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IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 1

Ultra-Narrowband Waveform for IoT Direct

Random Multiple Access to GEO Satellites

Christian A. Hofmann, Member, IEEE, and Andreas Knopp, Senior Member, IEEE

Abstract—Direct access of small terminals in the Internet

of Things (IoT) to geostationary satellites may provide wide

coverage and almost 100% availability for remote locations with-

out access to terrestrial networks. However, existing waveforms

and IoT solutions do not close the link to the geostationary

earth orbit (GEO) for massively deployed small devices. We

present a novel modulation and signaling scheme based on chirp-

spread spectrum (CSS) that enables reliable transmission at ultra

low bit-rate. The proposed structure for the transmit signal

applies unipolar codes in a novel manner, which allows random

multiple access to a common channel for a large number of

devices. Further, the transmit signal is designed to allow robust

signal detection with low effort even at high carrier frequency

offsets. We propose a system concept for the receiver including

synchronization, and provide the results of extensive simulations

carried out on system and link levels. As a result, we demonstrate

that the proposed scheme, referred to as Unipolar-coded Chirp-

Spread Spectrum (UCSS), enables true random multiple access

for a very large number of devices, closing the challenging link

between IoT devices and satellites in the GEO even at high carrier

frequencies from C-band to Ka-Band.

Index Terms—Efﬁcient Communications and Networking,

Machine-to-Machine Communications, Medium Access Control

Protocols, Satellite Communication, Spread Spectrum Commu-

nication, Chirp Modulation, Satellite Direct Access.

I. INTRODUCTION

MACHINE type communication (MTC) or machine-to-

machine (M2M) communication has gained an enor-

mous interest throughout industry and academia. Low power

wide area network (LPWAN) solutions enable the transmission

of small data packets from very small devices at minimum

power consumption over distances of several kilometers. They

are, therefore, attractive for a vast variety of applications in

the Internet of Things (IoT) [1]. If such devices are used

for the tracking of mobile objects or devices, a coverage

of the employed IoT service over the area of interest is

required. Satellite based systems guarantee ubiquitous service,

especially for objects in remote locations and areas without

terrestrial infrastructure. Generally, a terrestrial connection for

massive machine type communication (mMTC) is the ﬁrst

choice. The terrestrial service delivers sufﬁcient coverage and

availability in most applications. Nevertheless, the satellite

enabled access to the network serving as an additional and

alternative connection can provide connectivity in cases when

Manuscript received 08-Jul-2019; accepted 31-Jul-2019. Date of publication

xxxx xx, 20xx; The authors are with the Signal Processing Group of the

Institute of Information Technology, Bundeswehr University Munich, 85579

Neubiberg, Germany (e-mail: papers.sp@unibw.de). Copyright (c) 2019 IEEE.

Personal use of this material is permitted. However, permission to use this

material for any other purposes must be obtained from the IEEE by sending

a request to pubs-permissions@ieee.org.

the terrestrial network is not available. For many services

where the guaranteed network connection is a must, the

information could be transmitted via satellite if the IoT device

moves outside the service area of the terrestrial system, or

if the terrestrial system is temporarily not available. For

the tracking of wildlife, objects in very remote locations,

small aerial or maritime vehicles, a novel low-rate satellite

service may be the ﬁrst choice. Novel applications for sending

emergency messages in any region may rely on such satellites

services, especially in the mountains or in the oceans. Finally,

some services use satellite networks instead of terrestrial ser-

vices for security reasons. Further examples for satellite-based

narrowband (NB) IoT services are, for example, presented in

[2] and [3]. Moreover, the direct access of NB IoT devices to

non-terrestrial networks or satellite networks in low earth orbit

(LEO) and geostationary earth orbit (GEO) is also a topic of

the future research for 5G as recently stated by 3GPP in [4].

The access of an IoT device to a satellite system ensures a

wide coverage, while the direct access to the satellites makes

the devices independent of further terrestrial infrastructure [3].

Satellite constellations in LEO can provide global coverage

and are usually preferred for NB IoT systems due to lower path

loss to the satellite [5], [6]. Nevertheless, for an instantaneous

access 100% of time, a large number of costly satellites

with an inter-satellite network is required. In contrast, GEO

satellites ensure continuous service over a speciﬁed coverage

area and can provide global access outside the polar regions

with only three satellites. Usually, GEO satellite systems at

higher frequencies apply directive earth station antennas with

a high gain to close the link. At lower frequencies, such as

UHF or S-band [7], GEO systems allow communication with

omnidirectional antennas.

For MTC via satellite, so-called supervisory control and

data acquisition (SCADA) systems have been developed that

apply scrambled coded multiple access (SCMA) or interleave

division multiple access (IDMA) together with spreading to

enable low-rate communication and multiple access [7]. These

so-called non-orthogonal multiple access (NOMA) schemes

employ a low-rate forward error correction (FEC) and different

scramblers or interleavers for user separation. A joint mul-

tiuser decoding with interference cancellation allows multiple

users accessing the network non-orthogonally. However, the

available spectrum at UHF or S-band is very limited and the

available services cannot handle a huge number of devices for

mMTC.

In this work, we focus on the direct access of preferably

small terminals to GEO satellites in frequencies of the C-

band or above. We consider ultra low data rates with only a

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 2

couple of bits per second and a burst transmission with random

multiple access. This is sufﬁcient for many applications, such

as the transmission of sensor values, positioning data, or

emergency messages. In seeking for transceivers that are as

small as possible and universally deployable, their antenna

characteristic is usually non-directive or even omnidirectional.

The available transmit power is limited and the transmit spec-

tral power density is restricted due to regulatory limitations. In

that case, at a given carrier frequency, the available transmit

power and the satellite ﬁgure of merit mainly determine

the achievable data rate of the system. Here, link budget

calculations indicate data rates in the range of only a few

bit/s. Therefore, it is a big challenge today to close this link

to a GEO satellite.

If we allow the IoT device to transmit data in a random

multiple access scheme, to enable, for example, emergency

messages, the most challenging task at the receiver side is

to detect the short transmitted bursts. Most probably, the IoT

transmitter’s oscillator is a low-power, low-cost device with

low accuracy and stability. If the narrowband transmission

comprises only of a very small RF-bandwidth (a few Hertz),

the effort for searching the signal (acquisition) at any possible

carrier frequency offset (CFO) in a range of several kHz is

very high [8]. If alternatively a spread spectrum technique is

applied to lower the transmitted power density and/or enable

an easier detection at the Rx, a limited timespan for coherent

correlation, due to the low oscillator stability, must be accepted

[9]. Thus, the synchronization is considered the most important

limitation for ultra-low bit-rate transmissions, and the overhead

to achieve synchronization is large. To the authors’ best

knowledge, no system or technology has been published that

can communicate using omni-antennas to GEO satellites in

C-Band or above. Existing satellite IoT waveforms [5], [10]–

[12] are designed to close the link either for communication

via LEO satellites or for the operation at L- or S-band. In

this work, we present an approach for a modulation scheme

that enables robust synchronization with reduced overhead via

GEO satellites at frequency bands above L- or S-band. The

proposed modulation scheme applies a chirp-spread spectrum

(CSS) technique for a robust transmission and a simpliﬁed

signal acquisition. The modulated chirps are separated in

time according to a unipolar code enabling a non-orthogonal

code division multiple access (CDMA) to a shared wireless

transmission channel. Unipolar codes are used for CDMA in

optical transmissions and are also known as optical orthogonal

codes (OOCs). Therefore, we refer to the proposed modulation

scheme as Unipolar Coded Chirp-Spread Spectrum (UCSS).

The codewords of the OOC are constructed here to enable

asynchronous communication of multiple users with random

access (RA) to the channel. Thus, the proposed modulation

scheme allows the application of unslotted ALOHA [13] on

the medium access control (MAC) layer. If UCSS is, for

example, applied in a system with small sensors transmitting

to a common gateway via satellite, the sensors may operate in

simplex mode and do not require a receive entity. The multiple

access for machine type communication (MTC) in satellite

networks has been investigated by various groups; [14] gives

an overview about the available RA techniques. Similar to

gateway

devices

GEO satellite relay

xm(t)

downlink

Fig. 1. Scenario considering the return channel from numerous devices to a

common gateway station

spread spectrum ALOHA (SSA) introduced in [10], we apply

a spreading by using CSS, but we further introduce a unipolar

code to minimize the collisions between the transmitted sym-

bols. If UCSS is used in the return link towards a common

gateway, then a successive interference cancellation (SIC)

technique might be applied to further enhance the throughput

as shown in [15].

