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Linköping Studies in Science and TechnologyThesis No. 1494
Improved Techniques for Retransmission
and Relaying in Wireless Systems
Tumula V. K. Chaitanya
Division of Communication SystemsDepartment of Electrical Engineering (ISY)
Linköping University, SE-581 83 Linköping, Swedenwww.commsys.isy.liu.se
Linköping 2011
This is a Swedish Licentiate Thesis.
The Licentiate degree comprises 120 ECTS credits of postgraduate studies.
Improved Techniques for Retransmission and Relaying inWireless Systems
c© 2011 Tumula V. K. Chaitanya, unless otherwise noted.
LIU-TEK-LIC-2011:33ISBN 978-91-7393-144-1
ISSN 0280-7971Printed in Sweden by LiU-Tryck, Linköping 2011
“Anyone who fights for the future, lives in it today.”
– Ayn Rand
Abstract
The last three decades have seen significant advances in the wireless com-munication field. As the data rates of wireless systems are increasing, thedemand for mobile services also is increasing rapidly. Like other natural re-sources, radio spectrum suitable for mobile wireless communications is alsolimited. In order to keep up with this increasing demand, there is a require-ment of new signal processing algorithms.
Diversity is a technique used in wireless systems to combat the effects offading and thereby improve reliability of data transfer. There are manyways in which algorithms can exploit diversity in wireless channels. Hybrid-automatic repeat request (H-ARQ) schemes and relaying mechanisms are twosuch diversity extracting techniques. Even though these diversity achievingtechniques have been well understood in theory, there are many ways in whichone can optimize these techniques for specific application scenarios. In thisthesis, we focus on improving the performance of retransmission schemes andrelaying systems.
In the first part of the thesis, we improve the performance of H-ARQ schemesin the 3GPP- long term evolution (LTE) system by improving the perfor-mance of feedback signaling. We employ complex-field coding to extract theinherent frequency diversity available in the resources. Next, we provide asub-optimal solution to the outage-optimal power allocation problem in incre-mental redundancy based H-ARQ system, whose performance is practicallythe same as that of the optimal solution.
In the later part of the thesis, we propose a retransmission scheme based onsuperposition coding (SPC) for the symmetric relaying scenario. We providepacket error probability (PEP) expressions and solutions for the optimalfraction of power allocated for the partner’s data. Finally, we study theoptimal bits-to-symbol mappings for SPC and its effect on an H-ARQ schemeand the symmetric relaying scenario using SPC.
v
Acknowledgments
First of all, I would like to express my sincere gratitude to my supervisor,Prof. Erik G. Larsson for providing me the opportunity, guidance and thedirection for the first step of my research career.
Also, I am grateful to my colleagues at Communication Systems and Infor-mation Coding divisions. I specially like to thank Dr. Jonas Eriksson, whois never ‘busy’ and always open for discussions. I also want thank my of-ficemate Reza Moosavi and my fellow PhD student Mirsad Čirkić for manyvaluable technical and non-technical discussions. I wish to convey my sincerethanks and appreciation to Prof. Lasse Alfredsson and Prof. Mikael Olofssonfor their help in my teaching work.
I would also like to thank Dr. Niclas Wiberg for his help in LTE relatedinformation. A special thanks goes to my former colleagues, Dr. Erik Lind-skog, Dr. Harold Artés, and Dr. Bhavani Shankar for their assistance duringmy search for PhD studies.
Finally, I would like to thank my family and friends for their endless support.
