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Selective HARQ Transceiver Design for OFDM System
Zia Muhammad, Hasan Mahmood, Awais Ahmed, and Nazar Abbas Saqib

Abstract—We present a novel selective Hybrid Automatic Repeat reQuest (HARQ) based transceiver design for orthogonal frequency division multiplexing (OFDM) system. The proposed method is bandwidth efficient and has lower complexity as compared to conventional HARQ method adopted by communication standards such as long-term evolution (LTE). Our transceiver design introduces an additional retransmission layer at OFDM modulation level, which is independent of conventional HARQ methods. Instead of calculating computationally expensive soft information and applying forward error correction (FEC) on the soft information, receiver requests retransmission of information symbols corresponding to the subcarriers that have signal-tonoise ratio (SNR) below a set threshold at modulation level. We also provide criteria for selective retransmission and throughput analysis with new selective retransmission approach. We demonstrate that with limited feedback at modulation layer level, the proposed method enhances throughput of the system in all SNR regimes. The proposed selective HARQ method provides great flexibility for an application to optimize throughput based on its bit error rate (BER) requirement. Index Terms—Hybrid ARQ, partial retransmission, LDPC codes, OFDM, LTE, joint detection.

I. I NTRODUCTION VER the past decade, multiple-input multiple-output (MIMO) communication systems have been attraction for the research community due to its potential ability to achieve system capacity and channel diversity. LTE (4G) [1] and worldwide interoperability for microwave access (WiMAX) [2] systems have adopted orthogonal frequency division multiple access (OFDMA) technology due to low complexity receiver, better performance and its ability to allocate resources. In order to ensure error-free link and overcome the drawback of disjoint ARQ and FEC design [3], hybrid-ARQ (HARQ) has already been a key feature of the LTE and WiMAX standards. Several works have been conducted on HARQ above the modulation layer that involve ARQ and FEC [4] and references therein. Very little attention has been paid to diversity combining technique [5]– [7] at modulation level to achieve power and bandwidth efficiency. These methods retransmit partial copy of the original information without exploiting frequency diversity of the channel model. Furthermore, these methods [5]–[7] have higher complexity for frequency selective channels. Instead of transmitting partial copy of the original packet without

O

exploiting channel knowledge, we propose energy and bandwidth efficient method that retransmits selected modulated symbols (partial information) using partial channel feedback information and achieves higher throughput as compared to conventional HARQ methods. In this work, we exploit frequency diversity of the OFDM signaling and independence of channel realizations for the first transmission and subsequent partial retransmissions to design low complexity and bandwidth efficient transceiver. In our proposed transceiver, we introduce an additional retransmission layer at modulation level, which is independent of conventional HARQ. In the proposed retransmission scheme, receiver requests retransmission of information symbols that correspond to low SNR subcarriers. Since delay between first transmission and subsequent retransmission of the same information is longer than coherent time, we assume that wireless channel realizations are independent and would play a vital role to achieve higher diversity. In conventional HARQ, each FEC frame decoding involves computation of soft information and high complexity iterative FEC joint decoding. By turning on selective retransmission at modulation layer, which is independent of HARQ, the average number of retransmissions are lowered. This results into fewer FEC decoding and consequently lowers overall complexity of the receiver. In numerical results in Section IV, we consider both correlated and uncorrelated channels. We organize this manuscript as follows. First, we present system model, our proposed method for selective HARQ and performance of selective retransmission in Section II. In Section III, we provide throughput analysis of HARQ with selective retransmission. We discuss our results in Section IV. Finally, we conclude the proposed work in Section V. II. S YSTEM M ODEL AND T ECHNICAL A PPROACH A. System Model In this model, we consider a single-input single-output (SISO) communication system under OFDM signaling over frequency selective channel with bit-interleaved coded modulation (BICM) [8], [9]. FEC code encodes information bit vector U into codeword C. Codeword C is then interleaved by an interleaver π into new bit vector bk . Then bit stream bk is mapped onto symbol set A. Let s = [s(1) . . . s(Ns )]T be the information vector of symbols to be converted into OFDM signal x = [x(1) . . . x(Ns )]T of Ns subcarrier. We assume that frequency selective channel h has order L. Each element of h is an independent circularly symmetric Gaussian random 2 variable, identically distributed as hi ∼ NC (0, σh ). That is, each channel realization is uncorrelated in time. OFDM signaling converts frequency selective channel vector h into Ns parallel flat-fading orthogonal subcarriers. Let H( ) ∈ C,