As a main contribution, this paper presents UCSS as a

novel modulation and signaling scheme in close combination

with the synchronization concept to allow direct random

multiple access of numerous small devices to GEO satellites at

higher frequency bands. In section II, the satellite scenario is

described and an exemplary link budget is calculated. Section

III contains a detailed description of the proposed modula-

tion format and demonstrates how random multiple access

is achieved for a large number of users. A suitable receiver

design is presented in section IV. Here, we indicate how the

signal structure enables the acquisition and synchronization

without high overhead. In Section V, a performance evaluation

of UCSS is performed. Section VI provides a comparison of

our results to related work. The paper is concluded in section

VII.

II. SATE LL IT E LINK BUDGET

The proposed UCSS might be applied in the up- and

downlink of a small terminal transmitting and receiving signals

from a satellite at any orbit. In the downlink, the CDMA

properties of the waveform allow a transmission towards

multiple small terminals. The application of CSS enables an

immediate signal acquisition at the terminal. In the return

channel, i.e. the uplink from the terminals towards the satellite,

asynchronous random access is enabled for terminals with low

power and low cost hardware due to relaxed requirements

put on the frequency accuracy and stability. Furthermore, the

modulation format might be applied for instance to sensor

systems without downlink, since the multiple access scheme

is truly asynchronous and no synchronization information is

required to be received from the satellite.

As the transmit power of a small mobile device is the most

limiting factor in the link budget of the considered satellite

link, we concentrate on the user uplink towards the satellite.

In the following, we consider the return channel with a large

number of IoT devices transmitting via a transparent GEO

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 3

satellite and a gateway station serving as a common receiver

as depicted in Fig. 1.

The m-th user transmits the signal xm(t)at effective

isotropic radiated power (EIRP) EIRPTx,m. The uplink signal

is received by the satellite antenna with gain Gsat. The total

path loss introduced by the channel is Gp,m. The carrier power

over the noise density S

N0UL,min dB for the uplink is given

by S

N0UL,m

=10 lg EIRPTx,mGp,mGsat

N0(1)

=10 lg EIRPTx,mGp,m

k+G

Tsat

(2)

where N0denotes the noise power density of the additive white

Gaussian noise (AWGN) in the uplink at the receiver (Rx).

Furthermore, kstands for the Bolzmann constant and G

Tsat

is the ﬁgure of merit of the satellite in dB, which is the receive

antenna gain over the noise temperature. The signal-to-noise

power ratio (SNR) S

NUL,mis given by

S

NUL,m

=S

N0UL,m−10 lg {Bn}(3)

where Bnstands for the noise bandwidth of the system. If the

contribution of the downlink to the overall SNR is negligible,

or if the satellite is regenerative, the overall SNR of the m-th

user is S

Nm≈S

NUL,m.

Note, that the other users transmitting at the same time

cause interference to the desired user m. The mean interference

power Imis calculated from the signals of all Nu−1users,

transmitting in the same time interval [t1,t2]as the target user

m. If we assume mutually uncorrelated transmit signals for all

the users, then interference power Imfor user mis calculated

from the following equation:

Im=

1

t2−t1

t2

∫

t1

Nu

Õ

i=1,i,m|xi(t)|2dt.(4)

The signal-to-interference and noise power ratio (SINR) is

given by

S

I+Nm

="S

Nm−1

+S

Im−1#−1

(5)

where S

Imis the signal-to-interference power ratio (SIR) for

user m.

If the earth station comprises of a non-directional antenna,

the satellite channel becomes a fading channel due to multipath

propagation. We assume a fading process with lognormal

distributed channel coefﬁcients characterized by the standard

deviation σch to cover the propagation effects in our calcula-

tions.

To give an indication for the achievable data rate, we provide

a link budget for a link at C-band1to a GEO satellite’s global

1The calculated link budget is roughly also applicable to higher frequency

bands like Ku-band or Ka-band, if we assume that the receive dish-antenna

at the satellite has the same diameter.

beam with typical G

Tsat =−5 dB/Kat center of coverage. We

assume an IoT device2with EIRPTx,m=23 dBm transmitting

at 6 GHz, and a path loss of Gp,m=−201 dB.

For the example considered, the signal power over the noise

power density comes out to be S

N0m=15.6 dB/Hz which

gives a channel capacity of 29.9 bit/sin a bandwidth of 20 Hz.

If we assume a binary phase-shift keying (BPSK) transmission

with code rate 0.5 in 20 Hz, it would theoretically be possible

to transmit with a user bit-rate of 10 bit/sat Eb/N0=5.6 dB.

This means a device might transmit its position, which has

been source coded to a size of, for example, 40 bits, in a

timespan of 4 s. However, in practice, it is hardly possible to

use BPSK at such a low data rate. This is because the applied

matched ﬁltering at the Rx has such a low bandwidth that

the CFO, which is not constant over the duration of several

seconds, shifts the receive signal out of the receiver bandwidth.

Usually, in that case, spread spectrum is applied in order

to widen the utilized bandwidth. As a consequence, the signal

power density is reduced, shifting the received signal below the

noise ﬂoor. The acquisition of such a signal at an unknown

timing and an unknown CFO requires huge effort which is

also known from global navigation satellite systems (GNSSs).

If the IoT transmitter is only transmitting in short blocks for

a low percentage of time, the acquisition has to be repeated

for every transmitted block. This would require a very high

computational effort at the gateway station which is receiving

the signals of many devices. The presented modulation format

solves the highlighted set of problems, as it is designed to

enable ultra narrowband (uNB) transmissions in an effective

manner with low hardware requirements at the transmitter

and low effort for the acquisition and synchronization at the

receiver.

III. PROP OS ED MODULATION SCHEME (UCSS)

A. Overview

In the following, we give a brief overview of the proposed

UCSS modulation and synchronization format, while the re-

mainder of this section presents the detailed description.

Referring to Fig. 2 we consider the input data as bits in

blocks to be transmitted. The data block is encoded with a FEC

code before it is modulated by a differential phase-shift keying

(DPSK) modulator. Each modulated symbol is multiplied by a

Zadoff-Chu or constant amplitude auto-correlation (CAZAC)

chirp sequence (CS) which is referred to as a CSS technique.

This spreading provides us with a correlation gain proportional

to the length of the CS. In the next step, before the signal

is transmitted, we insert short pauses into the time signal

between the chirps. The pause times are chosen according

to a unipolar code, where each codeword represents one user.

Different users employing different codewords are supposed to

transmit asynchronously at the same time in a random-access

scheme.

2The transmit EIRP of the IoT device is assumed to be 23 dBm, as

this would most probably be the maximum transmitted power within 4 kHz

that is allowed when following all regulations issued by the International

Telecommunication Union (ITU). Furthermore, the same transmit power is

assumed for IoT devices with direct satellite access by 3GPP in [4].

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 4

FEC

encoder

M-DPSK

modulator

CSS-

Spreading

chirp

unipolar

encoder

codeword

DAC+

Tx RF

Rx RF

+ADC corr 1

chirp

M-DPSK

demod

FEC

decoder

corr 2

codeword

sync.

Fig. 2. Flowgraph of the proposed modulation scheme (UCSS) with transmitter and receiver

At the receiver, where the transmitted signals of all users

interfere, the received signal is ﬁrst correlated with the CS,

which can be considered as a CSS despreading. Hence, if all

users share a single CS, only one CSS despreader is required

at the gateway to despread the signals of all transmitting users.

The correlation result contains a correlation peak for every

symbol transmitted by any of the users. A collision at the Rx

occurs when two or more symbols have been received at the

same time. The unipolar coding at each Tx ensures that the

number of collisions between two Tx stations is limited to a

maximum number, which is a design parameter of the used

OOC. To identify the users that have been transmitting, the

result of the ﬁrst correlator is non-coherently correlated a sec-

ond time with a reference signal that contains the information

about the unipolar codeword. This second correlation could

be implemented with a low effort. It is performed for each

of the potentially transmitting users, while the ﬁrst correlation

is only required once for each CS used. A transmitted signal

is detected if the correlation result of the second correlator

exceeds a certain threshold. In the next step the timing is

recovered and the DPSK symbols are localized within the

output of the CSS despreader and differentially demodulated.

After the decoding, we obtain the transmitted bit-sequence as

the FEC corrects errors due to noise, interference, and signal

collisions.