Linköping, May 2011T. V. K. Chaitanya
vii
Contents
I Introduction 1
Introduction 31 Hybrid ARQ Schemes . . . . . . . . . . . . . . . . . . . . . . 4
1.1 Importance of the Feedback Channel . . . . . . . . . . 51.2 Information Theoretic Analysis of H-ARQ Schemes . . 6
2 Relaying Schemes . . . . . . . . . . . . . . . . . . . . . . . . . 83 Superposition Coding . . . . . . . . . . . . . . . . . . . . . . 10
3.1 Capacity of SPC . . . . . . . . . . . . . . . . . . . . . 113.2 SPC for Finite Input Symbol Alphabets . . . . . . . . 123.3 Applications of SPC . . . . . . . . . . . . . . . . . . . 13
4 Contributions of the Thesis . . . . . . . . . . . . . . . . . . . 14
II Included Papers 21
A Improved Error Protection for Uplink Control Signaling in3GPP-LTE via Complex-Field Coding 231 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Proposed Method for Control Signaling using Precoding . . . 314 Optimal Detectors with Imperfect Channel State Information
(CSI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.1 Conventional Coding Case . . . . . . . . . . . . . . . . 354.2 Proposed Precoding Case . . . . . . . . . . . . . . . . 37
5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 385.1 Results with Perfect Channel State Information (P-
CSI) at the Receiver . . . . . . . . . . . . . . . . . . . 385.2 Results with Imperfect Channel State Information (I-
CSI) at the Receiver . . . . . . . . . . . . . . . . . . . 405.3 Result with Two Receive Antennas . . . . . . . . . . . 43
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
ix
B Outage-Optimal Power Allocation forHybrid ARQ with Incremental Redundancy 471 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 System Model and Optimization Problems . . . . . . . . . . . 513 Packet Drop Probability Analysis . . . . . . . . . . . . . . . . 54
3.1 The special case of L = 2 . . . . . . . . . . . . . . . . 543.2 Root-Finding solution to (9): . . . . . . . . . . . . . . 57
4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 585 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60A Derivation of pout,1 and pout,2 . . . . . . . . . . . . . . . . . . 61B Proof that the discriminant of (17) is negative for Pgiven > 0
and λ > 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
C Superposition Modulation Based Symmetric Relaying withHybrid ARQ: Analysis and Optimization 651 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1.1 Related Work and Contributions . . . . . . . . . . . . 681.2 Organization of the Paper . . . . . . . . . . . . . . . . 70
2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 702.1 Non-cooperative Transmission . . . . . . . . . . . . . . 712.2 Classical DF Relay Transmission . . . . . . . . . . . . 732.3 Superposition Modulated Cooperative Transmission . 73
3 Retransmission Schemes for The Symmetric Relaying Scenario 743.1 Retransmission Scheme Based on Non-cooperative
Transmission . . . . . . . . . . . . . . . . . . . . . . . 743.2 Retransmission Scheme Based on DF Relaying . . . . 753.3 Proposed Retransmission Scheme for the Symmetric
Relaying Scenario . . . . . . . . . . . . . . . . . . . . . 764 Packet Error Probability Analysis . . . . . . . . . . . . . . . . 77
4.1 Analysis for the Diversity Combining Case . . . . . . . 794.1.1 Derivation of PEP0
div . . . . . . . . . . . . . 794.1.2 Derivation of PEP1
div . . . . . . . . . . . . . 804.2 Analysis for the Code Combining Case . . . . . . . . . 81
4.2.1 Derivation of PEP0cc . . . . . . . . . . . . . . 81
4.2.2 Derivation for PEP1cc . . . . . . . . . . . . . 81
4.3 Maximal Ratio Combining vs Code Combining . . . . 825 Optimization of The Superposition Ratio . . . . . . . . . . . . 82
5.1 For L = 0 . . . . . . . . . . . . . . . . . . . . . . . . . 825.2 For L = 1 . . . . . . . . . . . . . . . . . . . . . . . . . 84
6 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 856.1 Analytical vs. Empirical Results . . . . . . . . . . . . 866.2 Optimal Superposition Ratio . . . . . . . . . . . . . . 86
6.3 Performance Comparison for Different L . . . . . . . . 886.4 Varying Superposition Ratio for Retransmissions . . . 93
7 Conclusions and Discussion . . . . . . . . . . . . . . . . . . . 95A Proof of (5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96B Proof of (8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97C Proof of (11) . . . . . . . . . . . . . . . . . . . . . . . . . . . 100D Proof of (13) . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
