Transceiver design for MIMO wireless systems incorporating hybrid ARQ
ABSTRACT Hybrid ARQ, an extension of ARQ that incorporates forward error correction coding, is a retransmission scheme employed in current communications systems. The use of HARQ can contribute to efficient utilization of the available resources and the provision of reliable services in latest-generation systems. This article focuses on wireless systems using HARQ with emphasis on the multiple-input multiple-output paradigm. MIMO-HARQ offers new opportunities because of the additional degrees of freedom introduced by the multiple antennas at the transmitter and receiver. The architecture of MIMO transceivers that are based on bit-interleaved coded modulation and employ HARQ is described. Additionally, receiver implementations are presented and compared in terms of complexity, memory requirements, and performance.
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ABSTRACT: Truncated Type-I and Type-II HARQ schemes are compared, in terms of throughput, when incremental decode and forward relaying is used. The comparison is based on the outage analysis of both schemes. Two different scenarios are considered: ad-hoc relaying, where all users are at ground level, and infra-structured relaying, where the relay and the destination antennas are at a higher height than the user. Moreover, we also consider the effect of rate adaptation. Results show that Type-II (incremental redundancy) only significantly outperforms Type-I schemes (selection and Chase combining) in the case of ad-hoc relaying without rate adaptation, and in the low SNR region.Proceedings of the 73rd IEEE Vehicular Technology Conference, VTC Spring 2011, 15-18 May 2011, Budapest, Hungary; 01/2011 -
Conference Paper: Performance of a Partial Retransmissions Hybrid ARQ Scheme in Rayleigh Block Fading Channels.
Andre Gustavo Degraf Uchoa, Richard Demo Souza, Glauber Gomes de Oliveira Brante, Marcelo Eduardo Pellenz[Show abstract] [Hide abstract]
ABSTRACT: In [14], the authors study the performance of HARQ in Rayleigh block-fading channels by means of the outage probability. They consider a block-fading channel where the channel remains constant over a block but varies independently from one block to another, and that a codeword spans over F channel blocks. The general findings are that systems using HARQ achieve a significant improvement in terms of throughput with respect to systems not using HARQ. Moreover, they have shown that IR outperforms CC in that scenario. In this paper we propose a partial retransmission (PR) scheme to be used in non-ergodic block fading channels. In the proposed method, when a retransmission is requested by the destination, the transmitter sends only a fraction of the original codeword. If the channel can be characterized by having F independent blocks per transmission, then the original codeword is also divided into F fractions for the retransmissions. An appropriate power compensation scheme is applied to the partial retransmissions, so that the energy consumed per transmission is constant. The received subpackets are also symbol by symbol combined to the previous received ones. We characterize the performance of the proposed scheme by means of the outage probability and the throughput. The performance is compared to that of IR and CC, showing that the proposed method is able to outperform both schemes. Moreover, we also show that such gains do not come at the expense of an additional energy consumption. The rest of this paper is organized as follows. Section II introduces the system model and the proposed method. In Section III, we analyze the outage probabilities of the proposed scheme and the IR and CC HARQ methods. In Section IV, we compare the throughput of the HARQ methods, based on their outage probabilities, while in Section V we analyze the energy consumption. Finally, Section VI concludes the paper.Proceedings of the 73rd IEEE Vehicular Technology Conference, VTC Spring 2011, 15-18 May 2011, Budapest, Hungary; 01/2011 - [Show abstract] [Hide abstract]
ABSTRACT: In next generation wireless networks, high data rates under strict quality of service (QoS) constraints call for fl exible radio interfaces capable of adapting their configuration on the fly to the time-varying operating environment. Motivated by this need, this paper first derives a simple link performance pred iction model for bit interleaved coded orthogonal frequency division multiplexing (BIC-OFDM) systems using incremental redundancy (IR) hybrid automatic repeat request (HARQ) mechanisms. Then, an adaptive HARQ strategy is formulated whose aim is maximizing the goodput (GP) metric, i.e., the number of error-free information bits delivered to the user by unit of time, over the coding rate, the bit distribution and an on-off power allocation across the active subchannels. Simulation results corroborate the GP performance gains of the proposed approach compared with non-adaptive trans- missions, while keeping the computational complexity at affordable levels.01/2011;
Page 1
INTRODUCTION
Automatic repeat request (ARQ) protocols are
used to improve the reliability of communica-
tions networks. In systems employing ARQ, the
receiver asks for retransmission of packets that
are corrupted. Because only error detection is
required to determine whether a packet should
be accepted, the coding overhead is small, and
the system throughput is not considerably affect-
ed, especially when the channel quality is good.
However, when the channel deteriorates, the
retransmissions may result in significant through-
put loss. A possible remedy is to use an error
correcting code separate from ARQ in order to
provide a more reliable channel, but this also
reduces the throughput of the system. Instead of
following this layered approach, hybrid ARQ
(HARQ) systems attempt to reap the benefits of
both ARQ and forward error correction (FEC)
by combining the two schemes [1]. The HARQ
receiver handles error detection and correction
as well as retransmission requests simultaneous-
ly. A retransmission is requested only when the
receiver detects an uncorrectable error. More-
over, the packets are kept at the receiver to be
used again for decoding after each retransmis-
sion. By combining error correction and retrans-
mission, and appropriately choosing an FEC
scheme whose aim is to correct the most fre-
quent errors, HARQ can achieve better through-
put performance than ARQ for a given channel.
Because HARQ can contribute to more efficient
use of the available resources, it has been includ-
ed in latest-generation wireless systems such as
IEEE 802.16e [2] and 3GPP-LTE [3].
