFFT energy. In all estimations
however, the estimated noise variance has a signal energy
component bias, which seems to be the negligible while
using unused roots. For all the parameters discussed so far,
an example use case is as follows. For a mmW system with
BW of 100MHz and sub-carrier spacing of 120kHz for both
PRACH and data channels, the common wide-band FFT size
would be
=.
=1024. The IFFT size for
PRACH detection and timing analysis could be 𝑁 = 192
leading to a timing estimate resolution of ≈43.4𝑛𝑠. The
timing estimate windows can be split into positive and
negative windows (in some proportion) around a given
centre sample to be able to detect positive and negative
timing offsets respectively, depending on gNB requirements.
VI. PRACH RECEIVER IMPLEMENTATION
ASPECTS
A. Processing Complexity
The IFFT module used for time domain analysis in the
PRACH receiver often dictates the receiver complexity. This
is because, IFFT is typically implemented in hardware and
while processing multiple symbols (combined or not) per
VOLUME XX, 2020 20
antenna, per hypothesis (i.e., a given root), per TD/FD
occasion with a single IFFT engine could be prove limiting.
One can indeed limit the number of roots supported as a gNB
capability. Note that some formats may require roots greater
than what can be supported by gNB to derive 64 preambles
(or whatever is configured by gNB) to obtain maximum
coverage offered by the format. In those scenarios, gNB will
simply support up to max roots possible by gNB and 𝑁
should be configured appropriately (based on reduced
coverage) so that 64 preambles (or the number of preambles
to use as configured by gNB) can be derived with the number
root sequences which can supported.
Coherent combining provides a better implementation
complexity with performance gains as the number of roots to
be processed is lower. However, there could be a limit on
symbols which can be coherently combined without
degrading performance as noted previously (due to
frequency offset). Combining across the antennas before
detection could also be considered but will require precoding
coefficients information associated with the antennas. If
precoding information is not available, coherent combining
across antennas can be done in time domain after IFFT (as
shown in Figure 5-1).
B. Wideband FFT usage
A note on the wideband FFT usage when Δ𝑓 ≠Δ𝑓 .
For a given bandwidth and sampling rate, FFT size is
computed as 𝑁 =
, which for 100MHz bandwidth is
1024 for 120kHz SCS, 2048 for 60kHz SCS and so on. When
Δ𝑓 ≠Δ𝑓 and a narrowband chain is not available, FFT
size can be computed based on Δ𝑓=min (Δ𝑓,Δ𝑓) so
that FFT grid is aligned to the smaller sub-carrier spacing
(see Figure 2-5 in section II-B for different tone alignments).
However, when Δ𝑓 ≠Δ𝑓 , CP removal before
wideband FFT would introduce performance degradation on
data or PRACH. One way to mitigate the performance loss
could be as follows. While using a common FFT with
resolution based on lower SCS, FFT window is from end of
CP of higher SCS (longer CP) to end of symbol duration of
lower SCS. For example, consider 𝑓 =30.72𝑀𝑠𝑝𝑠 for a
20MHz BW with Δ𝑓 = 15kHz and Δ𝑓 = 30kHz.
Assume, PRACH and data are multiplexed in frequency.
Then the normal CP size (in microseconds) of higher SCS is
.
= 2.35𝜇𝑠 and symbol duration = 33.33 𝜇𝑠. For lower
SCS, CP and symbol sizes are 4.7𝜇𝑠 and 66.66𝜇𝑠
respectively. The FFT size required if only PRACH was
present is .
= 2048. FFT size if only data was
present is .
= 1024. Apply a 2048-point FFT after
removing 2.35𝜇𝑠 worth of CP samples on 66.66𝜇𝑠 worth
time samples. Basically, the FFT captures 1 symbol of
15kHz and 2 symbols of 30kHz. But with this approach, for
PRACH, 2.35𝜇𝑠 of CP portion has also been captured. These
time samples (before FFT) may have corruptions based on
multi-path fading which may affect some portion of the
spectrum (depends on the frequency components of that
corruption).