D Bits-to-Symbol Mappings for Superposition Coding 1091 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1112 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2.1 Scenario 1 . . . . . . . . . . . . . . . . . . . . . . . . . 1132.1.1 One additional retransmission case . . . . . . 1142.1.2 Two additional retransmissions case . . . . . 115
2.2 Scenario 2 . . . . . . . . . . . . . . . . . . . . . . . . 1152.2.1 Two user case . . . . . . . . . . . . . . . . . . 1162.2.2 Three user case . . . . . . . . . . . . . . . . . 117
3 Mutual Information Analysis . . . . . . . . . . . . . . . . . . 1173.1 Scenario 1 . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.1.1 One additional retransmission case . . . . . . 1183.1.2 Two additional retransmissions case . . . . . 119
3.2 Scenario 2 . . . . . . . . . . . . . . . . . . . . . . . . . 1213.2.1 Two user case . . . . . . . . . . . . . . . . . . 1213.2.2 Three user case . . . . . . . . . . . . . . . . . 123
4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235 Conclusions and Discussion . . . . . . . . . . . . . . . . . . . 126
Part I
Introduction
1
Introduction
From the first generation analog Nordic mobile telephony (NMT) system inthe early 1980’s to the current wireless broadband systems like 3GPP-longterm evolution (LTE) and LTE-advanced, the peak data rates for wirelesscommunication have increased many orders of magnitude. Significant ad-vances have been made in many aspects during this evolution in the lastthree decades. Some of these advances are in terms of channel access meth-ods, modulation methods and efficient signal processing algorithms. Themain contributions to this evolution involve the usage of multi-carrier mod-ulation techniques and the invention of multi-antenna systems.
Reliable and efficient communication over wireless networks has been thefocus of research in the telecommunications field for a long time. Often, re-liability over wireless networks is effected by fading, which causes the signalstrength to vary at the receiver and this results in a loss of data packets.Even though fading is not good for reliable communication, the idea of inde-pendent fading channels lead to the concept of diversity. Diversity is an ap-proach used in wireless systems to combat the effects of fading and thereby toprovide reliable data transfer [1]. Retransmissions (time diversity), multiple-input-multiple-output (MIMO) methods (antenna or space diversity) are twocommonly used diversity achieving techniques in many practical systems likeWLAN [2], WiMAX [3], 3GPP-LTE [4]. Other forms of diversity such asmultiuser diversity [5] and cooperative diversity [6] are also finding theirpresence in current wireless standards in terms of opportunistic schedulingand relay communications, respectively.
3
4 Introduction
Even though many of these diversity achieving techniques have been wellunderstood in theory, there are many ways in which one can optimize thesetechniques for specific application scenarios. In this thesis, we focus on im-proving the performance of retransmission schemes and relaying systems.
In the following, we give a brief introduction to different hybrid-automaticrepeat request (H-ARQ) schemes along with their information theoretic anal-ysis in Section 1. In Section 2, we briefly describe various relaying schemes.A brief introduction to superposition coding and its applications to variouscommunication systems is presented in Section 3. Finally, we list the contri-butions of the thesis along with short descriptions of the included papers inSection 4.
1 Hybrid ARQ Schemes
Early versions of retransmission schemes were called automatic repeat request(ARQ) schemes. These schemes are used when a feedback channel from thereceiver to the transmitter is available. One such ARQ mechanism is to ap-pend error detection bits to the data packet before transmitting it. Afterreceiving the data packet, the receiver checks for errors in the received data.If there are errors, the receiver sends a negative-acknowledgment (NACK)signal on the feedback channel asking for a retransmission. If the packetis received without any error, it sends an acknowledgment (ACK) signal tothe transmitter. Many types of ARQ schemes have been proposed for effi-cient usage of resources [7]. However, ARQ schemes suffer from a reductionin throughput. In H-ARQ schemes, throughput performance is improvedby combining conventional ARQ mechanisms with forward error correction(FEC) schemes. There are different types of H-ARQ schemes proposed inliterature, and they are mainly classified into type I and type II H-ARQschemes [8]:
• Type I H-ARQ Schemes: In these schemes, the receiver does not com-bine the information across different (re)transmissions. If the packet isin error, the receiver discards it.