The simplest HARQ scheme, called Chase
(or code) combining HARQ (CC-HARQ) or
type I HARQ, consists of retransmitting the
same symbol sequence repeatedly until the
receiver decodes the packet successfully. More
sophisticated incremental redundancy (IR-)
HARQ schemes (Type II/III) transmit different
symbol sequences in general. The difference
emanates from employing different coding
schemes for the same data, using different cod-
ing polynomials, or modulating different subsets
of the encoder output. The focus of this article is
the use of HARQ in latest-generation wireless
systems that employ bit-interleaved coded modu-
lation (BICM). The architecture of BICM-based
wireless systems employing HARQ is described
by considering a special case of IR-HARQ as an
example, where a different subset of bits of a
mother code is sent during each transmission.
Because IR-HARQ can benefit from a coding
gain, it generally performs better than CC-
HARQ for optimal receiver implementations.
However, suboptimal practical implementations
may affect the performance of IR-HARQ, espe-
cially in multiple-input multiple-output (MIMO)
systems. On the other hand, when CC-HARQ is
used, data are only coded once at the transmit-
ter. Moreover, it is possible to reduce complexity
and memory by combining received symbols, as
explained in more detail in the following. Hence,
for systems that cannot afford large complexity
and storage requirements, it may be preferable
to use CC-HARQ instead of IR-HARQ.
Arguably, the most important recent physical
layer enhancement of wireless systems is the use
IEEE Communications Magazine • January 2009
32
0163-6804/09/$25.00 © 2009 IEEE
ABSTRACT
Hybrid ARQ, an extension of ARQ that incor-
porates forward error correction coding, is a
retransmission scheme employed in current com-
munications systems. The use of HARQ can
contribute to efficient utilization of the available
resources and the provision of reliable services
in latest-generation systems. This article focuses
on wireless systems using HARQ with emphasis
on the multiple-input multiple-output paradigm.
MIMO-HARQ offers new opportunities because
of the additional degrees of freedom introduced
by the multiple antennas at the transmitter and
receiver. The architecture of MIMO transceivers
that are based on bit-interleaved coded modula-
tion and employ HARQ is described. Addition-
ally, receiver implementations are presented and
compared in terms of complexity, memory
requirements, and performance.
ADVANCES IN SIGNAL PROCESSING FOR
COMMUNICATIONS
Jungwon Lee and Hui-Ling Lou, Marvell Semiconductor
Dimitris Toumpakaris, University of Patras
Edward W. Jang and John M. Cioffi, Stanford University
Transceiver Design for MIMO Wireless
Systems Incorporating Hybrid ARQ
Page 2
IEEE Communications Magazine • January 2009
33
of MIMO transmission. Multiple antennas pro-
vide additional degrees of freedom, leading to
significant capacity increase. Multiple antennas
can also be used to provide beamforming gains
and reduce the outage probability. Therefore, it
is of particular interest to examine how HARQ
can be incorporated into MIMO transceivers
and its impact on the system performance, com-
plexity, and storage requirements. The perfor-
mance of MIMO-HARQ depends not only on
noise and temporal channel variations that affect
SISO-HARQ as well, but also on the interfer-
ence between the signals transmitted by the mul-
tiple antennas. As described later in this article,
in some cases the design involves a trade-off
between system performance and receiver com-
plexity and memory requirements. Simplifying
the receiver of a MIMO-HARQ system to
reduce storage and complexity may increase sen-
sitivity to interstream interference.
Not only can HARQ be viewed as a retrans-
mission technique that exploits time diversity; it
can also be used in the context of systems that
employ macrodiversity. If a mobile station com-
municates with two or more base stations that
can exchange information, the system can com-
bine the signals of the base stations before
decoding using the same techniques as for
HARQ. In that case, the HARQ receiver stor-
age requirements translate to requirements on
the necessary bandwidth for the communication
between the base stations. Therefore, results
derived for HARQ can be applied to such sys-
tems, which may become increasingly common
in the future.
This article is organized as follows. In the
next section the architecture of a single-input
single-output (SISO) transceiver using BICM
and HARQ is presented. The MIMO case is
then considered with different receiver imple-
mentations. The following section contains some
discussion of MIMO system design based on the
employed HARQ scheme, receiver complexity,
and storage requirements. Finally, some con-
cluding remarks are provided.
SISO-HARQ SYSTEMS
EMPLOYING BICM
Figure 1 depicts the transmitter of a MIMO sys-
tem employing BICM and HARQ. In a typical
SISO system the architecture of Fig. 1a can be
employed, with the difference that the last block,
which maps symbols to different antennas, is not
necessary because the system only uses one
antenna. A bit sequence d = [d[0], d[1], …, d[L
– 1]] of length L is encoded using a rate r moth-
er code to produce the encoded bit sequence c
= [c[0], c[1], …, c[L/r – 1]]. For example, in
IEEE 802.16e-compliant systems, a rate-1/3 con-
volutional turbo code (CTC) can be employed
[2]. For each block of L bits, 3L bits are pro-
duced. The first L (systematic) bits are the origi-
nal input bits. The encoder block also contains
the interleaving operations, if any. A subset of
the mother code bits is selected for transmission.
When CC-HARQ is used, the bit selection mod-
ule always outputs the same sequence. For IR-
HARQ, the indices of the selected bits depend
on the transmission index. An example of IR-
HARQ bit selection for IEEE 802.16 systems is
given in Fig. 2. Although the CTC case is exam-
ined in the figure, the bit selection is similar
when convolutional coding, block turbo coding,
or LDPC codes are used. In Fig. 2a, 2L bits are
sent during each transmission. During the first
transmission, b(0)= [c[0], c[1], …, c[2L – 1]] =
[d[0], d[1], …, d[L – 1], cL, c[L + 1], …, c[2L –
1]]. During the second transmission, b(1)=
[c[2L], c[2L + 1], …, c[3L – 1], c[0], c[1], …, c[L
– 1]] = [c[2L], c[2L + 1], …, c[3L – 1], d[0],
d[1], …, d[L – 1]], where the fact that the first L
bits of the CTC are the systematic bits is used.
I Figure 1. Transmitter architectures for MIMO systems employing BICM and
HARQ. For SISO systems, the blocks mapping symbols to antennas are not
used.