If this multi-path is from a previous PRACH signal, the
corruption will likely impact PRACH channel. Further, note
that 2.5us worth of PRACH symbol end was cut off, because
of beginning the FFT earlier than 4.7us. The FFT window
for PRACH is basically mis-aligned. Since most PRACH
formats has multiple repetitions symbols to boost SNR, it
may be possible to tolerate such signal corruptions due to
common wideband FFT usage. Alternatively, CP size worth
4.7𝜇𝑠 could be dropped before computing the FFT. But,
2.35𝜇𝑠 worth of symbol information of higher SCS
(PUSCH) will also be removed, which can significantly
degrade uplink throughput performance. This may not be
acceptable. Also, with a common FFT approach, processing
of PUSCH will incur extra delay of 1 symbol which may not
be desirable. This is because we are buffering for at least
2.35𝜇𝑠 + 66.66𝜇𝑠 before firing off the FFT. Whereas,
PUSCH 1st symbol was already available by 2.35𝜇𝑠 +
33.33𝜇𝑠 mark. Given the above issues, it might be desirable
to have separate DFE chains for PRACH and data.
Figure 5-1:Small/Large delay PRACH preamble detector outline (see [35]).
FFT FFT
FFT FFT
Compare received signal energies in first and last FFT windows
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
C
P
Data
Symb
0
Symb
1
Symb
2
Symb
3
Symb
4
Symb
5
Symb
6
Symb
7
Time domain occasion 0 Time domain occasion 1
CP RACH RACH R AC H RACH
CP RACH RAC H RACH RACH
CP RACH RACH R ACH RAC H
CP RACH RAC H RACH RACH
FFT
Frequency
Time
PRACH
with large
delay
PRACH
with small
delay
Symb
8
VOLUME XX, 2020 21
C. PRACH processing with delays greater than symbol
duration
Delays up to the length of one PRACH OFDM symbols
can be detected by frequency domain matched filters as
outlined in Figure 5-3 [37]. However, this receiver structure
results in a delay ambiguity when the delay exceeds the
length of the PRACH OFDM symbol (i.e., >𝑁). This can
happen, for example, while using C2 format with start
symbol 0 in slots with longer CP duration. A modified
PRACH preamble detector is then required. An example of
a PRACH preamble detector for handling large delays (see
[35]) is illustrated in Figure 5-3. Here, a detector is included
which compares the received signal in first and last FFT time
windows resulting in a decision if delays are smaller or larger
than the length of the PRACH OFDM symbol. This decision
can then be combined with a delay estimator as in Figure 5-
1 (see [35] and [37]) resulting in a timing estimate with high
time resolution and support possible propagation delays
larger than one PRACH OFDM symbol. Such a large delay
estimator may be required when PRACH format C2 needs to
be configured. See [35] and [36] for methods on resolving
detection ambiguity.
D. RAN4 Performance requirements.
Radio Performance and Protocol aspect requirements for
base station [6] are specified by the 3GPP Radio Access
Network working group 4, also known as RAN4 and can be
used to bench mark the performance of a PRACH receiver.
The performance recommendations made by RAN4
committee for both base-station performance [6] and base-
station conformance testing [39] are shown in Table 4 for
FR2. The performance recommendations are for AWGN and
Tapped Delay Line (TDL) channel with delay spread of 30
ns and maximum Doppler of 300Hz. The probability of
correct detection is defined in section 11.4.2.2.1 of [6] and
the minimum requirements are listed in section 11.4.2.2.2 of
[6]. PRACH test preambles used for RAN4 performance
study are defined in annex A.6 of [6] and delay profiles for
each of the channel model is defined in annex G.2.1.1 of [6].
The minimum SNR (in dB) listed in Table 4 is the SNR at
which 1% missed detection was achieved, timing error
tolerance was less than the values specified in Table
11.4.2.2-1 of [6] and the false alarm was less than 0.1%.