• Type II H-ARQ Schemes: In these schemes, the receiver combinesthe information from different (re)transmissions to decode the packet.These are further classified into:
1. Hybrid ARQ Schemes 5
– Diversity Combining Schemes: These are the type-II H-ARQschemes in which all the retransmissions carry the same infor-mation, i.e., the message is encoded using the same channel codeduring each transmission and the transmitted signal contains thesame coded bits. The receiver uses maximum-ratio-combining(MRC) to decode the data packet. These schemes are also knownas H-ARQ schemes with chase combining (CC).
– Code Combining Schemes: In these type-II H-ARQ schemes, suc-cessive retransmissions carry ‘new’ information to the receiver.During retransmissions, additional parity bits are sent to the des-tination, thereby effectively forming a longer codeword with asmaller rate. The receiver uses code combining to decode thedata packet. These schemes are also known as H-ARQ schemeswith incremental redundancy (IR).
One disadvantage of retransmission schemes in practice is that additionaldelays are introduced in the system. However in many practical systems,the number of retransmissions allowed is limited to avoid an unacceptabletime delay before the successful transmission of a packet. This limit on thenumber of allowed retransmissions however introduces residual packet errors.
1.1 Importance of the Feedback Channel
Reliability of the ACK/NACK feedback signaling is important for the systemperformance. Errors in decoding these feedback signals result in wastageof resources (if an ACK signal is decoded as NACK) and loss of data atthe receiver (if NACK signal is decoded as ACK). Many practical systemsuse one bit for H-ARQ acknowledgments. Now with the introduction ofMIMO systems, the transmitter can use layered transmissions to increasethe throughput. In such cases, the receivers can send more than one bitfeedback (one for each layer). For example, in 3GPP-LTE systems, in thedownlink, the base station sends a one bit H-ARQ acknowledgment. In theuplink, the mobile station can send either one or two bits feedback dependingupon the number layers in the downlink transmission. Since there is only onebit for feedback in LTE downlink, this bit is repetition coded (with rate-13 ) toimprove reliability. However in the uplink, in case of extended cyclic prefix(CP) configuration, the H-ARQ acknowledgment bits are encoded togetherwith other control signaling bits using the (NI , 20) Reed-Muller code [9],where NI ≤ 13 denotes the total number of bits for control signaling.
6 Introduction
Modulator
b1, b2, . . . , bU
Encoder
c1, c2, . . . , cV
Interleaver
s1, s2, . . . , sW
h1,1 h2,1 h1,2 hB,1
N1 N2 N1 NB
M1 M2 M1 MB
Ns
Figure 1: System model for H-ARQ schemes.
1.2 Information Theoretic Analysis of H-ARQ Schemes
In this section, we give an information theoretic understanding of H-ARQschemes involving CC and IR. A block-fading communication system modelusing a H-ARQ scheme is shown in Fig. 1. A block of U information bitsare encoded (both error detection and error correction capabilities) to ob-tain V coded bits for transmission on the channel. The coded bits are thenmodulated using a Q- ary constellation S with equal probability for all theconstellation points. The modulation symbols s1, s2, . . . , sW are then dividedinto B code blocks x1,x2, . . . ,xB of N1, N2, . . . NB symbols each. W denotesthe total number of modulation symbols. Depending on the H-ARQ scheme,a code block xb can be transmitted Tb times. The propagation channel isassumed to be block-fading, which means that the channel gain remains con-stant during one code block transmission and changes independently betweendifferent code blocks. The total number of fading blocks involved in the trans-mission is
∑Bb=1 Tb. The total number of channel symbols isNs =
∑Bb=1 TbNb.
The lth reception of the bth code block can be written as:
yb,l = hb,lxb +wb,l, 1 ≤ b ≤ B, 1 ≤ l ≤ Tb (1)
where hb,l and wb,l are the complex fading coefficient and the additive whiteGaussian noise (AWGN), respectively. The noise samples are assumed to bei.i.d. and independent across the code blocks with distribution CN (0, 1).