_ x(i)
Symbols-to-
antennas
mapping
s(i)
Bits-to-
symbols
mapping
b(i)
Encoder
(a) MIMO-HARQ transmitter
d
Bit
selection
c
_ x(i)
Symbol
vector
selection
_ x‘
Symbols-to-
antennas
mapping
s‘
Encoder
(b) MIMO-HARQ transmitter employing symbol vector selection
d
Bits-to-
symbols
mapping
c
I Figure 2. Examples of bit selection for IR-HARQ transmission.
d
Data bits
L
c
Data bits
L
Parity bits 1
L
b(0)
Data bits
L
Data bits
LL/5
Parity bits 1
L
b(1)
Parity bits 2
L
Parity bits 1
Parity
bits 2
4L/52L/5
Data bits
L
b(2)
Data bits
L
(a) Rate-1/2 output(b) Rate-5/6 output
Parity
bits 2
Data bits
3L/53L/5
•
•
•
•
•
•
Parity bits 1
L
Parity bits 2
L
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IEEE Communications Magazine • January 2009
34
Therefore, the systematic bits are included in
both transmissions, whereas different parity bits
are sent during the odd and even transmissions.
In Fig. 2b, 6L/5 bits are sent during each trans-
mission. The second transmission only contains
parity bits, whereas during the third transmis-
sion, only the first 3L/5 systematic bits are sent.
The second rate-5/6 scheme is more susceptible
to errors, but requires fewer resources, because
fewer bits need to be sent during each transmis-
sion. b(i)is then sent to a bits-to-symbols map-
per. Typical modulation schemes are binary
phase shift keying (BPSK), quaternary PSK
(QPSK), 16-quadrature amplitude modulation
(QAM), and 64-QAM. The symbol sequence s(i)
= [s(i)[0], s(i)[1], …, s(i)[M]] is then sent to the
channel using single- or multicarrier schemes.
Both IEEE 802.16e and 3GPP-LTE rely on mul-
ticarrier transmission. The length M of the sym-
bol sequence depends on the modulation scheme
and is equal to the length of b(i)divided by the
number of bits mapped to each symbol s(i)[m].
As mentioned previously, in general, the bit
sequence d may be re-encoded at each transmis-
sion i. For example, in [4] the re-encoded bit
sequence results in a sequence c(i). By appropri-
ate design of the coded sequence c(i)and the bit
selection process, the coding gain of IR-HARQ
can be improved. Code design that also exploits
the MIMO channel to improve the performance
of HARQ is an active area of research [5].
Although IR-HARQ code design is a very inter-
esting topic per se, this article attempts to
address the implementation of a transceiver for
HARQ and the design trade-offs from a generic
point of view. Clearly, the exact performance
and complexity trade-offs will depend on the
details of the HARQ scheme employed. The
specific IEEE 802.16e IR-HARQ scheme
assumed in the remainder of the article merely
serves as an example and to facilitate the discus-
sion of the transceiver architectures.
Figure 3a presents a receiver for the HARQ
system of Fig. 1a. Flat fading is considered, and
the effect of the channel can be modeled as mul-
tiplication with a complex number. Therefore,
I Figure 3. Receiver architectures for MIMO systems employing BICM and HARQ.
^d
+
LLRs
γnt(i)
+
LLR
calculator
x^nt(i)wnt(i)
D
D
γ1(i)
+
LLR
calculator
x^1(i)w1(i)
γ0(i)
LLR
calculator
x^nt
LLR
calculator
•
•
•
x^1
ML detector and
LLR calculator
Channel
estimates H(i)
Decoder
Symbol
combining
LLRs
^
d
^
d
^
d
^
d
^
d
ML detector and
LLR calculator
Channel
estimates H(i)
(a) MIMO-HARQ receiver (d) Pre-equalization symbol-level combining MIMO-HARQ receiver
(b) Symbol-level combining MIMO-HARQ receiver (e) Post-equalization symbol combining MIMO-HARQ receiver
(c) Bit-level combining MIMO-HARQ receiver (f) Bit-level combining MIMO-HARQ receiver employing equalization
_ y(0)
_ y(1)
•
•
•
•
•
•
•
•
•
x^nt(i)
•
•
•
•
•
•
_ y(i)
LLR
calculator
x^0
Channel
combining
MIMO
equalizer
MIMO
equalizer
MIMO
decoder
Decoder
H(i)
_ y(i)
+
D
D
LLR
calculator
x^0(i)w0(i)
H(i)
MIMO
equalizer
H(i)
_ y(i)
_ _ y
~
H
~
Symbol
combining
_ y(i)
Channel
combining
Decoder
LLRs
_ y
~[m]=Σ
i H(i)*[m]_ y(i)[m]
~
H[m]=Σ
i H(i)*[m]H(i)[m]
MIMO
equalizer
H(i)
Decoder
Decoder
_ y(i)
_ _
~y
H
~
_ y(N)
LLR
calculator
LLR
calculator
LLR
accumulation
x^1(i)
LLR
calculator
x^0(i)
•
•
•
Page 4
IEEE Communications Magazine • January 2009
35
the only difference with from MIMO case shown
in the figure is that for SISO-HARQ, the com-
plex matrix H(i)[m], where m is the symbol index,
comprises only one complex element, h(i)[m].
For OFDM systems, h(i)[m] equals the frequency
response of the subcarrier through which symbol
m is transmitted. A maximum likelihood (ML)
detector uses all channel outputs y(i)= [y(i)[0],
y(i)[1], …, y(i)[M]] corresponding to different
transmissions i, together with the channel esti-
mates h(i)= [h(i)[0], h(i)[1], …, h(i)[M]] to calcu-
late the log-likelihood ratio (LLR) for each bit
of the mother code c. Therefore, the detector
also incorporates knowledge of the employed
code, the bit selection pattern, and the bit-to-
symbol mapping. For example, in Fig. 2a, after
the first transmission, the LLRs of the first 2L
bits of the mother code are calculated, whereas
the LLRs for the remaining L bits are set to
zero. The LLRs are then sent to the decoder
that produces an estimate dˆfor the original bit
sequence d. If the receiver determines that dˆis
corrupted, a second transmission is requested.