B. Chirp-Spread-Spectrum

The history of the use of spread spectrum systems goes back

to World War II, and the application of a chirp was one of the

ﬁrst attempts for the spreading of signals [16]. Applications

of CSS are found in radar systems, military communications,

ranging systems, and robust communication at low power

spectral density. Signals spread by a chirp occupy a broad

band of the spectrum and provide enhanced protection against

interference, unwanted detection, multipath propagation, fre-

quency shifts from Doppler shifts, or oscillator inaccuracy

[17]–[19]. CSS is often the choice for applications requiring

high power efﬁciency and low data rates. In particular, IEEE

802.15.4a speciﬁes CSS as a technique for use in Low-Rate

Wireless Personal Area Networks (LR-WPAN) [20]. A chirp

is a sinusoidal signal whose frequency increases or decreases

linearly over a certain time span. The modulation of the chirps

in order to transmit data is achieved in different ways. In

[21], [22] for example, the frequencies which the individual

chirp signals start from are varied to encode information.

Phase modulation of chirps is performed in [23] where the

transmitted chirps are modulated by a DPSK symbol. To

enable multiple access to a shared medium it is proposed to

use chirps with different slopes for different users in [24].

The IEEE 802.15.4a standard also enables multiple access by

the use of so-called bi-orthogonal chirps in combination with

phase modulation of chirps and subchirps. In [25] orthogonal

chirps are applied to increase the spectral efﬁciency of CSS.

In this work, we propose phase modulation of identical

chirps as described in section III-D, while we use the location

of the chirps within the signal for the separation of multiple

users transmitting at the same time and at the same carrier

frequency.

C. Unipolar Coding

The application of CDMA to ﬁber optical channels has

driven the development of unipolar codes to separate several

users communicating asynchronously over a shared optical

ﬁber.

The so called OOCs are unipolar sequences consisting of

Zero-Bits and One-Bits, with good auto- and cross-correlation

properties [26]. In the following we use the construction

method in [27] for constructing the OOCs due to its low

complexity. As the variety of available codes in the literature

is large, there is room for the optimization of the code used

depending upon the application. Especially the number of

transmitted One-Bits in relation to the number of different

available orthogonal codewords can be optimized to ﬁt the

requirements of the application in terms of transmit energy

and number of users.

According to [27] a codeword c(n)is calculated using the

so-called quadratic placement operator yµ(ξ)for the µ-th user

deﬁned as

yµ(ξ) ≡ µξ(ξ+1)

2mod β(6)

with 0≤ξ≤β−1and 1≤µ≤β−1. The parameter β

is a prime number and deﬁnes the length Looc of a codeword

which is Looc =β2. Furthermore, the number of One-Bits Ns

within every codeword is Ns=β. The µ-th codeword out of

Nooc =β−1possible codewords is given by

cµ(n)=

1if yµ(ξ)+ξ β =n

for µ=1,2, ..., β −1

and ξ=jn

βk

for n=1,2, ..., β2−1

0elsewhere.

(7)

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 5

TABLE I

CODEWORDS FOR β=5

user codeword

1 10000 01000 00010 01000 10000

2 10000 00100 01000 00100 10000

3 10000 00010 00001 00010 10000

4 10000 00001 00100 00010 10000

Table I shows exemplary codewords for the Nooc =4users

of a code with β=5. The auto-correlation of a codeword is

deﬁned by

Rc,c(k)=

Looc−1

Õ

n=0

c(n)c(n−k)(8)

and the cross-correlation of two codewords c1(n)and c2(n)is

given by

Rc1,c2(k)=

Looc−1

Õ

n=0

c1(n)c2(n−k)(9)

with −Looc +1≤k≤Looc −1. In [27] it is proven

that the auto-correlation of any codeword excluding the zero

shift has strictly values of λa=max

k,0Rc,c(k)≤2. The

cross-correlation of any two codewords is always λk=

max Rc1,c2(k)≤4.

While we use the described code according to [27], there

exist further codes and design methods for codewords that

enable the modiﬁcation of λaand λkas well as the number

of codewords and the number of One-Bits [28]. This leaves

room for an optimization of the applied code with respect to

the parameters of the intended communication system.

D. Transmit Signal

This subsection describes the calculation of the transmit sig-

nal. Here, OOC and CSS are combined to create unique signals

for different users. A detailed block diagram description of

the transmitter is given in Fig. 3. We assume a block based

transmission, where a block consists of Nbit data bits xb(n)for

n=1, ..., Nbit that are encoded as a ﬁrst step using a FEC.

The code rate Rc=Nbit

Ncgives the number Ncof coded data

bits xc(n). The coded bits are the input of a DPSK modulator

with modulation order M. The Nm=Nc/ld{M}modulated

symbols xm(n)are multiplied either by a chirp sequence s(n)

or by the complex conjugate chirp s∗(n). We use s(n)and

s∗(n)alternating as spreading sequences to enable a robust raw

CFO estimation as presented in section IV-C. As a spreading

sequence, we use a CAZAC sequence, which is also known as

Zadoff-Chu sequence. It has initially been proposed in [29] and

[30]. In [31] it has been shown that its cyclic auto-correlation

function (ACF) Rs,s(k)for arbitrary length Lsof the sequence

is zero for k,0, i.e. it is equal to the delta function. A

CAZAC sequence s(n)of length Lsis denoted as column

vector s=[s(0), ..., s(n), ..., s(Ls−1)]>and is generated by

s(n)=ejπMsn2

Lsfor Lseven, and n=0,1, ..., Ls−1(10)

s(n)=ejπMsn(n+1)

Lsfor Lsodd, and n=0,1, ..., Ls−1.(11)

Here, Lsand Msare two integer numbers that are relatively

prime.

In the next step we introduce pause times between the chirps

by inserting dummy samples into the signal. As the number of

inserted dummy samples is chosen according to a codeword of

the OOC, we refer to this step as OOC-encoding. A transmitted

block contains a pair of chirps per One-Bit in the OOC.

Between the pairs of chirps, we insert one dummy sample per

Zero-Bit in the OOC. Here, we have to ensure that the number

of One-Bits (Ns) within the codeword is sufﬁcient to encode

all Nmtransmit symbols3. As we transmit two chirps for every

One-Bit in the OOC, we need an OOC with Ns≥dNm/2e.

The dummy samples between the correlation sequences are

set to 1 in order to ensure the constant envelope property of

the radio frequency (RF) signal4.

By that we create coded correlation signals that are dis-

tinguishable at the receiver by applying one correlation per

codeword.

Assume that ˜pµ(l)for l=1...Nscontains the indices of all

One-Bits within the µ-th codeword, i.e. ˜pµ(l)is the index of

the l-th One-Bit in cµ(n). Then

zµ,l=˜pµ(l) − ˜pµ(l+1) − 1(12)

gives the numbers of Zero-Bits between two One-Bits within

the codeword of the OOC.

The transmit signal vector xis different for each codeword

µand, thus, denoted by xµ

xµ=[xm(1) · s>,xm(2) · sH,o>(zµ,1),

xm(3) · s>,xm(4) · sH,o>(zµ,2),

... ,

xm(2l−1) · s>,xm(2l) · sH,o>(zµ,l),

... ,

xm(Nm−1) · s>,xm(Nm) · sH,]>

(13)

where o(zµ,l)stands for a vector containing zµ,lOnes. The

construction of the transmit signal according to (13) is also

sketched in Fig. 4 and the upper diagram in Fig. 7 shows

an example for the real-part of a base-band transmit signal

calculated from (13) with Ls=100 and Ms=1.

Every frame contains Nspairs of correlation sequences, i.e.

2·Nsindividual correlation sequences. The number of symbols

after spreading ( Nframe) of the transmitted frame is dependent

upon the chosen OOC as well as upon Lsand is given by

Nframe =2·Ns·Ls+N2

s−Ns(14)

where the ﬁrst part of the sum is the length of all correlation

sequences within one block and the second part is the length

of all pause times according to the OCC. Equation (14) is valid

if the code from [27] is used as described in section III-C.

E. User Separation for Random Multiple Access

The proposed UCSS allows a random multiple access to

the channel due to the unipolar encoding of the used CS,

3In fact the number Nshas to be even larger, because later we insert training

symbols for carrier frequency offset estimation.

4Instead of 1 any other complex value with absolute value equal to 1 would

also fulﬁll the condition for a constant envelope signal.