1. Hybrid ARQ Schemes 7
Let SNRb,l denote the average symbol signal-to-noise ratio (SNR) experiencedby the lth reception of the code block xb, then SNRb,l , |hb,l|2. Let SNR
denote the collection of SNRb,l values. In this thesis, we use informationoutage probability as the performance metric for comparison of different H-ARQ schemes. Which can be defined as:
Pout , Pr (I (SNR) ≤ U) (2)
where I (SNR) is the accumulated mutual information at the receiver con-ditioned on SNR. The accumulated mutual information can be written as:
I (SNR) =
B∑
b=1
NbC
(Tb∑
l=1
SNRb,l
)
(3)
where C (SNR) is the symmetric AWGN capacity1 of S at signal-to-noise-ratio SNR, given by [10]:
C (SNR) , log2Q−ˆ
v∈C
e−|v|2
πQ
∑
s∈Slog2
∑
s∈Se|v|2−
∣
∣
∣
∣
v+√
SNR(s−s)
∣
∣
∣
∣
2
dv (4)
and C is the complex-field. The relative performance of different H-ARQschemes can be compared based on (2).
In our work, we assume that there is a limit on the number of retransmissions,say L. For CC based H-ARQ schemes, we have B = 1, N1 = N . The singlecode block is repeated T1 = L times. For CC case, we have:
ICC (SNR) = N C
(L∑
l=1
SNRl
)
(5)
where SNRl is the SNR for the lth transmission. In case of CC, if theaccumulated mutual information of the initial transmission N C (SNR1) issmaller than the number of information bits, then the transmission is inoutage. The transmitter sends the same code block and hence there byimproving N C (
∑
l SNRl) so that the combined received packet has a smallprobability of being in outage.
For IR, assuming that all the code blocks have the same size and each codeblock is transmitted only once, we have B = L,Nb = N and Tb = 1, for 1 ≤
1Throughout the thesis, we use logarithm with base 2 and hence the unit for capacityis bits per channel use (bpcu).
8 Introduction
S
R
D
XR = f (YR)
YD1, YD2
YR
XS
Figure 2: Basic model of a relay communication channel.
b ≤ B. In this case, the accumulated mutual information can be written as:
IIR (SNR) = N
L∑
l=1
C (SNRl) =
L∑
l=1
IIR (SNRl) (6)
Using the convexity property of the capacity function in (4), we can showthat IIR (SNR) ≥ ICC (SNR). Note that in most parts of our work in thisthesis, while analyzing the H-ARQ schemes using outage analysis, we assumeGaussian signaling with code block sizes approaching infinity. Hence we canreplace the AWGN capacity equation in (4) with the following:
C (SNR) = log2 (1 + SNR) (7)
2 Relaying Schemes
The three-terminal communication channel [11, 12] has attracted much re-search interest recently in the wireless communications field [6, 13, 14]. Abasic model of relay communication channel is shown in Fig. 2. A sourcenode S wants to communicate with a destination node D. A node R over-hears this communication and assists S in such a way that the reliabilityof its information at the destination node is increased. Node R is generallycalled a relay node. The main idea of relay networks is to increase the re-liability of the data transmission when the source-to-destination link is inoutage. The basic functionality of a relay communication in itself is similarto the retransmission of data using H-ARQ in point-to-point communication.With adaptive relaying, the relay only transmits the additional informationneeded to decode the source packet, which is similar to the IR based H-ARQschemes.