The decision may be based on parity bits includ-
ed in d, such as a cyclic redundancy check (CRC)
code, or metrics obtained while decoding. After
the second transmission, both y(0)and y(1)are
used, together with the channel estimates h(0)
and h(1), to yield LLRs for all the bits of the
mother code. The LLRs for the systematic bits
are more reliable after the second transmission,
because new information has been received.
Decoding proceeds with LLRs for all bits of the
mother code. If the decoded sequence dˆis still
found to be corrupted, a third transmission is
requested, and so on. The standard retransmis-
sion strategies of ARQ, such as stop-and-wait,
go-back-N, and selective-repeat, can also be used
for HARQ.
As the number of transmissions grows, the
ML detector and LLR calculator block becomes
increasingly complex. The block has to be
designed for the maximum allowed number of
transmissions, N. The required memory is also
an issue, because all received symbols and chan-
nel estimates need to be stored until decoding
succeeds or the maximum number of transmis-
sions is reached. As explained below, when CC-
HARQ is used, the design of the receiver can be
simplified and the required memory reduced
without affecting performance. Receiver simplifi-
cation can also be achieved for IR-HARQ by
controlling the bit selection scheme at the trans-
mitter.
When CC-HARQ is employed, the same bit
sequence b is produced during all transmissions.
Therefore, the symbol sequence s(i)sent to the
channel does not depend on i. It can be shown
that instead of feeding directly all received
sequences y(i)and channel estimates h(i)to the
ML detector and LLR calculator block, they can
be used to derive an equivalent sequence y~and
an equivalent channel estimates sequence h
performing maximal-ratio combining (MRC) [6].
Only y~and h
tor and LLR calculator to produce the LLRs for
the mother code bits. This symbol-level combin-
ing scheme is shown in Fig. 3b. For the SISO
case, the matrix sequences H(i)should be
replaced by sequences h(i)of scalars, whereas
~by
~need to be used by the ML detec-
sequences of received vectors y _(i)are replaced by
sequences of scalars y(i). The symbol-level com-
bining scheme is equivalent to the receiver of
Fig. 3a and is therefore optimal. The storage
requirements at the receiver are reduced by a
factor equal to the limit on total transmissions,
N. Combining y(i)and h(i)consists of multiplying
with complex scalar values (h*(i)[m]) [6]. The
approach of Fig. 3b can also be used in IR-
HARQ systems as long as the bit selector is
designed so that the alignment between bits and
symbols does not change. For example, for 16-
QAM, if each symbol is formed using bits [c[4m],
c[4m + 1], c[4m + 2], c[4m + 3]], a new symbol
containing [c[4m], c[4m + 1], c[4m + 2], c[4m +
3]] will be generated after a certain number of
retransmissions. Then the received symbols con-
taining the same bits in the same order can be
combined before detection. For example, in one
of the modulation and coding schemes used in
IEEE 802.16e systems where the data packet
length is 54 bytes, the CTC rate is 1/3, and 64-
QAM is used, 54 × 8 × 3 = 1296 bits correspond
to 1296/8 = 162 64-QAM symbols. The simpli-
fied receiver can be used, because bits 8m to 8m
+ 7 will always be mapped to symbol m. For IR-
HARQ, the required storage at the receiver is
proportional to the maximum number of differ-
ent symbols s that can be generated, which
equals L/(r × b), where r is the rate of the moth-
er code, L is the length of the original data
sequence, and b is the number of bits transmit-
ted in each symbol. Hence, more storage is
required than with CC-HARQ. This also means
that the ML detector and LLR calculator block
becomes more complex because it needs to pro-
cess an equivalent symbol sequence of length
L/(r × b) that is larger than M.
If bits and symbols are not aligned, it may not
be possible to use the receiver of Fig. 3b, because
the number of different symbols s may exceed
L/(r × b) and become very large. In order to sim-
plify the receiver, ML detection and LLR calcu-
lation can be performed separately for each y(i),
as shown in Fig. 3c. The LLRs per mother code
bit and per transmission are then simply added
together to produce the LLR value sent to the
decoder. This bit-level combining scheme has
suboptimal performance. However, the perfor-
mance loss in SISO systems is generally small.
By using bit-level combining, the storage require-
ments at the receiver are reduced when the bits
of the mother code are fewer than the maximum
number of received symbols s and channel esti-
mates h that need to be stored. This is true, in
general, unless the allowed maximum number of
retransmissions is small. The complexity of the
ML detector and LLR calculator block is also
reduced.
Since the performance loss of the bit-level
combining receiver is not significant for SISO-
HARQ systems, IR-HARQ generally performs
better than CC-HARQ even when bit-level com-
bining is used. This happens because the loss
incurred by the suboptimal implementation of
the receiver is usually smaller than the coding
gain of IR-HARQ. However, as explained in the
following section, because of interstream inter-
ference, bit-level combining in MIMO-HARQ
may result in significant performance degrada-
When CC-HARQ is
used, the design of
the receiver can be
simplified and the
required memory
can be reduced
without affecting
performance.
Receiver
simplification can
also be achieved for
IR-HARQ by
controlling the bit
selection scheme at
the transmitter.
Page 5
IEEE Communications Magazine • January 2009
36
tion. Thus, for practical MIMO receiver imple-
mentations subject to complexity and memory
constraints, the choice between CC-HARQ and
IR-HARQ may not always be straightforward.
It should also be noted that some cases have
been identified where CC-HARQ performs bet-
ter than IR-HARQ in SISO systems even when
the optimal receiver of Fig. 3a is employed.