Manuscript received August 15, 2013. The associate editor coordinating the review of this letter and approving it for publication was I. Djordjevic. Z. Muhammad, H. Mahmood, and A. Ahmed are with the Department of Electronics, Quaid-i-Azam University, Islamabad, Pakistan (e-mail: {mzia, hasan}@qau.edu.pk, awaisahmed04@yahoo.com). N. A. Saqib is with the Department of Computer Engineering, College of Electrical and Mechanical Engineering, NUST, Peshawar Road, Rawalpindi, Pakistan (e-mail: nazar.abbas@ceme.nust.edu.pk). Digital Object Identifier 10.1109/LCOMM.2013.101613.131869

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z p ( ) and H p ( ) be the observation and channel gain of the retransmitted symbol. Then receiver model for retransmitted subcarriers is z p ( ) = H p ( ) · s( ) + wp ( ),
Fig. 1. System model for Hybrid ARQ under OFDM signaling.

(2)

where = 1, 2, . . . , Ns be the channel gain of -th subcarrier that carries information symbol s( ) ∈ A [10]. Then, z( ) = H( )s( ) + w( ), (1)

where wp ( ) is noise realization of the selectively retransmitted subcarrier. Thus, joint system model for selective HARQ (S-HARQ) system is z( ) = z( ) zp( ) = H( ) H p( ) · s( ) + w( ) wp ( ) (3)

=H( )s( ) + v( ), where v( ) = [w( ) wp ( )]T . Note that selective retransmission of information symbols corresponding to low SNR subcarriers, that is |H( )| ≤ τ , is equivalent to adding a receive antenna that results into higher receive diversity. For SISO OFDM signaling, the joint channel vector H( ) for the first and second transmission is of length 2. For higher SNR subcarrier for which |H( )| > τ , vectors z, H and v are scalars. C. Performance of Selective Retransmission Now we discuss how selective retransmission layer can achieve BER of full retransmission and increase bandwidth efficiency of the OFDM system over uncorrelated channel. For an OFDM signaling, the subcarriers for a particular channel realization have strong correlation within coherent bandwidth. Since frequency selective channel realizations are independent along time, channel gains of realizations at time k and k+1 are independent. Therefore, channel gain Hk ( ) and Hk+1 ( + 1), for = 1, · · · , Ns − 1, are also independent and identically distributed [10]. The zero-forcing estimate of information symbol transmitted over -th subcarrier is [10] s( ) = ˆ H ∗( ) z( ) = s( ) + |H( )|2 H ∗( ) w( ) = w( ) , (4) ˜ |H( )|2

where w( ) ∈ C is a complex Gaussian noise of -th subcarrier with zero-mean and variance N0 . There are Ns many H( ) complex gains obtained by applying FFT-matrix on frequency selective channel vector h. FFT transformation is applied to the observation vector after removing cyclic prefix (CP) resulting into vector z. The receiver then computes loglikelihood ratio (LLR) metric corresponding to -th subcarrier from z( ) using channel gain H( ). The LLR metric λk is a single vector of LLR computed from Ns subcarriers. The permuted LLR metric λk is then deinterleaved by π −1 into λk , which is used as an input to FEC ˆ decoder. The output of FEC, U is an estimate of transmitted information bit vector U. In conventional HARQ such as incremental redundancy based HARQ (IR-HARQ) and Chase combining HARQ (CCHARQ), if bit errors are detected in the frame or packet, partial or full retransmission request is initiated by FEC decoder to FEC encoder as shown by bottom dotted line in Figure 1. In the proposed method, we introduce retransmission framework at the modulation layer based on channel quality. For SISO OFDM system, channel norm |H( )| reflects the quality of the -th subcarrier. Receiver initiates selective retransmission request through feedback channel shown by upper dotted line in Figure 1. B. Selective Retransmission Method We propose a selective retransmission method that works independent of conventional HARQ with or without FEC. In conventional HARQ, receiver initiates retransmission request if cyclic redundancy check (CRC) fails. In our approach, modulation layer initiates targeted retransmission of information symbols that correspond to the subcarriers that have gain |H( )| ≤ τ independent of conventional HARQ. We consider one selective retransmission of low SNR subcarriers for each OFDM symbol. Decision of information symbols to be retransmitted is made based on channel norm prior to decoding. Receiver performs joint detection of information symbols that undergo selective retransmission by combining observation from first transmission and selective retransmission. We denote this selective retransmission method by S-HARQ. Note that CC-HARQ and IR-HARQ along with S-HARQ at modulation layer are denoted by SC-HARQ and SI-HARQ, respectively. Objective of selective retransmission at modulation layer level is to lower the overall number of conventional HARQ requests and receiver complexity. The indices of OFDM subcarriers that have channel norm |H( )| smaller than a specific threshold τ are fedback to the transmitter as partial feedback. Let