2. Relaying Schemes 9
We are interested only in half-duplex relays with non-overlapping transmis-sions from the source node and the relay node. Assuming that S and Rtransmit in orthogonal time slots, the relay communication in Fig. 2 can beexplained as follows. Assuming coded transmissions, during the first timeslot, S encodes an information block X to obtain a coded information blockXs = α (X) and transmits to D, and R also listens to this transmission.α denotes the encoding function. Assuming a block-fading channel, the re-ceived signal at nodes D and R during the first time slot can be expressedas:
YD1= hSDXS +ND1
YR = hSRXS +NR (8)
where ND1and NR denote the AWGN at the destination and the relay during
the first time slot. hSD and hSR denote the fading channel gains for the linksS → D and S → R. During the second time slot, R forwards the code blockXR = f (YR) to D. The received signal at the destination node during thesecond time slot can be written as:
YD2= hRDXR +ND2
(9)
where ND2is the AWGN at the destination during the second time slot. hRD
is the channel gain for the link R→ D. Assuming perfect channel knowledgeat node D, it uses YD1
and YD2to decode X.
Depending on the resources available, R can perform different operations onYR and these operations f (.) form the basis for different relaying schemes2.We list some of them here:
• Amplify-and-forward (AF): In AF scheme, the relay node R simplyamplifies YR and forwards it to the destination, i.e.,
XR = f (YR) = gYR, g > 0. (10)
where g is a scaling factor whose value depends on the channel gainhSR and the average power constraint at R. The outage analysis of theAF scheme can be found in [13].
2Note that there are schemes which can be used when relay does not have any memory.Such relaying methods are known as instantaneous relaying schemes [15, 16, 17].
10 Introduction
• Decode-and-forward (DF): In DF based schemes, the relay decodes theinformation received from S and then re-encodes it to obtain XR andforwards it to the destination. In this case we can write the relayingoperation as:
XR = f (YR) = β
(
argmaxX
p (XS|YR, hSR)
)
(11)
where β denotes the encoding function at the relay node3. If β = αand R forwards the complete XR, the relaying scheme is called DFwith repetition coding [13]. If R repeats only a part of the codewordXR, the relaying scheme is known as DF with partial repetition coding[18]. However if R uses a different channel code (β 6= α), the relayingscheme is known as DF with parallel coding [19]. Outage analysis ofvarious DF schemes is treated in depth in [18].
• Compress-and-forward (CF): In CF based schemes, the relay node Rforwards a quantized and compressed version of YR to the destination.During the compress operation, R exploits the fact that YR and YD1
are correlated [12].
When multiple relays (which are geographically separated) assist the source-to-destination link, their transmit antennas can form a distributed antennaarray. In such cases, one can apply the techniques of space-time coding toextract the transmit diversity as well [20].
3 Superposition Coding
A large part of our work in this thesis uses the concept of superpositioncoding (SPC) [1]. In a superposition coded system, two or more users data istransmitted simultaneously. Note that there are many ways in which one cansuperpose users data, for example in the modulation domain as in [21, 22] orin the GF (2) domain as in [23, 24]. In the following, we consider only thesuperposition in the modulation domain for simplicity, and since that is usedin the rest of the thesis.
3. Superposition Coding 11
Base station
User 1 User 2 User K
h1h2
hK
Figure 3: Downlink system model.
3.1 Capacity of SPC
Consider a K-user downlink broadcast channel model as shown in Fig. 3.The received signal at each user can be written as:
yk [m] = hkx [m] + wk [m] , k = 1, 2, . . . ,K and m = 1, 2, ... (12)
where wk [m] ∼ CN (0, N0) is i.i.d. complex Gaussian noise and yk [m] isthe received signal for user k at time m. hk denotes the fixed channel gainfrom the base station to user k and x [m] is the transmitted signal from thebase station. If hk is known to both the base station and the user k, theoptimal transmission strategy is to encode the information of each user usingan i.i.d. Gaussian code spread over the entire bandwidth. The total availabletransmit power P at the base station is split between the users’ streams suchthat
x [m] =K∑
k=1
xk [m] , m = 1, 2, ... (13)
with E |xk [m]|2 = Pk and∑K
k=1 Pk = P . Assuming that each users datastream is formed using a capacity achieving code, the boundary of the ca-pacity region is characterized by the parametrized rate tuples [1]:
Rk = log2
1 +Pk |hk|2
N0 +(∑K
j=k+1 Pj
)
|hk|2
, k = 1, 2, . . . ,K
3Note that XR should satisfy the average power constraint at R.