Examples include systems where the effect of
fading on different IR-HARQ codewords varies,
especially when the codewords that contain the
systematic part of the code are severely affected
[7].
HARQ APPLIED TO
MIMO SYSTEMS
As shown in Fig. 1a, compared to the SISO case,
the transmitter for MIMO-HARQ includes an
additional symbols-to-antennas mapping block
after the generation of the modulated symbols
s(i)that determines from which antenna each
symbol will be transmitted. In the general case, a
given symbol s may be transmitted from more
than one antenna, or the antennas may transmit
linear combinations of the original symbols.
Specifically, the symbols-to-antennas mapper
generates a sequence of nt× 1 symbol vectors x(i)
= [x _(i)[0], x _(i)[1], …, x _(i)[K]] based on the symbol
sequence s(i)= [s(i)[0], s(i)[1], …, s(i)[M]], where
ntis the number of transmit antennas. Each vec-
tor x _ is sent through the MIMO channel, result-
ing in an nr× 1 vector y _at the receiver, where nr
is the number of receive antennas. As in the
SISO case, flat fading is considered, and the
effect of the MIMO channel is modeled using a
sequence H(i)of nr× ntmatrices. The capacity
and diversity gains that can be achieved depend
on the correlation between the received signals
(i.e., the condition of the channel matrix. Ideally,
a well conditioned channel matrix is desired.
Therefore, in addition to noise and fading, the
two factors affecting transmission in SISO sys-
tems, MIMO systems are also subject to inter-
stream interference. When the interference is
high, transmission may be severely affected even
when the received power per antenna is large.
HARQ can be used in MIMO systems to com-
bat interstream interference in addition to noise
and channel gain fluctuations caused by fading.
Although not shown in the figure, the symbol-to-
antenna mapper may also employ a space-time
block code (STBC).
When CC-HARQ is employed, the simplified
transmitter of Fig. 1b can be used. The transmit-
ter can also be used for IR-HARQ, as long as
the alignment between bits and signal vectors
does not change. A bits-to-symbols mapper cre-
ates a symbol sequence s′ ′ based on the encoded
bits sequence c, and is followed by a symbols-to-
antennas mapper that transforms s′ ′ to a symbol
vector sequence x′ ′. The transmitter is simpler
because the symbol vector sequence x′ ′ can be
precomputed. However, the main benefit is the
simplification of the receiver, as described in the
following.
Similar to the SISO case, as shown in Fig. 3a,
the nr× 1 received symbol vectors can be sent to
an ML detector and LLR calculator block that
combats interstream interference in addition to
compensating for noise and channel fading. The
ML detector and LLR calculator block is more
complex than the SISO case, because matrix and
vector operations are involved. Once the LLRs
are produced, decoding proceeds in exactly the
same way as in SISO systems.
Some questions now emerge. When the align-
ment between bits and symbol vectors is fixed,
can symbol-level combining be used for MIMO-
HARQ similar to the SISO case? As shown
later, that is indeed possible by an extension of
the SISO-MRC scheme. Can the receiver be
simplified if the alignment between bits and sym-
bol vectors is not fixed or symbol-level combin-
ing is not possible in early retransmissions, and
what are the implications to the system perfor-
mance and complexity? As described below, the
performance penalty when trying to simplify the
receiver of MIMO-HARQ systems using bit-
level combining is larger than in SISO systems.
The performance degradation increases further
when equalization is used instead of ML detec-
tion. Therefore, when realistic MIMO receiver
implementations are desired, a careful assess-
ment of the performance loss of IR-HARQ
because of bit-level combining should be made.
These questions are addressed in more detail in
the remainder of this section.
CC-HARQ is considered first. The observa-
tions can be extended to the case of IR-HARQ
where bit-to-symbol vector alignment is pre-
served. The same symbol vector sequence x is
sent during each retransmission. As in the SISO
case, instead of using the receiver of Fig. 3a, the
architecture of Fig. 3b can be employed. It can
be shown that an MRC-like combining scheme
can be used to form an equivalent nt× 1 symbol
vector sequence y _
matrix sequence H
vector and channel matrix estimate sequences
y _(i)and H(i), respectively. Each H
tian matrix of size nt× nt[6]. Thus, the MIMO-
HARQ problem is converted to an equivalent
single-transmission MIMO problem, because the
sizes of y _
retransmission. An ML detector and LLR calcu-
lator block that uses only one symbol vector
sequence and one channel estimate sequence
can then be used. Therefore, the memory
requirements of the symbol-level combining
receiver of Fig. 3b are reduced from those of the
receiver of Fig. 3a. This simplification of the
receiver is aided by reusing the same ML detec-
tor and LLR combiner block after each trans-
mission. Moreover, numerical techniques such as
QR decomposition can be used for implementa-
tion [6]. The receivers of Figs. 3a and 3b are
equivalent, so there is no loss in performance.
For IR-HARQ, the receiver of Fig. 3b can be
used by considering all different symbol vectors
that may be generated. The length of y _
will be at least as large as K, the length of x(i).
When the alignment between bits and symbol
vectors is not fixed, the bit-level combining
receiver of Fig. 3c can be employed if using sym-
bol-level combining is impractical. However, this
architecture is not optimal and may result in sig-
nificant performance degradation when the dif-
ferent paths of the MIMO channel are
~and an equivalent channel
~from the received symbol
~[m] is a Hermi-
~and H
~remain the same after each
~and H
~
The performance
penalty when trying
to simplify the
receiver of
MIMO-HARQ
systems using
bit-level combining is
larger compared to
SISO systems.
The performance
degradation
increases further
when equalization is
used instead of
ML detection.