N0 ) is distribution of effective noise |H( )|2 after channel equalization. The proposed approach selectively retransmits information symbols corresponding to the weak subcarriers having norm of channel gain below a set threshold 2 τ . Now for complex channel gain of variance σh , |H( )| has τ2 Rayleigh distribution. Thus, P (|H( )| > τ ) = exp(− 2σ2 ) h [11]. We denote an event |H( )| > τ by ξ. Then, |H( )| ≤ τ is a complement of event ξ denoted by ξ c . Note that P (ξ c ) = τ2 P (|H( )| ≤ τ ) = 1−exp(− 2σ2 ) is the probability that a subh carrier is selected for retransmission. Receiver performs joint detection for retransmitted symbols. Therefore, probability of symbol error is where w( ) ∼ N (0, ˜ Pe = P (ξ) Pes|ξ + P (ξ c ) Pef |ξc (5)

where Pes|ξ and Pef |ξc are the cconditional error probabilities of single and selected retransmissions, respectively. Let d be the minimum distance of a constellation set, then for first transmission, pairwise error probability for a fixed H( ) is √ Q d|H( )| [10]. Similarly, channel vector for joint detection N
0

when an event ξ c occurs is H( ) = H( ) H p ( ) and d|H( )| √ . Note that |H( )| and pairwise error probability is Q N
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|H( )| have Rayleigh distribution conditioned on events ξ and ξ c , respectively. Therefore, Pes|ξ and Pef |ξc can be obtained

√ √ by conditional expectation of Q d|H( )| and Q d|H( )| N0 N0 over Rayleigh fading channels H( ) and H( ), respectively [11]. The symbol error probability Pe for selective retransmission in (5) without FEC is

where α = Pe1 Pe2 and l is running index. Note that 1 + 2α + 1 3α2 + · · · + lαl−1 = (1−α)2 . It can be shown that 1 + 3α + 5α2 + · · · + (2l − 1)αl−1 = 1+α (1 − α)
2.

(9)

Pe = EH Q

d|H( )| √ N0

|ξ

+EH Q

d|H( )| √ N0

|ξ c

. (6)

The estimate of information symbols can be improved by multiple retransmissions. The proposed S-HARQ method at modulation layer is limited to a single partial retransmission. Therefore, BER of joint detection under selective retransmission is bounded by full retransmission (Chase combining). Let Pe = be the target error probability of S-HARQ for a given noise variance N0 , then |H( )| = N0 Q−1 ( ) = τ. (7)

Since α = Pe1 Pe2 = (1 − Pc1 )(1 − Pc2 ) < 1, the above series converge. Therefore, average number of transmissions in above mentioned framework are 1+α 1 + 2(1 − Pc1 )Pc2 η =Pc1 (1 − α)2 (1 − α)2 2 2 2Pc1 − Pc1 − 3Pc1 Pc2 + 2Pc2 + Pc1 Pc2 = . (10) (Pc1 + Pc2 − Pc1 Pc2 )2 Average number of transmissions to receive error-free packet 1 [12], where all packets have with simple ARQ is ηa = Pc1 same size. Hence, throughput is Ta = η1 = Pc1 . Similarly, a 1 throughput of CC-type HARQ is Tc = η , where η is the average number of transmissions given in (10). However, in IR-HARQ, the size of the first transmission and retransmission are not equal. Therefore, in order to compute throughput of IR-HARQ, the bandwidth consumption of each transmission needs to be considered. For throughput analysis of IR-HARQ with S-HARQ enabled, consider the first transmission with high rate R1 LDPC code. In case of CRC failure, receiver requests more parity bits. In response to IR-HARQ request, k k more parity bits are transmitted. As a result of R2 − R1 IR, new LDPC code has lower rate R2 . Thus, in each IRk k k HARQ round, R1 bits and R2 − R1 bits are transmitted during the first transmission and retransmission, respectively to deliver k information bits. We denote overhead due to OFDM subcarriers selected for retransmission when selective retransmission is enabled by m. Let η = η , where function η returns integer value of η. When η is even, the total number of transmitted bits to receive k error-free bits is η 1 1 + Δη , (11) n =k(m + 1) 2 R2 R1 where Δη = η − η . Similarly, when η is odd, n =k(m + 1) η 1 1 + + 2 R2 R1 1 1 − R2 R1 Δη . (12)