Table 4 also lists RAN4 performance reported from Nokia
and Ericsson where margins ≥3𝑑𝐵 are seen for most
scenarios. A simulation study of the PRACH receiver
outlined in this paper, revealed that performance margins
were comparable to [40]. Interestingly, these margins could
be achieved only with a PRACH receiver using coherent
combining of PRACH symbols before detection.
VII. CONCLUSION
In this paper, downlink and uplink initial access
channels in 5G-NR was studied in detail. With the 5G-NR
3GPP specifications details being quite dense getting clear
information can prove to be a tedious task. Several design
details associated with the physical layer procedures of
initial access channels, which are skipped in the 3GPP 5G
NR specifications were explained in detail in this paper.
Three important contributions were made in paper. First,
the design details and justifications associated with both
downlink and uplink access channels were discussed.
Aspects of signal generation and phase correction were
presented with mathematical analysis. Secondly, receiver
design aspects of NR PRACH were discussed in detail with
illustrating examples. Lastly, implementation aspects of a
PRACH receiver and its performance comparisons with
3GPP defined Radio Performance and Protocol aspect
requirements or RAN4 requirements were presented for
millimeter wave access. The work in this paper will be of
significant value to researchers and system design
engineers looking to design efficient initial access
algorithms within the framework of 5G-NR systems.
VIII. ACKNOWLEDGEMENTS
The author would like to thank Raja Bachu, for his
inputs on system design aspects; Luca Blessent and Junyi Li
for supporting the work in this paper.
Results
from
Chann
el
(annex
J)
𝝃
in
Hz
Min.
SNR (dB)
for Short Formats in FR2
A1 A2 A3 B4 C0 C2
Table
8.4.1.5.2
-2 of
[39]
AWGN 0 -8.4 -11. 2 - 13.0 -15.6 - 5.5 -11.1
Table
11.4.2.2.
2-2 of
[6]
AWGN 0 -8.7 -11. 5 - 13.3 -15.9 - 5.8 -11.4
Nokia
[40]
AWGN 0 - 11.43 -14.45 - 15.78 -18.48 -
8.43
-
14.42
Ericsson
[41]
AWGN 0 -11.6 - 14.6 -16.4 -19.2 NA NA
Table
8.4.1.5.2
-2 of
[39]
TDLA
30-300
Low
4K -1.1 -3.8 -5.2 -6.9 1.8 -3.6
Table
11.4.2.2.
2-2 of
[6]
TDLA
30-300
Low
4K -1.7 -4.4 -5.8 -7.5 1.2 -4.2
Nokia
[40]
TDLA
30-300
Low
4K -4. 15 -7.01 -8.54 -11.01 -
1.13
-7.05
Ericsson
[41]
TDLA
30-300
Low
4K -4.2 -7.2 -8.6 -9.8 NA NA
Table 4:RAN4 performance requirements from [6] and [39] and
comparison with two different network operators reported
performance.
VOLUME XX, 2020 22
IX. REFERENCES
[1] “Small Cells taking cellular to new heights with IoT tech and global
deployments”,
https://www.qualcomm.com/news/onq/2018/03/16/mwc-2018-small-
cells-taking-cellular-new-heights-iot-tech-and-global-deployments ,
Mobile World Congress (MWC), March 2018.
[2] Jin Liu et.al., “Initial Access, Mobility, and User-Centric Multi-Beam
Operation in 5G New Radio”, IEEE Communications Magazine,
March 2018.
[3] 3rd Generation Pa rtnership Pr oje ct, “ Techni cal Specification
Group Radio Access Network; Evo lved Universal Terrestrial
Radio Access ; Physical Channels and Modulation” , 3GPP TS
36.211 V14.1.0., Dec. 2016.
[4] 3rd Generation Pa rtnership Pr oje ct, “ Techni cal Specification
Group Radio Access Network; NR; NR and NG-RAN Overall
Description, Stage 2”, 3<