Page 6
IEEE Communications Magazine • January 2009
37
correlated. The main cause is not the combining
of bits instead of symbol vectors, but the sepa-
rate detection and LLR calculation after each
transmission. When the channel matrix H is ill
conditioned, erroneous decisions may be made
about the individual elements of a symbol vector
x even when the quality of the received symbol
vector is good. On the other hand, when symbol-
level combining is used, detection and LLR cal-
culation are performed after gathering
information from all retransmissions. From the
viewpoint of the architecture of Fig. 3b, the con-
dition of the H(i)[m] equivalent matrix is better
than that of some of the matrices H
Although bit-level combining is suboptimal, it
is also less complex, because the same blocks are
reused in Fig. 3c regardless of the number of
retransmissions. The required storage is also
reduced because only the accumulated LLRs of
the bits of the mother code need to be stored.
In some systems the ML detector and LLR
calculator block may be too complex to imple-
ment, even in the simplified receiver of Fig. 3b.
In this case equalization across the spatial
streams can be used (recall that flat fading is
assumed). Linear or decision feedback equaliz-
ers (DFEs) (zero-forcing [ZF] or minimum
mean square error [MMSE]) can be employed.
The MIMO equalization schemes described
above are well known and not particular to
HARQ. They can be implemented efficiently,
for example, using QR decomposition. This brief
overview is given in order to facilitate the discus-
sions in the remainder of this section.
When CC-HARQ is employed, the receiver
of Fig. 3d can be used. First, the spatial streams
are decoupled using an equalizer. Then, for each
element xj
sequence x^, separate LLR calculators are used
that take into account the mapping of the trans-
mit symbols into symbol vectors and the corre-
sponding channel estimates. In general, the xj
are soft values and are not sliced to the nearest
constellation symbol. Each time symbol vectors
from a new transmission arrive, they are com-
bined with the symbol vectors of all previous
transmissions, and the equivalent symbol vectors
are re-equalized using the equivalent channel
matrix sequence. Similar to the ML case, the
pre-equalization symbol-level combining operation
does not result in information loss. For this rea-
son, the scheme of Fig. 3d exhibits the best per-
formance among all equalization-based
architectures [8]. After each retransmission, the
equivalent vector sequence y _
receiver, together with the equivalent channel
matrix sequence H
of size nt× nt. Hence, K × nt× (nt+ 1)/2 com-
plex entries are required for H
plex entries for y _
In order to reduce storage, a post-equalization
symbol-level combining scheme, shown in Fig. 3e,
can be used. The received signal vectors y _(i)are
equalized after each retransmission, and the
resulting symbol vector sequences x
bined before LLR calculation. Only the y _(i)are
used to obtain the x
optimal way to combine the x
which consists of multiplying each element xj
x
~[m].
^of the equalized symbol vector
^
~is stored at the
~. Each H
~[m] is Hermitian and
~and K × ntcom-
~.
^(i)are com-
^(i). It can be shown that the
^(i)is using MRC,
^(i)of
^(i)with a complex weight that depends on the
channel estimate H(i)and accumulating the
result with the values from previous transmis-
sions [8]. The resulting weighted sum is normal-
ized before LLR calculation. Post-equalization
symbol-level combining reduces receiver memory
because instead of a sequence of K Hermitian
matrices, only K × ntnormalization weights γj(i)
need to be stored in addition to the weighted
and accumulated x
tion symbol-level combining exhibits perfor-
mance loss compared to pre-equalization
combining [8, 9]. Therefore, for fixed bit-to-sym-
bol vector alignment, use of post-equalization
combining is motivated by the need to reduce
the storage at the receiver. Even when ntis
small, the savings can be significant when K is
large. The storage requirements can be reduced
further (by K × ntcomplex values per transmis-
sion) by combining the xj
[9] at the cost of additional performance degra-
dation. The receiver of Fig. 3e can also be used
for IR-HARQ. The difference is that K should
be replaced by the number of all possible symbol
vectors x that may be sent from the transmitter
before reaching the transmission limit N.
When the bit-to-symbol vector alignment is
not fixed or the number of symbol vectors is
large, the structure of Fig. 3f can be employed,
whose difference with that of Fig. 3e is that the
LLRs are calculated directly after equalization.
The performance of the receiver of Fig. 3f is
inferior compared to the other schemes. The
largest part of the performance degradation is
caused by the separate equalization after each
transmission without combining information
from different transmissions. What needs to be
stored now are the LLRs of the bits of the moth-
er code c that are sent to the channel. Hence, if
use of the receiver is considered for HARQ with
fixed bit-to-symbol vector alignment, in order to
determine whether memory reduction can be
achieved compared to other architectures, the
total number of different symbols that are sent
to the channel needs to be taken into account.
Table 1 summarizes the MIMO-HARQ
receiver architectures presented in this section
and their memory requirements.
^(i). However, post-equaliza-
^(i)using equal weights
COMPARISON OF RECEIVER
ARCHITECTURES AND EXAMPLES
In the previous section it was argued that the
receiver implementation depends on the transmis-
sion scheme (CC- or IR-HARQ), whether the
alignment between bits and symbol vectors is
fixed, and the constraints in memory and complex-
ity. Simplifying the receiver may come at a price.
As an example of the performance degrada-
tion caused by suboptimal receiver implementa-
tions, an IEEE 802.16e compliant system using
partial usage of subchannels (PUSC) and spatial
multiplexing (Matrix B) is considered [2]. Two
transmit and two receive antennas are employed,
communicating through a vehicular Type A
channel with a high degree of spatial correlation
and Doppler speed equal to 120 km/h. The data
are encoded using the mother rate-1/3 CTC. Bits
are punctured sequentially to produce sequences
of equal length, as in Fig. 2.
In some systems,
the ML detector and
LLR calculator block
may be too complex
to implement.
In this case,
equalization across
the spatial streams
can be used. Linear
or Decision-Feedback
Equalizers (DFE)
(Zero-Forcing [ZF] or
Minimum
Mean-Square Error
[MMSE]) can be
employed.