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 6

xb(n)

data

FEC

encoder

M-DPSK

modulator

xc(n)xm(n)

s(n)

s∗(n)

unipolar (OOC)

encoder

code word for

µ-th user: pµ

DAC +

Tx RF

xs(n)x(n)

Fig. 3. Detailed ﬂow graph of the proposed transmitter

Tx symbols xm(1) · sxm(2) · s∗11 xm(3) · sxm(4) · s∗111 ... xm(Nm−1) · sxm(Nm) · s∗

OOC codeword

for user µ100 1000 1

...

zµ,1zeros zµ, 2zeros

correlation

sequence (CAZAC)

data symbols

ss∗ss∗ss∗

xm(1)xm(2)xm(3)xm(4)xm(Nm−1)xm(Nm)

Fig. 4. Generation of the Tx symbols from data symbols by chirp spread spectrum and unipolar coding

0.2 0.40.60.8 1

·104

2

4

6

8·10−2

CAZAC sequence length Ls

CCF /Ls

max CCF value

mean value over all CCF

cyclic CCF upper bound: √Ls

Fig. 5. Maximum and mean cross-correlation values for all combinations of

two different CAZAC sequences over different sequence length Ls

comparable to a CDMA scheme as described in section III-C.

If the number of existing OOC words is not sufﬁcient to serve

all desired users for a satellite IoT system, we can of course

increase the system capacity by enabling orthogonal multiple

access in the frequency, time or spatial domain. Nevertheless it

is possible to increase the number of user codes by alternating

the used CS and, hence, increase the number of separable users

at the same frequency and in the same timeslot. Because of

this we are able to generate a very large number of codes that

can be assigned to a large number of users. Certainly, if all

users would transmit at the same time, the SINR will be very

low and the user detection is impossible due to interference.

However, we are able to design a system where we can

guarantee random multiple access to a very large number

of users, where only a subset of all users is transmitting at

the same time, given the up-times of the individual users are

limited in time and mutually uncorrelated.

The properties of the used CAZAC sequences as family of

correlation sequences with good cross correlation properties

are investigated in [32] and [33]. Let us denote a single

CAZAC sequence s(n)with length Lsand parameter Msby

s(n,Ls,Ms). Since Lsand Msare integers that have to be

relatively prime, we are able to maximize the number of

CAZAC sequences per family to Ls−1if Lsis prime. It

can be shown that √Lsis an upper limit for the cyclic cross

correlation function (CCF) for any two s(n,Ls,i),s(n,Ls,j)

for i,j. In our case, the CCF at the receiver does not fulﬁll

the requirements for a cyclic CCF as we inserted dummy

samples (Ones) between consecutive sequences. Thus, the

values for the CCF results exceed √Lsand are analyzed in

the following. To analyze all possible CCF results, simulations

have been performed and the results are presented in Fig. 5.

Here, the maximum value and the mean value for the CCF

for all possible combinations of CAZACs with different Ms

are shown over Ls. The ﬁgure reveals that the mean values

of the CCF strictly exceed the upper bound from the cyclic

CCF. Nevertheless, the maximum values are at about 2.3√Ls

which is only a limited degradation of the cross correlation

properties.

Consequently, the families of CAZAC sequences with prime

values for Lsare used here to enlarge the number of orthogonal

sequences. In fact, we can assign Nu,max =(Ls−1) · Nooc

different codes to the users.

This number can be further increased by ﬁnding OOCs with

larger number of codewords Nooc or by using longer CS. If

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 7

we further allow different lengths Lsfor the CS of different

users, we can generate even more codes.

With the methods described so far, we are able to design

a very large number of different combinations of OOC code-

words and CS parameters. We call each combination of the

parameters "user identiﬁcation" (UID) in the following.

The most important beneﬁt of this technology is the re-

duction of the transmitted data. Each user is identiﬁed by its

UID and can be separated at a gateway that is receiving the

signals of several users at the same time. Hence, no ID needs

to be transmitted within the frame which reduces the overhead

and leaves more bits for user data. Furthermore, if every user

has an individual permanent UID, we do not need to assign

orthogonal resource blocks (time slots, spectrum, or spread

codes) to users dynamically. Thus no signaling information

needs to be transmitted and true random multiple access is

enabled.

IV. RECEIVER

A. Coherent and Non-Coherent Correlation

At the receiver side we obtain the digitized receive signal,

which is denoted by r(n). It may contain the superposition

of different individually delayed transmit signals xµ(n). More-

over, we assume an AWGN channel with a given SNR and a

CFO ∆fc.

We assume that the receiver applies a sufﬁciently high

oversampling to enable asynchronous sampling. Nevertheless,

for the ease of notation, we use signals at oversampling factor

1. In the ﬁrst step, the received signal is correlated with s(n)

and s∗(n). The correlation result Rr,s(k)for the CCF of r(n)

and s(n)is given by

Rr,s(k)=

Nmax−1

Õ

n=0

r∗(n) · s(n+k)(15)

where Nmax is the number of recorded samples. The correlation

results Rr,s(k)and Rr,s∗(k)for s(n)and s∗(n), respectively,

are sequences of peaks. For the ease of notation we deﬁne

u1(k):=Rr,s(k)and u2(k):=Rr,s∗(k). As an example the

result for a correlation with s(n)and s∗(n)is depicted in Fig. 7

for Ls=100 in the absence of noise and only one transmitting

user.

The expected locations of the peaks within u1(k)are given

by

˜q1(l)=˜pµ(l)+(l−1) · 2Ls.(16)

Accordingly, ˜q2(l)contains the indices of the expected

correlation peaks in u2(k)

˜q2(l)=˜pµ(l)+(2l−1) · Ls.(17)

To perform the non-coherent correlation, a reference signal

q1(n)is deﬁned by

q1(n)=1if n∈˜q1

0else.(18)

A reference signal q2(n)for the non-coherent correlation of

the complex conjugate signals is deﬁned by

q2(n)=1if n∈˜q2

0else.(19)

The non-coherent correlation is calculated as

Ru1,q1(k)=

Nmax−1

Õ

n=0|u1(n)|·q1(n+k)(20)

where Ru1,q1(k)is the non-coherent correlation result for s.

The non-coherent correlation result Ru2,q2(k)for the complex

conjugate correlation sequences s∗is calculated as

Ru2,q2(k)=

Nmax−1

Õ

n=0|u2(n)|·q2(n+k).(21)

Again, for the ease of notation, we denote v1(k):=Ru1,q1(k)

and v2(k):=Ru2,q2(k)in the following. The calculated outputs

of the correlators are used in the following subsection to detect

the transmitted frames in noise. Examples for the output of the

second correlator are shown in the lower part of Fig. 7

B. Frame Detection

At the receiver the most challenging task is the detection of

the short, narrowband signal in noise, as the signal is expected

to be several 10 dBs below the thermal noise ﬂoor and the

exact CFO is unknown. The proposed UCSS produces one

correlation peak at the output of each of the two non-coherent

correlators that are calculated using equations (20) and (21).

As this correlation is performed twice, we obtain two results

that can be used for the detection of the transmitted signal.

The peaks are sufﬁciently high to detect a signal at any CFO.

The problem at hand is the detection of a peak in noise, which

is described in [34] together with the optimum solution. We

ﬁrst concentrate on the detection of one peak in one of the

correlation results. If the detection is repeated for the second

correlation, the conﬁdence about the presence of a transmitted

signal might be further enhanced.

In the following we derive the probability distribution of the

correlation results v1(k)and v2(k)and determine a criterion

for the detection of a transmitted frame in a noisy receive

signal.

The noise at the receiver contains the thermal noise and

the interference from many other users5and is described by

a complex Gaussian random variable with η=ηQ+jηIand

ηQ, ηI∈ N(0, σ)such that σ2

η=2·σ2.

Let us assume that the constant amplitude of the desired

signal at the receiver is α. We are interested in the peaks within

the ﬁrst correlation result u1(k). In the absence of noise each

peak has the magnitude

eu1(k=kpeak)=˜upeak =α·Ls.(22)

The noise part ˇupeak within the correlation result is the sum

of Lscomplex Gaussian random numbers with power σ2

ˇu=

Ls·σ2

η. Hence, the peak values upeak are given by upeak =

˜upeak +ˇupeak, and the magnitude |upeak |of the peak is a random

number with Ricean distribution [35, pp. 50-52].

The values of the ﬁrst correlation outside the peak positions

u1(k,kpeak)=unoise (23)

5Here, we assume that the sum signal of several different users transmitting

simultaneously is complex Gaussian random variable due to the central limit

theorem.

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 8

˜η(t)

Rx RF +

ADC

r(n)

corr.

corr.

s(n)

s∗(n)

u1(k)

u2(k)

correct

CFO

correct

CFO

non-coh.

correlation

non-coh.

correlation

q1(n)

q2(n)

peak-

detection

peak-

detection

v1(k)

v2(k)

CFO

estimaton

timing

estimation

M-DPSK

demod.