12 Introduction
−√ 1−
γ −√ γ
−√ 1−
γ +√ γ
√ 1−γ −
√ γ
√ 1−γ +
√ γ
(a) Constellation for x when x1, x2 ∈ {±1}.
2√γ
2√γ
2(√
1− γ −√γ)
2(√1−γ−
√γ)
I-phase
Q-phase
(b) Constellation for x when x1, x2 ∈ {±1± j}.
Figure 4: Constellation for the super-symbol x for a two user case when x1, x2belong to BPSK and QPSK constellations with ρ1 =
√γ,ρ2 =
√1− γ
and θ1 = θ2 = 0 deg. γ denotes the fraction of the total power allocatedto one of the users.
for all possible power splits∑K
k=1 Pk = P . The boundary is achieved bythe superposition coding operation in (13) at the transmitter and succes-sive interference cancellation (SIC) at the receivers. In SIC, the users withstronger channel gains first decode the weaker users data and subtract itbefore decoding their own data.
3.2 SPC for Finite Input Symbol Alphabets
If practical systems, the modulation symbols xk [m] in (13) come from a finiteinput alphabet. For example if xk ∈ A, ∀k, where A corresponds to a finitedimensional constellation such as PAM or QAM with unit average energy,
3. Superposition Coding 13
the superposed modulation symbols in general can be written as [25]4:
x =K∑
k=1
ρkejθkxk. (14)
where ρk denotes the amplitude scaling factor and θk denotes the phase ro-tation parameter (in case of complex modulation symbols) for user k’s data.Note that when ρk = 1
K and θk = 0,∀k, then the signal points correspondingto the super-symbol x ∈ B exhibit a non-uniform nature. Example constella-tions of x for a two user superposition case when x1, x2 belong to BPSK andQPSK constellations are shown in Fig. 4. In Rayleigh fading channels, onecan optimize θk to maximize the product distance between the constellationpoints for the super-symbol x to obtain performance improvements as in [26].In this thesis, we work with the superposition of BPSK constellations withθk = 0,∀k.
3.3 Applications of SPC
SPC has found its application in relaying systems, where a single relay ormultiple relays assist a set of users to convey their information to a destina-tion using SPC. Recently, SPC has also been proposed for H-ARQ systemsfor efficient utilization of resources. In H-ARQ schemes using SPC, duringthe retransmissions, the source sends superposed information of a new datapacket as well as additional parity bits of the erroneous packet. These twoapplications along with other practical aspects of SPC are discussed in [25].
The signal-space diversity (SSD) concept introduced in [27] can also be inter-preted as a variation of SPC, in which the modulation symbols are precodedwith an orthonormal (unitary for complex case) matrix and transmitted overthe channel to extract the diversity available in the channel. For example,suppose that two real uncoded modulation symbols x1 and x2 are sent tothe destination in two channel uses with fading gains h1 and h2 respectively.If any of these channel fades are deep, then the receiver cannot detect thesymbols correctly. In SSD, instead of sending x1 and x2 on the channel, wesend the precoded modulation symbols s1 and s2 obtained as follows:
[s1s2
]
=
[ψ11 ψ12
ψ21 ψ22
]
︸ ︷︷ ︸
,Ψ
[x1x2
]
(15)
4We drop the index m for notational convenience.
14 Introduction
where Ψ is an orthonormal matrix. As we can see from (15), the precodedmodulation symbols are also linear combinations of x1 and x2, similar to theoperation shown in (14). The SSD concept was later generalized to complexmodulation symbols with elements of Ψ ∈ C and evolved as complex-fieldcoding (CFC) [28]. CFC has also found its application in relay communica-tions [29].
4 Contributions of the Thesis
In the major part of the thesis, we consider different aspects of H-ARQschemes in point-to-point communication as well as relay communications. Inthe last part, we consider bits-to-symbol-mapping for SPC, with applicationsin H-ARQ and relay systems.