Page 7
IEEE Communications Magazine • January 2009
38
In Fig. 4a the bit-level combining receiver of
Fig. 3f is employed using zero-forcing linear
equalization (ZF-BLC). 64-QAM and the rate-
1/2 code of Fig. 2a are considered. IR-HARQ
has a coding gain of more than 1 dB over CC-
HARQ because of the additional parity bits that
are transmitted. However, when the optimal pre-
equalization symbol-combining receiver of Fig.
3d is used with CC-HARQ (MRC-ZF), the sys-
tem exhibits a gain of almost 2 dB over IR-
HARQ. CC-HARQ also outperforms IR-HARQ
when ML detection is used instead of equaliza-
tion, as seen from curves MRC-ML and ML-
BLC that correspond to the receivers of Figs. 3b
and 3c, respectively. The performance advantage
of IR-HARQ can be recaptured using the receiv-
er of Fig. 3a at the cost of increased complexity
and memory requirements.
When a rate-5/6 code is used, the coding gain
of IR-HARQ over CC-HARQ is much larger
than the rate-1/2 code (on the order of 4 dB, as
shown in Fig. 4b). Therefore, although symbol-
level combining improves the performance of
CC-HARQ, IR-HARQ still achieves a gain of
approximately 1 dB. The gain is attained for
both equalizer-based and ML-based implemen-
tations.
CONCLUDING REMARKS
This article examines the implementation of
HARQ in wireless systems employing BICM,
mainly in the MIMO context. Because of the
introduction of new dimensions, a number of
different architectures can be used for the receiv-
er. In general, the designer needs to take into
account the complexity and memory constraints,
channel characteristics, and maximum allowed
? ? Table 1. Comparison of memory requirements and performance of MIMO-HARQ receiver implementa-
tions.
Receiver implementationStorage requirements Comments
Generic (Fig. 3a)
K × N × nr× (1 + nt)
K: length of symbol vector sequence per
HARQ transmission
N: maximum number of transmissions
nt/nr: number of transmit/receive antennas
Can be used with any HARQ scheme.
Optimal.
Symbol-level combining
with ML detection (Fig. 3b)
For CC-HARQ:
For IR-HARQ:
KCn
n
t
t
×××+
+
2
1
1
Kn
n
t
t
××+
+
2
1
1
C: number of distinct equivalent symbol
vectors and equivalent channel estimate
sequences
C = L/(r × b × nt× K) for fixed bit-to-symbol
vector alignment.
Optimal.
Bit-level combining with
ML detection (Fig. 3c)
CC-HARQ: K × nt× b
IR-HARQ: L/r
r: rate of mother code
L: length of original data sequence (in bits)
b: bits per symbol.
Suboptimal.
Pre-equalization symbol-
level combining (Fig. 3d)
For CC-HARQ:
For IR-HARQ:
KCn
n
t
t
×××+
+
2
1
1
Kn
n
t
t
××+
+
2
1
1
C: number of distinct equivalent symbol
vectors and equivalent channel estimate
sequences
C = L/(r × b × nt× K) for fixed bit-to-symbol
vector alignment.
Inferior to generic.
Post-equalization symbol-
level combining (Fig. 3e)
For CC-HARQ: 2 × K × nt
For IR-HARQ: 2 × K × C × nt
C: number of distinct equivalent symbol
vectors and equivalent channel estimate
sequences
C = L/(r × b × nt× K) for fixed bit-to-symbol
vector alignment.
Inferior to pre-equalization combining.
Bit-level combining with
equalization (Fig. 3f)
CC-HARQ: K × nt× b
IR-HARQ: L/r
r : rate of mother code
L: length of original data sequence (in bits)
b: bits per symbol
Inferior to all the above.
The designer needs
to take into account
the complexity and
memory constraints,
the channel
characteristics,
and the maximum
allowed number of
retransmissions
before deciding on
the MIMO-HARQ
scheme.
Page 8
IEEE Communications Magazine • January 2009
39
number of retransmissions before deciding on
the MIMO-HARQ scheme. In order to improve
the performance of HARQ with low receiver
complexity, proper bit-to-symbol vector align-
ment can be used to enable symbol-level com-
bining at the receiver. Moreover, new code
designs could focus on developing IR-HARQ
schemes that are robust to suboptimal receiver
implementations.
REFERENCES
[1] S. Lin, D. J. Costello, Jr., and M. J. Miller, “Automatic-
Repeat Request Error-Control Schemes,” IEEE Commun.
Mag., vol. 22, Dec. 1984, pp. 5–17.
[2] IEEE Std. 802.16e-2005, “IEEE Standard for Local and
Metropolitan Area Networks, Part 16: Air Interface for
Fixed Broadband Wireless Access Systems, Amendment
2: Physical and Medium Access Control Layers for Com-
bined Fixed and Mobile Operation in Licensed Bands,”
Feb. 2006.
[3] 3GPP TS 25.201 V8.0.0 (2008-03), “3rd Generation
Partnership Project; Technical Specification Group Radio
Access Network; Physical Layer — General Description
(Release 8).”
[4] K. R. Narayanan and G. Stüber, “A Novel ARQ Tech-
nique Using the Turbo Coding Principle,” IEEE Com-
mun. Lett., vol. 1, no. 2, Mar. 1997, pp. 49–51.
[5] Z. Ding and M. Rice, “Hybrid-ARQ Code Combining for
MIMO Using Multidimensional Space-Time Trellis
Codes,” Proc. IEEE ISIT ’07, Glasgow, Scotland, June
2007.
[6] E. W. Jang et al., “Optimal Combining Schemes for
MIMO Systems with Hybrid ARQ,” Proc. IEEE ISIT ’07,
Nice, France, June 2007.
[7] J.-F. Cheng, “Coding Performance of Hybrid ARQ
schemes,” IEEE Trans. Commun., vol. 54, no. 6, June
2006, pp. 1017–29.
[8] D. Toumpakaris et al., “Storage-Performance Tradeoff
for Receivers of MIMO Systems Using Hybrid ARQ,”
Proc. 9th IEEE Int’l. Wksp. Sig. Processing Advances in
Digital Commun., Recife, Brazil, July 2008.