ˆx(n)FEC

decoder

ˆxc(n)ˆxb(n)

Fig. 6. Detailed ﬂow graph of the proposed receiver for the detection of one transmitting user

−1

0

1

R{x(n)}

0

50

100

|u1|

0

50

100

|u2|

0

500

|v1|

100 200 300 400 500 600 700 800 900 1,000

0

500

|v2|

transmit signal (real part):

ﬁrst correlation of rwith s:

ﬁrst correlation of rwith s∗:

second correlation of |u1|with OOC codeword:

second correlation of |u2|with OOC codeword:

Fig. 7. Examples for the transmit signal and correlation results with Ls=100 and Ns=7

are also complex Gaussian random numbers with power

Ls·σ2

η, and their magnitude |unoise |is a random number with

Rayleigh distributed values.

The magnitude of the ﬁrst correlation result is the input of

the second correlator. In the following the result of the second

correlation is presented and analyzed.

The main peak within the result v1(k)of the second corre-

lator is referred to as v1(k=kpeak)=vpeak . Several additional

peaks exist within v1(k)which are neglected for the moment.

The value of vpeak is the sum of Nspeaks |upeak |. We are

interested in the mean value µv,peak and the standard deviation

σv,peak of vpeak. The mean µv,peak is Nstimes the mean value

of |unoise |and is given according to the mean of a Ricean

distributed random number [35, p. 52] by

µv,peak =Ns·µu,peak =

=Ns·σpLsπ

2e−κ/2(1+κ)I0κ

2+κI1κ

2(24)

where µu,peak is the mean value of the peaks in the ﬁrst

correlation result, κ=(α·Ls)2

2σ2is the Rice factor, and Iiis

the modiﬁed Bessel function of the ﬁrst kind and order i. The

variance σ2

v,peak of vpeak is given by

σ2

v,peak =Ns·σ2

u,peak =

Ns·2Lsσ2+(α·Ls)2−µ2

u,peak.(25)

If we assume that the number of chirps Nsis sufﬁciently

large, we can apply the central limit theorem and assume

that vpeak follows a Gaussian distribution. We are then able

to calculate the probability P(vpeak <vth)that vpeak exceeds a

certain threshold vth by

P(vpeak <vth)=Qvth +µv,peak

σv,peak (26)

where Q(·) is the Q-function. The value P(vpeak <vth)is the

probability for not detecting a peak in the second correlation

result with a threshold vth. Hence, Pd=1−P(vpeak <vth)is

the probability that the peak would be detected.

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 9

If the threshold vth is exceeded by noise, a peak is falsely

detected. To evaluate the probability of a false detection, we

analyze the distribution of the second correlation result v1(k)

outside the peak position v1(k,kpeak)=vnoise .

The signal vnoise is dominated by a strong part which results

from noise and also contains secondary peaks dependent upon

the ACF and CCF of the used OOC. It is described by the

mean value µv,noise and the variance σ2

v,noise. The noise part

unoise within the ﬁrst correlation result is zero mean with

variance σ2

u,noise =Ls·σ2

η. Its magnitude |ˇunoise |is a Rayleigh

distributed number with mean value pπ

2σand variance 4−π

2σ2.

Outside the main peak and any secondary peaks, the output

of the second correlation is a sum of Nssignals |unoise |. Hence

the mean value µv,noise and the variance σv,noise of vnoise are

given by

µv,noise =Ns·rσ2Ls

π

2,(27)

σ2

v,noise =Ns·4−π

2σ2Ls.(28)

If the second correlation "collects" one or more peaks of the

ﬁrst correlation, a secondary peak is obtained. The maximum

number of peaks Npeak that are summed up during the second

correlation is given by the parameter λaof the used OOC. In

general the mean and the variance of vnoise are given by

µv,noise(Npeak)=(Ns−Npeak) ·rσ2Ls

π

2+Npeak ·µu,peak,(29)

σ2

v,noise(Npeak)=(Ns−Npeak)· 4−π

2σ2Ls+Npeak ·σ2

u,peak.(30)

Additional secondary peaks due to multiple users transmitting

at the same time will occur in a real transmission. This is

analyzed by simulation in the sequel.

For the calculation of the probability Pfthat the noise

exceeds the threshold vth, which means that a peak is falsely

detected, we use the worst case value for µv,noise(Npeak )and

σv,noise(Npeak). This occurs for Npeak =λa. As we assume that

vnoise follows a Gaussian distribution, we can calculate Pfwith

Pf=P(vnoise >vth)=Qvth −µv,noise(λa)

σv,noise(λa).(31)

Fig. 8 depicts the calculated probability of detection over the

SNR for different values of vth for Ls=1000 and Ns=70. We

use a normalized threshold vth,n that is given by vth,n =vth

√Ls·Ns

for the ease of notation. For the design of a communication

system, a desired value for Pfneeds to be chosen according to

Fig. 8. The value of Pfascertains the required value for vth,n

and further determines Pd. A lower chosen value of Pfleads

to a lower value of Pdfor a given SNR. In other words, the

lower Pf, the higher is the required SNR to achieve a certain

Pd.

Fig. 9 presents results for the required SNR to achieve the

given Pf=10−6and Pd>0.999 for different values of Nsand

Ls. From the ﬁgure, for example, it is revealed that by using

Ns=60 correlation sequences with Ls=100 000 symbols, a

reliable detection at the SNR at the receiver input of −50 dB

is enabled.

−36 −34 −32 −30 −28

0.9999

0.999

0.99

0.9

0

SNR in dB @ Rx input

detecteion probability Pd

Ls=1000,Ns=70

vth,n =1,Pf=0.0467

vth,n =1.05,Pf=0.00787

vth,n =1.1,Pf=0.00081

vth,n =1.15,Pf=5.02e−05

vth,n =1.2,Pf=1.86e−06

vth,n =1.25,Pf=4.07e−08

vth,n =1.3,Pf=5.26e−10

vth,n ↑;Pf↓

Fig. 8. Probability of detection over the signal-to-noise ratio (SNR) for

different threshold levels vth,n and the resulting probability of false detection

Pf;Ls=1000,Ns=70

0 20 40 60 80 100 120 140 160 180 200

-50

-40

-30

-20

number of correlation sequences Ns

SNR for Pf=1e−06 and Pd>0.999

Ls=100

Ls=1000

Ls=10000

Ls=100000

Fig. 9. Required signal-to-noise ratio (SNR) in dB to achieve Pf=10−6

and Pd>0.999 over the number of correlation sequences Nswith different

lengths Ls

C. Carrier Frequency Recovery

For the correct demodulation of the data symbols it is

required to estimate and remove the CFO in the received

signals. Our proposed approach applies an estimation of the

CFO in two steps according to [36]. In a raw estimation the

correlation peak positions within v1(k)and v2(k)are evaluated.

This enables a coarse estimation of high frequency errors.

The ﬁne CFO estimation is based on the evaluation of two

consecutive peaks within u1(k)or u2(k).

The coarse CFO estimation relies on a special property

of the used CAZAC sequences which was ﬁrst introduced

in [37]. The authors show that a frequency shift of the

CAZAC sequence results in a time-shifted version of the

original sequence. We can make use of this property for

CFO estimation, as the location of the main peak within the

correlation result will be a function of the CFO. Unfortunately

we cannot directly measure the time offset due to the absence

of a time reference. Therefore, we also transmit a complex-

conjugate version of the CAZAC and use the fact that the peak

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 10

of the conjugate signal is shifted into the opposite direction.

Hence the distance between the two peaks is a measurable

value that indicates the CFO. In particular, we estimate the

CFO by maximizing the CCF of v1(k)and v2(k)and calculate

the CFO for Ms=1according to6

\

∆fc,raw =

1

2Ls·arg max

k(

Nmax

Õ

n=−Nmax

v1(n) · v2(n+k))(32)

where Nmax is an integer limiting the correlation length to

reasonable values for ∆fc,raw. Here, the CFO is normalized by

the symbol rate fs=1/Tswith

∆fc=∆fHz

c/fs(33)

where ∆fHz

cdenotes the CFO in Hertz and Tsis the symbol

duration.

The lengths Ls,1and Ls,2of the CAZAC sequences de-

termine the resolution of the estimation. The accuracy of

the estimated CFO is limited to 1/max(Ls,1,Ls,2). Thus, the

accuracy increases with increasing Ls.