Therefore, receiver requests retransmission for subcarriers that have gain |H( )| < τ . III. T HROUGHPUT ANALYSIS For throughput analysis of SISO OFDM system under selective retransmission at modulation layer, we consider only one S-HARQ retransmission for each OFDM frame if needed. However, for conventional HARQ, we consider multiple rounds of retransmissions. Each HARQ retransmission round consists of first transmission followed by Chase-type (CC) or incremental redundancy (IR) retransmission. As we discussed earlier, a S-HARQ retransmission at modulation layer is initiated for the subcarriers, which has channel gain |H( )| < τ and is independent of conventional HARQ. It is clear from (7) that the number of subcarriers selected for retransmission is non-linear function of threshold τ . Note that throughput analysis is applicable for both correlated and uncorrelated channels.The receiver performs joint detection by exploiting information from first transmission and retransmission of S-HARQ to improve performance using (4). In case of failure to receive error-free data, conventional HARQ is initiated by buffering soft information corresponding to the retransmission request. Note that the modulation layer is unaware of conventional HARQ request. If FEC fails to decode error-free data as a result of HARQ, buffered soft information is discarded and new round of transmission is initiated. Let 1 and 2 be the BERs of the first transmission and retransmission, respectively. Then corresponding probabilities that received error-free frame of length fL bits are Pc1 = (1− 1 )fL and Pc2 = (1− 2)fL , respectively. The frame error probabilities of first transmission and retransmission are Pe1 = 1 − Pc1 and Pe2 = 1 − Pc2 , respectively. The average number of transmissions needed to deliver error-free frame is
2 η =Pc1 + 2Pe1 Pc2 + 3Pe1 Pe2 Pc1 + 4Pe1 Pe2 Pc2 + 2 2 3 2 3 3 5Pe1 Pe2 Pc1 + 6Pe1 Pe2 Pc2 + 7Pe1 Pe2 Pc1 · · ·

k Therefore, throughput of IR-HARQ is Ti = n , where k and n are error-free bits delivered and number of bits transmitted, respectively.

IV. S IMULATIONS Now we present the efficacy of the proposed S-HARQ, SC-HARQ and SI-HARQ methods on throughput of type-I and type-II HARQ (Chase combining and incremental redundancy). In simulation setup, we consider SISO OFDM signaling over 10-tap Rayleigh fading frequency selective channel with 648 subcarriers and 4-QAM constellation. We assume that block fading channel realizations are uncorrelated in time. We also evaluate BER and throughput gain of S-HARQ method as compared to Chase combining with and without FEC code. In this section, we demonstrate the throughput gain when selective retransmission at modulation layer is enabled. For type-I and type-II HARQ, we consider LDPC code (648,

=Pc1 1 + 3α + 5α2 + · · · + (2l − 1)αl−1 + 2Pe1 Pc2 1 + 2α + 3α2 + · · · + lαl−1

(8)

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SI−HARQ IR−HARQ SC−HARQ(648,324) S−HARQ(648,324) CC−HARQ(648,324) SC−HARQ(648,324), 80Hz CC−HARQ(648,324), 80Hz Doppler shift of 80 Hz

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Fig. 4. Throughput gain of SC-HARQ and SI-HARQ over conventional CC-HARQ and IR-HARQ, respectively.