[9] E. N. Onggosanusi et al., “Hybrid ARQ Transmission and
Combining for MIMO Systems,” Proc. IEEE ICC, vol. 5,
May 2003, pp. 3205–09.
BIOGRAPHIES
JUNGWON LEE [S’00, M’05] (jungwon@stanfordalumni.org)
received a Ph.D. degree in electrical engineering from Stan-
ford University in 2005. From 2000 to 2003 he worked as
an intern for National Semiconductor, Telcordia Technolo-
gies, and AT&T Shannon Labs Research, and as a consul-
tant for Ikanos Communications. Since 2003 he has worked
for Marvell Semiconductor Inc., Santa Clara, California,
where he is now a principal engineer/senior manager. His
specific research interests are in wireless and wireline com-
munication theory with emphasis on OFDM and single-car-
rier system design, transmission optimization, resource
allocation, cross-layer design, and estimation and detection
theory.
DIMITRIS TOUMPAKARIS [S’98, M’04] (dtouba@upatras.gr)
received his Diploma in electrical and computer engineer-
ing from the National Technical University of Athens,
Greece, in 1997, and his M.S. and Ph.D. degrees in electri-
cal engineering from Stanford University in 1999 and 2003,
respectively. He was a senior design engineer in Marvell
Semiconductor Inc., Santa Clara, California, from 2003 to
2006. He has also worked as an intern for Bell-Labs, CERN,
and France Télécom, and as a consultant for Ikanos Com-
munications and Marvell Semiconductor Inc. He is currently
I Figure 4. MIMO system, Type-A vehicular channel, 120 km/h, high inter-stream correlation, PUSC, spatial multiplexing: a) 64-QAM,
code rate = 5/6, packet size = 54 bytes; b) 64-QAM, code rate = 5/6, packet size = 60 bytes.
SNR [dB]
(a)
10
10-5
10-4
BER
10-3
10-2
10-1
100
101
1214 16 18202224
1 transmission, ZF
2 transmissions, CC, MRC-ZF
2 transmissions, CC, ZF-BLC
2 transmissions, IR, ZF-BLC
2 transmissions, CC, MRC-ML
2 transmissions, IR, ML-BLC
SNR [dB]
(b)
10-5
10-4
BER
10-3
10-2
10-1
100
101
30252015
1 transmission, ZF
2 transmissions, CC, MRC-ZF
2 transmissions, CC, ZF-BLC
2 transmissions, IR, ZF-BLC
2 transmissions, CC, MRC-ML
2 transmissions, IR, ML-BLC
Page 9
IEEE Communications Magazine • January 2009
40
an assistant professor in the Wireless Telecommunications
Laboratory, Department of Electrical and Computer Engi-
neering, University of Patras, Greece. His current research
interests include information theory with emphasis on
multi-user communications systems, digital communica-
tion, synchronization and estimation, and cross-layer opti-
mization.
EDWARD W. JANG [S’04] (ej1130@stanford.edu) received his
B.S. degree in electrical engineering from Seoul National
University, Korea, in 2002, and his M.S. degree in electrical
engineering from Stanford University in 2004. He is cur-
rently pursuing his Ph.D. degree at Stanford University. His
research interests include transmission schemes for systems
with a limited feedback rate and MIMO systems with
HARQ.
HUI-LING LOU (lou@stanfordalumni.org) is a senior engineer-
ing director at Marvell Semiconductor, Santa Clara, Califor-
nia, leading teams responsible for physical layer standards,
systems, and architecture design and development for
mobile WiMax chip sets, and investigating next generation
wireless technologies. She has also formed and led physical
layer standards and systems teams that designed, devel-
oped and productized Marvell’s first 802.11n, Bluetooth,
and digital FM chip sets. Prior to Marvell, she spent nine
years at Bell Laboratories Research, Murray Hill, New Jersey,
where she designed algorithms, systems, and efficient
hardware architectures for cellular and digital broadcasting
systems. She also developed a reconfigurable trellis codec
chip for Amati Communications as a consultant in 1992.
She completed her M.S.E.E. and Ph.D. degrees at Stanford
University in 1988 and 1992, respectively. She has more
than 60 patents, granted and pending, and has published
more than 50 peer-reviewed publications.
JOHN M. CIOFFI [F‘96] (cioffi@stanford.edu) received his
B.S.in electrical engineering in 1978 from the University of
Illinois and his Ph.D. in electrical engineering in 1984 from
Stanford University. He was with Bell Laboratories,
1978–1984, and IBM Research, 1984–1986. He has been
a professor of electrical engineering at Stanford since
1986. He founded Amati Com. Corp in 1991 (purchased by
TI in 1997) and was officer/director from 1991–1997. He
currently is on the board of cirectors of ASSIA (Chairman),
ClariPhy, Teranetics, Vector Silicon Inc., and the Marconi
Foundation. He is on the advisory boards of Focus Ven-
tures, Quantenna, and Amicus. His specific interests are in
the area of high-performance digital transmission. Various
awards include International Marconi Fellow (2006), Holder
of Hitachi America Professorship in Electrical Engineering at
Stanford (2002); Member, National Academy of Engineer-
ing (2001); IEEE Kobayashi Medal (2001); IEEE Millennium
Medal (2000); IEE JJ Tomson Medal (2000); 1999 U. of Illi-
nois Outstanding Alumnus, 1991 and 2007 IEEE Communi-
cations Magazine best paper; 1995 ANSI T1 Outstanding
Achievement Award; NSF Presidential Investigator
(1987–1992), ISSLS 2004, ICC 2006, 2007, and 2008 Con-
ference Best-Paper awards. He has published over 250
papers and holds over 80 patents, of which many are
heavily licensed including key necessary patents for the
international standards in ADSL, VDSL, DSM, and WiMAX.
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