This estimation method is able to measure very high CFOs.

The upper limit ∆fc,max for the CFO that could be determined

without ambiguity is ∆fc,max=0.5−1/max(Ls,1,Ls,2). This is

almost independent of the length Lsof the CAZAC sequences.

Instead, the upper limit for the CFO in Hertz is determined

by the symbol rate fsof the transmitted CAZAC sequences

given by

∆fHz

c,max=0.5−1

max(Ls,1,Ls,2)·fs.(34)

As the accuracy of this coarse estimation is limited, we add

training symbols to the transmitted data and can obtain an

accurate CFO estimation over a wide range for the frequency

error [36].

D. Symbol Detection and Demodulation

According to equations (16) and (17) we are aware of

the locations ˜q1(l)of the peaks within the ﬁrst correlation

results u1(k)and u2(k). Thus, evaluating u1(k)and u2(k)at

the locations ˜q1(l)and ˜q2(l), respectively delivers the received

symbol vector ˆx(n). After the demodulation of the signal by

the M-DPSK demodulator, the estimated coded bits ˆxc(n)are

handed over to the decoder, which delivers the decoded user

bits ˆxb(n).

V. PERFORMANCE EVALUATION

A. Multiple Access

In section IV-B the detection of signals from single users in

AWGN has been investigated theoretically and the required

SNR has been determined to detect a transmitted frame

with a given probability of detection. If multiple users are

transmitting simultaneously, the interference within the desired

user signal is measured by the SINR deﬁned in (5).

6For Ms>1the shift of peak positions within the correlation result cannot

be calculated from the CFO using equation (32). In that case the CFO is, for

example, calculated using a lookup table.

0 100 200 300 400 500

-30

-25

-20

number of active users Nu

SINR in dB @ Rx input

SNR = ∞

SNR = -20 dB

SNR = -22 dB

SNR = -24 dB

SNR = -26 dB

SNR = -28 dB

SNR = -30 dB

Fig. 10. Signal-to-interference and noise ratio (SINR) over the number of

users transmitting simultaneously for different values of the signal-to-noise

ratio (SNR); Ls=1009,Ns=71

−32 −30 −28 −26 −24 −22

0

0.2

0.4

0.6

0.8

1

SNR in dB @ Rx input

detection probability Pd

Nu=2

Nu=100

Nu=200

Nu=300

Nu=400

Nu=500

−32 −30 −28

0

0.2

0.4

0.6

0.8

1

SINR in dB @ Rx input

Fig. 11. Detection probability Pdover the signal-to-noise ratio (SNR) for

different numbers of users Nutransmitting simultaneously (left); detection

probability Pdover the signal-to-interference and noise ratio (SINR) for

different numbers of users transmitting simultaneously (right)

An analysis of the detection probability in a multiple access

scenario is performed here by Monte Carlo simulations. We

set the number of symbols within a CS to Ls=1009 and used

Ns=71 CS for the transmitted frame. We were then able to

choose one codeword cµfor µ=1...Nooc out of Nooc possible

codewords. Furthermore, we could choose the parameter Ms

for the CS between 1 and Ls−1.

We used the OOC according to [27] and obtain Nooc =

Ns−1different codewords. Thus the maximum number of

distinguishable user codes (UIDs) Nu,max =Nooc · (Ls−1)=

66 528.

From the available user codes we randomly picked Nucode-

words and assigned them to Nuusers transmitting at the same

time. The signals were randomly shifted in time and added to

a sum signal with random, uniformly distributed phase. We

now consider a single user mout of the Nutransmitting users,

and determine the SINR, after adding AWGN at a given SNR

for the m-th user. Fig. 10 shows the results for the SINR over

Nufor different values of the SNR. As expected the SINR

decreases with increased number of transmitting users. If we

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 11

TABLE II

SIMULATION PARAMETERS

parameter value

chirp sequence (CS) length Ls1009 symbols

CSS correlation gain ≈30 dB

nr. of chirp pairs per frame Ns67

nr. of chirps per frame 2·Ns134

modulation 2-DPSK

FEC coding rate 1/2BCH

user bits per frame Nbit 64

frame length Nframe incl. dummy symb. 139 494 symbols

now want to detect a speciﬁc user within the received sum

signal, we need to evaluate the result of the second correlation

as described in section IV-B. The probability Pdof the correct

detection of a transmitted frame has been calculated from the

results of Monte Carlo simulations. We again set Ls=1009

and Ns=71 and the threshold for the detection of the

correlation peak was vth,n =1.3ensuring a false detection

probability Pf≤5.26 ·10−10.

The results for Pdover the SNR for different numbers of

transmitting users Nuare depicted in the left sub-ﬁgure of Fig.

11. The ﬁgure shows that with more users Nutransmitting si-

multaneously, a higher SNR is required to ensure the detection

of an individual user. Hence, for the system design, the link

budget needs to incorporate the self interference from other

users. This is also well known from CDMA. If we consider the

detection performance over the SINR, as depicted in the right

sub-ﬁgure of Fig. 11, we can estimate the detection probability

from the SINR independently of the number of transmitting

users Nu. Thus we are able to predict the number of users

that can be detected at given probability Pdby combining the

results of Fig. 9 and Fig. 10. If we are, for example, using

Ns=71 correlation sequences of length Ls=1009, we can

obtain from Fig. 9 that the required SNR is −28 dB for for

Pf=10−6and Pd>0.999. Assuming that the interference of

a large number of users is a white Gaussian noise signal, than

we can use this information to predict the detection probability

in the noise and interference channel. From Fig. 10 we read

the number of users at SINR of −28 dB and obtain that about

250 users can be detected at an SNR of −26 dB, 400 users can

be detected at an SNR of −24 dB, and more than 500 users

can be detected at an SNR of −22 dB.

It is possible to design a system that is able to detect

a larger number of simultaneously transmitting users, if Ls

is increased. Doing so, the correlation gain is higher and

the detection is possible at lower SNR as shown in Fig. 9.

Hence, UCSS has a large potential to be adapted to different

requirements imposed by the link budget, the data rate, and

the number of users for random multiple access. The biggest

beneﬁt is achieved if the average transmission rate of a single

terminal is low, e.g. only one packet per hour or per day.

In that case we can assign different UIDs to a very large

number of users. As long as the number of users transmitting

simultaneously stays below a speciﬁc limit, we can detect all

users transmitting without collisions.

−28 −26 −24 −22 −20 −18 −16 −14 −12

10−4

10−3

10−2

10−1

100

SNR in dB @ Rx input

FER

Nu=1

Nu=100

Nu=250

Nu=400

Nu=500

Fig. 12. Frame error rate (FER) over the signal-to-noise ratio (SNR) for

different numbers of users transmitting simultaneously; Ls=1009,Ns=67;

2-DPSK with rate 1/2-BCH coding; without fading

−28 −27 −26 −25 −24 −23 −22

10−4

10−3

10−2

10−1

100

SINR in dB @ Rx input

FER

Nu=1

Nu=100

Nu=250

Nu=400

Nu=500

Fig. 13. Frame error rate (FER) over the signal-to-interference and noise

ratio (SINR) for different numbers of users transmitting simultaneously; Ls=

1009,Ns=67; 2-DPSK with rate 1/2-BCH coding; without channel fading

B. Frame Error Rate

In the following a performance analysis is presented based

on simulations of UCSS in a satellite channel with lognormal

fading. The simulation parameters are given in Table II.

If we use these parameters for a system with a link budget

according to the one calculated in section II, and transmit at

a sample rate of fs=10 kHz. Then the resulting SNR will be

−24.4 dB. The entire frame is transmitted within 13.95 s at a

user bit-rate of 4.59 bit/s.

Fig. 12 shows the simulation results for the frame error

rate (FER) over the SNR. Here, the SNR at the receiver

input is considered for a single user before despreading.

Interference from multiple users who transmit simultaneously

is not included in the SNR, rather in the SINR. The simulation

results were produced without channel fading. If the number

of users transmitting simultaneously equals One (Nu=1),

an FER of 1·10−3is achieved at an SNR of −25 dB. Since

more users transmitting at the same time add interference, the

required SNR for the correct detection of a frame is increased,

as derived from the curves in the ﬁgure with Nu>1.