S−HARQ CC−HARQ ARQ S−HARQ(648,324) CC−HARQ(648,324) ARQ(648,324)

mission approach achieves throughput gain over conventional CC-HARQ. We observe consistent gain in throughput with selective retransmission in all SNR regimes. V. C ONCLUSION We propose an innovative method for bandwidth efficient and low complexity selective retransmission framework using OFDM modulation. We demonstrate that the proposed method is independent of conventional HARQ schemes adopted in LTE and WiMAX standards and offers significant throughput gain in all SNR regimes. Furthermore, the new method can be incorporated in LTE with minimal changes to physical layer of 4G standard. The proposed S-HARQ method also provides higher flexibility for the applications based on their BER requirement and error correcting capability of FEC. R EFERENCES
[1] “Long Term Evolution of the 3GPP Radio Technology,” http:/www.3gpp.org. [2] “Broadband Wireless Metropolitan Area Netwrok (WirelessMAN),” http://standards.ieee.org/getieee802/802.16.html. [3] S. Lin and P. S. Yu, “A hybrid ARQ scheme with parity retransmission for error control of satellite channels,” IEEE Trans. Commun., vol. COM-30, no. 7, pp. 1701–1719, Jul. 1982. [4] S. Y. Park and D. Love, “Hybrid ARQ protocol for multi-antenna multicasting using a common feedback channel,” IEEE Trans. Commun., vol. 59, no. 6, pp. 1530–1542, Jun. 2011. [5] H. Samra, Z. Ding, and P. M. Hahn, “Optimal symbol mapping diversity for multiple packet transmissions,” in Proc. 2003 IEEE Conf. on Acoustic, Speech and Signal Processing, vol. 4, pp. IV–181–184. [6] R. Jermey and Z. Ding, “Channel estimation and equalization techniques in downsampled ARQ systems,” IEEE Trans. Signal Process., vol. 55, no. 5, pp. 2251–2262, May 2007. [7] M. Zia and Z. Ding, “Joint ARQ receiver design for bandwidth efficient MIMO systems,” in Proc. 2008 IEEE Conf. on Global Telecommunications, pp. 1–5. [8] G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 927–946, May 1998. [9] S. H. Muller, “Coding approach for multiple antenna transmission in fast fading OFDM,” IEEE Trans. Signal Process., vol. 50, no. 10, pp. 2443–2450, Oct. 2002. [10] E. G. Larsson and P. Stoica, Space-Time Block Coding for Wireless Communications. Cambridge, 2003. [11] H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing. Prentice Hall, 2001. [12] S. Lin, D. J. Costello, and M. J. Miller, “Automatic repeat request error control schemes,” IEEE Commun. Mag., vol. 22, no. 12, pp. 5–14, Dec. 1984.

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Fig. 3. Throughput gain of S-HARQ over CC-HARQ with and without LDPC code (648, 324).

324). We use sum-product algorithm with 50 iterations as a FEC decoder. For throughput analysis, the block length is fL = 256 bits. First, we compare BER performance of S-HARQ with full retransmission (Chase combining) in Figure 2. The figure shows that BER of S-HARQ is comparable to full retransmission without and with LDPC code. It is important to note that in S-HARQ, we enable selective retransmission only during retransmission. However, in SC-HARQ and SI-HARQ, selective retransmission is enabled for each OFDM symbol. When we enable selective retransmission for each OFDM symbol, S-HARQ becomes SC-HARQ. Figure 3 shows that the throughput of S-HARQ is higher than CC-HARQ without and with FEC. In order to compare throughput of SI-HARQ and IR-HARQ, rates R1 = 3 and 4 R2 = 1 are opted for first transmission and subsequent 2 retransmission, respectively. Figure 4 shows that throughput gain of SI-HARQ over IR-HARQ is much higher as compared to the throughput gain of coded S-HARQ over coded CCHARQ. This due to the fact that selective retransmission is enabled for each OFDM symbol of SI-HARQ. It is clear from Figure 4 that throughput of SC-HARQ is significantly higher than throughput of conventional CC-HARQ. The throughput gains of SC-HARQ and SI-HARQ over CC-HARQ and IRHARQ , respectively, are comparable. Figure 4 also provides throughput comparison between conventional CC-HARQ and SC-HARQ with LDPC (648, 324) code in the presence of Doppler frequency fd = 80 Hz at baud rate of 105 Hz. It is evident from simulation results that proposed selective retrans-