Brief summaries of the papers included in this thesis are as follows:
Paper A: Improved Error Protection for Uplink Control Signalingin 3GPP-LTE via Complex-Field Coding
Authored by T. V. K. Chaitanya, E. G. Larsson, and N. Wiberg.
Published in the proceedings of 71st Vehicular Technology Conference, 2010.
We study the uplink control signaling in 3GPP-Long Term Evolution (LTE)systems. Specifically, we propose a precoding method that uses complex-field coding (CFC) to improve the performance of the PUCCH format 2control signaling. In the case of perfect channel state information (CSI) atthe receiver and with a single receive antenna, the proposed method offerssignificant gains compared to the coding currently used in 3GPP-LTE. How-ever the gains are marginal with two receive antennas. In order to examinethe impact of channel estimation errors, we also derive the optimal detectorfor the case of imperfect receiver CSI, both for conventional coding and forthe proposed CFC method.
Paper B: Outage-Optimal Power Allocation for Hybrid ARQ withIncremental Redundancy
Authored by T. V. K. Chaitanya and E. G. Larsson.
To appear in the IEEE Transactions on Wireless Communications, 2011.
4. Contributions of the Thesis 15
We consider the optimization of power in incremental redundancy (IR) basedhybrid automatic repeat request (HARQ) schemes when the maximum num-ber of (re)transmissions is fixed. We formulate two optimization problems:(i) minimizing the packet drop probability (PDP) under a total average trans-mit power constraint, and (ii) minimizing the average transmit power undera fixed PDP constraint. We consider in detail the special case of only twoallowed transmissions, and we prove that the two optimization problems areequivalent. For this special case, we also provide a sub-optimal root-findingsolution and compare its performance with the optimal solution obtainedthrough an exhaustive search. The results show that the optimal power allo-cation can provide significant gains over the equal power solution in terms ofaverage transmit power spent. The performance of the proposed root-findingsolution is practically the same as that of the optimal solution.
Paper C: Superposition Modulation Based Symmetric Relayingwith Hybrid ARQ: Analysis and Optimization
Authored by T. V. K. Chaitanya and E. G. Larsson.
This paper is an evolved version of [31], presented at IEEE VTC, 2010.
We present a retransmission scheme based on superposition modulation forthe symmetric relaying scenario when the number of retransmissions for adata packet is limited. We consider both diversity combining based as wellas code combining based retransmission schemes. Under the assumptionthat the receiver implements a mechanism that use all accumulated receivedmutual information when decoding the message, we derive packet error prob-ability (PEP) expressions for the proposed retransmission scheme for the casewhen only one retransmission is allowed. Based on the PEP expressions de-rived, we provide a closed-form solution for the optimal superposition ratio(the fraction of power used for the relaying operation). Simulation resultsshow that the proposed retransmission scheme offers significant gains com-pared to a retransmission scheme based on classical decode-and-forward (DF)relaying.
Paper D: Bits-to-Symbol Mappings for Superposition Coding
Authored by T. V. K. Chaitanya and E. G. Larsson.
Submitted to the IEEE Global Communications Conference, 2011.
16 Introduction
Superposition coding can be used in scenarios where orthogonal sharing of re-sources is not efficient. In this paper, we consider two such scenarios in whichsuperposition coding is used to send two or more users data (or packets ofdata) to the destination with efficient utilization of resources. Conventionalway of superposing users data in Euclidean space leads to a natural map-ping of bits-to-superposed-symbols. We propose the use of Gray mapping ofbits-to-superposed-symbols and study the effect in terms of mutual informa-tion at the destination for the two scenarios considered in this paper. Wealso present some numerical results showing that using a Gray mapping ofbits-to-superposed-symbols has better performance compared to the conven-tional natural mapping. From the results, we also conclude that the choice ofoptimal superposition ratio values for the AWGN channel using Gray map-ping of bits for two and three user scenarios results in 4-PAM and 8-PAMconstellation points for the superposed modulation symbols respectively.
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