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 12

0 100 200 300 400 500 600

0

100

200

300

400

transmission rate λu

throughput %

SNR=-10dB

SNR=-15dB

SNR=-20dB

SNR=-23dB

SNR=-25dB

Fig. 14. Throughput over the transmission rate; Monte Carlo simulation with

Poisson distributed channel access; Ls=1009,Ns=67; 2-DPSK with rate

1/2-BCH coding; without fading

The results for the FER over the SINR are presented in

Fig. 13 for different numbers Nuof transmitting users Nu. For

Nu=1the SNR equals the SINR and the results match with

those from Fig. 12. Please note that the abscissa of Fig. 12

and Fig. 13 are scaled differently. If only one user is active,

the transmission is limited by the thermal noise, then with

more users transmitting at the same time, the interference

power increases and the transmission gets more and more

interference-limited. It is observed in Fig. 13 that the required

SINR to achieve a given FER is lower for larger numbers

of transmitting users Nu. This means that with interference-

limited transmission, the proposed modulation scheme per-

forms better than for the noise-limited cases due to the used

orthogonal CAZAC sequences.

The results show that we are able to receive, demodulate

and decode frames at very low SNR in a random multiple

access scheme. The operating SNR can further be reduced if

the correlation gain is increased by choosing higher values for

Ls. The performance over the SNR for a given Lsmight be

enhanced by the application of a different FEC code7.

C. System Throughput

If UCSS is applied to a MTC system with numerous devices,

the throughput of the entire system is of interest. Generally, the

channel access behavior of the users is modeled by a Poisson

distributed random number [14].

The Poisson distribution gives the probability P(i, λs)that

an event occurs itimes in a given time interval, where λsis

the mean number of events. The probability P(i, λs)is given

by

P(i, λs)=λi

s

i!e−λs;i=0,1,2, ..., ∞.(35)

We deﬁne the mean number λuof users starting their trans-

mission during a time interval tframe that is equal to the length

7During our analysis we applied LDPC codes, polar codes, and BCH codes,

which all showed similar performance for the very short block length used

here. Nevertheless, the optimization of the FEC may provide a small gain in

performance, but is not in focus of this paper.

of one frame. Here a frame consists of Nframe transmitted

symbols. If we run a simulation with sampled baseband signals

at oversampling factor νin discrete time, we need to calculate

the probability that a new user starts its transmission at a given

discrete time bin. It is given by (35) using

λs=λu

Nframe ·ν.(36)

We refer to λuas transmission rate in the following. The

throughput of the system is measured by the number of

successfully detected and error free transmitted frames within

a time interval. We deﬁne the throughput %as the number of

transmitted frames within tframe. Thus, %=λuindicates that no

frame has been lost. The number of erroneous or lost frames

is used to calculate the frame loss ratio (FLR).

We performed Monte Carlo simulations modeling the user

activity according to a Poisson distribution with transmission

rate λu. The parameters used for the simulation were also

taken from Table II as already introduced in the previous

subsection. Fig. 14 presents the results for the throughput %

over the transmission rate λufor different values of the SNR

in the absence of fading. The ﬁgure, for example, shows that

at SNR =−20 dB, the transmission is possible with low FLR

almost at a rate λu=300.

The throughput is reduced, if individual fading is added

to the transmitted frames as derived from Fig. 15, where the

throughput is presented for different values of the Lognormal

fading. The same simulation results are presented in a different

way in Fig. 16, which shows the results for the FLR over

the transmission rate for a ﬁxed SNR of −20 dB for different

values of σch. For transmission rates λu<450 and with

increasing values of σch, the throughput decreases and the

FLR increases. This behavior is due to the fading of user

signals, which are received with lower power and the increased

interference from signals with higher power. At the same time,

the fading process also increases the power of a portion of user

signals. These signals are detected correctly even at higher

transmission rates λu>450.

In the literature it has been shown that unequal receive

powers of superimposed signals from different users in a mul-

tiple access scenario enhance the performance of interference

cancellation approaches [15]. If the proposed UCSS is applied

to the return link of a satellite network, where many users

transmit towards a common gateway, then interference cancel-

lation methods like SIC or iterative interference cancellation

(IIC) could be applied. In that case, the achieved throughput

of the entire system is increased considerably.

D. Practical Veriﬁcation

The feasibility of ultra-low-rate communication with UCSS

has been demonstrated by an over-the-air (OTA) demon-

stration. Therefore, we implemented the waveform into a

software deﬁned radio (SDR) based testbed. We transmitted 64

bits within blocks using DBPSK modulated chirps of length

Ls=1009 and a rate 1/2 BCH code as FEC. The symbol rate

after spreading has been set to 12.5 kHz, which corresponds

to a user bit rate of 5.7 bit/s. As transmitter we used an

Ettus B205 USRP SDR and a standard block upconverter

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 13

0 100 200 300 400 500 600

0

100

200

300

transmission rate λu

throughput %

σch = 0 dB

σch = 1 dB

σch = 2 dB

σch = 3 dB

Fig. 15. Throughput over the transmission rate at mean SNR for each user of

−20 dB for different values for the standard deviation σch of the lognormal

fading process; Monte Carlo simulation with Poisson distributed channel

access; Ls=1009,Ns=67; 2-DPSK with rate 1/2-BCH coding

100 200 300 400 500 600

10−2

10−1

100

transmission rate λu

frame loss rate (FLR)

σch = 0 dB

σch = 1 dB

σch = 2 dB

σch = 3 dB

Fig. 16. FLR over the transmission rate at mean SNR for each user of −20 dB

for different values for the standard deviation σch of the lognormal fading

process

(BUC) to shift the signal to the carrier frequency of 8 GHz.

A rectangular patch with dimensions 18.7 mm ×14.7 mm as

depicted in Fig. 17 served as transmit antenna. The signal has

been received by a transparent bent-pipe GEO satellite and

relayed towards the ground station antenna of the Munich

Center for Space Communications in Neubiberg, Germany.

The signal has been received by a 4.9 m dish antenna, down-

converted and sampled by an Ettus B210 SDR. After the

receive-signal processing, which includes detection, clock and

frequency recovery, demodulation and decoding, we evaluate

the transmitted information bits. From the received signal we

further estimate the SNR from the correlation peak vpeak by

S

N=

vpeak

(Ls·Ns)2·σ2

η

.(37)

Here, we assume that the signal part within the received signal

r(n), which is at least 20 dB below the noise ﬂoor, is negligible

against the noise part. We are then able to calculate the noise

power σ2

ηby

σ2

η=En|r(n)|2o.(38)

Fig. 17. SDR based hardware demonstrator used as transmitter for the

practical veriﬁcation with X-band patch antenna

TABLE III

TES T RES ULTS

SNR in dB transmitted Nr. of error

(measured) blocks free blocks

<-24 2634 961

-24 1874 1633

-23 1995 1942

-22 2136 2125

-21 1652 1651

-20 1132 1132

>-20 1353 1353

From the received data we evaluated all blocks transmitted

during a total time of 48 h with clear sky conditions. We varied

the transmit EIRP between −15 dBW and −5 dBW to achieve

a certain statistic for the SNR values at the receiver. The

measured values for the SNR were rounded to integers to allow

a compact presentation of the results in table III. The table

shows the number of transmitted data blocks and the number

of blocks that have been received without error for a given

SNR at the receiver input. The results provide evidence for the

successful data transmission from a low-power terminal with

very compact antenna via a satellite in the GEO. However, we

recall that the presented results are a ﬁrst feasibility test of the

waveform. No optimization of the transmission system or the

user antenna has been performed so far. This is left for future

work.

VI. COMPARISON TO RELATE D WORK

In this section, the proposed transmission scheme is com-

pared to existing, related work. It is important to note that none

of the MTC waveforms available in the literature is speciﬁed

for rates as low as required for the access to GEO satellites

at higher frequency bands. Of course, it is possible to adopt

the signaling parameters to reduce the symbol rate of existing

waveforms. But this does not imply that the synchronization

of the receiver can be achieved and maintained for a reliable

communication with small devices. In the following section,

we will analyze the main drawbacks of adopting existing

waveforms for ultra low-rate mMTC.

For low-rate MTC via satellite, SCADA systems applying

SCMA or IDMA as physical layer technology are an existing

solution for direct access to GEO satellites. However, they

close the link to the GEO only at lower frequencies bands,

where the available spectrum is not sufﬁcient for massive

MTC.

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 14

Among the elaborated LPWAN schemes available for terres-

trial communication [38], we have chosen LoRa to benchmark

our results. LoRa is a patented wireless communication tech-

nology with proprietary physical layer protocol [12], [39]. Like

the proposed UCSS, LoRa also applies CSS for the modulation

and enables communication at very low rate for terrestrial

services.

A. Correlation Gain in the Presence of Phase Noise

As derived in section I, the most challenging task in

conjunction with the envisaged GEO link is the acquisition

of the signal in noise. The link budget calculated in section

II provides us with a S

N0=15.6 dB/Hz, which is very

low and enables communication with positive SNR only in

a bandwidth of a few Hertz. In practice this is not feasible, as

the implemented oscillator’s phase noise will shift the signal

away from its center frequency and outside of the matched

ﬁlter at the receiver. For this reason, most of the LPWAN

protocols apply spreading. After spreading, the signal occupies

a larger bandwidth. The despreading at the receiver makes use

of the correlation gain in order to detect the signal. In the

absence of phase noise, the correlation gain is theoretically

not limited, while for practical systems, the phase noise limits

the correlation gain, and therefore limits the maximum time

for coherent correlation.

Here, for the analysis of the achievable correlation gain, we

use a phase noise model taken from [40], where the noisy

signal8r(n)is calculated from the noise-free signal x(n)by

r(n)=x(n) · ejπφ(n).(39)

According to [40], the phase noise φ(n)is a sum of three

independent noise processes:

φ(n)=φ1(n)+φ2(n)+φ3(n)(40)

Each of the three phase noise contributions is modeled with

following variances

σ2

PN =σ2

PN,1 =100 ·σ2

PN,2 =10 ·σ2

PN,3.(41)

The model was applied and Monte Carlo simulations were

performed for different values of σ2

PN. The results presented

in Fig. 18 show the reduced correlation gain with increasing

phase noise. For UCSS we applied a coherent correlation over

chirp sequences with length Ls=1009 and an incoherent

correlation over Ns=67 sequences. A similar correlation

gain is achieved using a single chirp with length Ls=70 000

symbols. It is derived from the ﬁgure that with increasing

phase noise, UCSS gains about 5 dB correlation gain over

conventional chirp correlation.

Further we applied a BPSK modulated pseudo random

number (PRN)-sequence as used by SCMA and IDMA with

Ls=70 000 symbols as preamble. As indicated in Fig. 18,

the PRN-sequence loses another 4 dB compared to the chirp.

To conclude, the results demonstrate that UCSS is superior to

conventional techniques for signal acquisition in the presence

8Here, we concentrate on the effects of phase noise and omit any other

noise, such as thermal noise or interference.

10−810−710−610−510−4

40

45

50

phase noise variance σ2

PN

correlation gain in dB

UCSS

Chirp

PRN Code

Fig. 18. Correlation gain over the variance of the modeled phase noise process

of phase noise. The link to GEO satellites considered here

requires a comparably long time for signal acquisition, where

the phase noise is a limiting parameter.

B. Overhead for Acquisition, Synchronization, User Separa-

tion

In many modern communication systems the signal acqui-

sition is achieved by a preamble. The length of the preamble

must be sufﬁcient to enable its detection in noise. It is a

design parameter, which is usually kept as low as possible

to minimize the overhead. With communications at ultra low

rate, the length of the preamble becomes a considerable time

span. To provide an example we consider the optimal detection

of a signal in Gaussian noise by the Newman-Pearson-Test

as derived in [34, Sec. 7.2]. From the calculations there, we

can derive the required energy of a signal over the noise

power density E

N0for given probabilities of detection Pdand

false alarm Pf. For example, an E

N0>15.05 dB is required

for Pf=10−6and Pd>0.999. Thus, the length of the

preamble is approximately 1 second if a link budget with S

N0

=15.6 dB/Hz is assumed as calculated in section II. Not only

that this is a very long time, which is not available for data

transmission, it is furthermore most likely that the stability of

the applied oscillators does not allow such a long coherent

integration.

To overcome this issue, we designed UCSS in a way to use

every transmitted chirp for acquisition and data transmission

at the same time. In particular, the amplitude of the chirps

contributes to the acquisition, while the data is modulated onto

the chip phases. By introducing short pause times according to

the OOC, we are able to even improve the acquisition and are

able to separate and identify different users transmitting at the

same time. The non-coherent integration of the chirps enables

acquisition even with unstable oscillators. In Fig. 19 the signal

structure of UCSS is sketched and the chirps containing user

data are in white color labeled with "D". The signal parts

colored in gray indicate the overhead, which consists of the

pause times and the dummy chirps for CFO estimation. The

IEEE INTERNET OF THINGS JOURNAL, VOL. XX, 20XX 15

legend: overhead data

UCSS (proposed)

C C D D D D D D D D D D D D D D D ...

LoRa CSS

CCCCCCCCCCCC DDDDDD...

preamble based (SCMA/IDMA)

preamble data ...

Fig. 19. Packet structure of different technologies for low-rate communication

with highlighted overhead

exact overhead is dependent upon the applied OOC and the

length Ls.

In comparison, for acquisition and synchronization, LoRa

uses 12.25 chirps as preamble, which wastes transmission time

and energy. Furthermore, as the preamble is the same for all

users, the information about the transmitters ID has to be sent

in the data part.

SCMA and IDMA either apply a unique word (UW) [11]

or a chirp sequence [41] as preamble. Different UWs or chirps

are used for the signals of different users to enable a separation

within the sum signal at the receiver. Here the preamble

enables acquisition, synchronization and user separation, but

still uses a considerable part of transmission time and energy,

which becomes unavailable for data transmission.

To give an example, we calculated the communication

overhead of Lora, SCMA and UCSS in comparison and

present the results9in Fig. 20. Here, we assume Ls=1000 and

choose Ns=67 accordingly to support the desired number of

transmitted bits per block. The code rate is 1/2 for all schemes.

For Lora modulation, we set the spreading factor to 13, which

requires similar SNR as UCSS with Ls=1000. For SCMA we

used a preamble length of 1 s. In that case, the probabilities

of detection of SCMA and UCSS are comparable. For the

data part of SCMA we assume a successful transmission at an

Eb/N0of 3 dB and calculated the corresponding length of the

data part at S

N0=15.6 dB/Hz.

As expected from intuition, the ﬁgure reveals that the

percentage of overhead of Lora and SCMA decreases with the

block length. The overhead of UCSS increases for larger sizes

of the blocks, as longer pause times between the chirps are

necessary for the OOC. Hence, UCSS requires less overhead

compared to preamble based schemes for short block lengths

and is outperformed with increasing lengths of the blocks.

In our example UCSS is outperformed by SCMA, if blocks

are carrying more than 190 transmitted user data bits. This is

well in line with our intention to create a waveform for ultra-

low rate and very short messages to be relayed over a GEO

satellite.

VII. CONCLUSION

In this work we presented a novel Unipolar Coded Chirp-

Spread Spectrum (UCSS) modulation scheme to enable the

9Please note that the results for LoRa and SCMA only present the calculated

overhead for the signal acquisition with the link budget provided in section II.

It has not been analyzed if the communication using these modulation formats

at ultra low rate is feasible at all.

0 100 200 300 400 500

0

20

40

60

80

number of user bits per block

overhead in %

UCSS

LoRa

SCMA

Fig. 20. Overhead for acquisition and synchronization in percent over the

number of user bits transmitted per block

direct access of small devices to satellites in the geostationary

earth orbit (GEO) for ultra narrowband (uNB) communica-

tions. The chirp-spreading of the information symbols allows

the instantaneous acquisition and detection of the signal at the

receiver even at unknown larger carrier frequency offsets. After

despreading, we combine the results non-coherently to gain a

sufﬁciently high SNR for the correct detection of transmitted

frames in presence of noise, since a coherent correlation over

longer periods of time fails due to oscillator instabilities. By

further inserting short pauses between the transmitted bits, we

shape a kind of unipolar coding and enable a random multiple

access of many transmitters using different code sequences or

different chirps. With a very large number of such individual

signal properties, we can assign one signal property to only

one user/device and are able to determine the transmitting

user without wasting information bits for the assignment of

a user identiﬁcation. UCSS has been analyzed by exhaustive

simulations on system and link level. An over-the-air test

successfully veriﬁed the ability of UCSS to transmit data with

a very compact antenna via a satellite already existing in the

GEO.

The proposed UCSS is able to transmit a small number of

bits within a frame and achieves acquisition and synchroniza-

tion without any preamble or header. It enables random mul-

tiple access for a very large number of devices transmitting at

only a low percentage of time without any signaling channel or

any medium access control entity. By this the communication

overhead is reduced dramatically, making UCSS a very power

efﬁcient modulation. Thus, UCSS is ideal for applications with

small amounts of transmitted data like small sensors, GPS

trackers or emergency pagers.

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