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Hybrid ARQ Protocols Using Space-time CodesAnh Van Nguyen, Student Member; ZEEE and Mary Ann Ingram, Membel; IEEE

School of Electrical and Com puter Engineering, Georgia Institute of Technolog y, Atlanta, G AE-mails: anguyen@ee.gatech.edu, mai@ee.gatech.eduAb.wuct- Autom atic repeat-request (ARQ) p rotocols using transmit di-versity are investigated in this paper. The p erformance of space-time codes(STC) in a pure ARQ protocol (ST-ARQ) is first examined. Two hy-brid ARQ schemes using ST C are then proposed: space-time hybrid ARQ(ST-HARQ) and turbo space-time hybrid ARQ (TST-HARQ).For the ST-HARQ scheme, the previous transmitted packets are combined with thecurrent received packet. In this scheme, the diversity gain is increasedwith every retransmission resulting in a higher probability of an acceptedpacket. ForTST-H ARQ, the transmitted packets are code combined and it-eratively decoded. Perform ance analysis of ST-ARQ and ST-HAR Q will beapproximated and shown to agree sell with simulated results. TST-HARQwill be shown to ha ve the highest throu ghput efficiency compared to ST-HAR Q and ST-A RQ in quasi-static and fast flat Rayleigh fading channels.

I. I N T R O D U C T I O NThe recent rapid growth in wireless comm unica tions has ledto the demand of high data rates and reliable communications.Unfortunately, the wireless channel medium contains multipathfading which can lim it the systems performance. It is well un-derstood that a way to combat multipath fading is to achievetemp oral, frequency, or spatial diversity. An effective way toachieve diversity is the use of multiple antennas. Tarokh et .

al. [ l ] and, independently, Guey et. al. [2] introduced space-time coding to achieve diversity using multiple transmit anten-nas. Spac e-tim e code s are modulated co des that satisfy the rankcriterion [ I ] for full spatial diversity. Hammons and El Gama1[3] later made a con nectio n between traditional error-correctioncodes and space-time codes. They showed that convolutionalcodes that satisfy their binary rank criterion can to be used asspace-time codes.Although space-time coding is an effective way to combatmultipath fading, a wireless comm unica tion system needs an au-tomatic repeat-request (ARQ) protoco l to achieve reliable datacomm unication. A pure A RQ protoco l accomplishes this but atthe expense of very low throughput when the channel is noisy.Various hybrid versions of the AR Q protocol have been createdto increase the syste ms hrou ghp ut without sacrificing error per-formance. These hybrid ARQ (HARQ ) protocols have been ex-tensively researched and are well understood. For an introduc-tion and a review of ARQ protocols, the reader can refer to [4],

HA RQ protocols that use code combining or diversity com-bining have been shown to be effective in adapting to changingchannel conditions [4]. Recently, HA RQ protocols combinedwith the turbo principle [6] have been used to achieve reliablecomm unication of data packets [ 7 ] , 8] . Other researchers, suchas [9], have shown that space-time codes in OF DM can be ef-fective in ARQ protoco ls. The autho r in [101proposed the usetransmit diversity where the sam e information is transmitted in aThe authors wish to thank the Yamacraw Mission, of the State of Georgia, U.

[51.

S. A. http://www.yamacraw.org or partially supp orting this research.

/ \p:+.qFq-$p+\ /Source

Fig. 1 . Space-time coding for multiple transmit an d receive antennas

staggered fa.shion between antennas. In this paper, we com binethe three concepts of HARQ, turbo principle, and space-timecoding.First, the performance of the simple ARQ protocol usingspace-time codes (ST-ARQ) is studied. We then propo se twonovel versions of a space-time hybrid A RQ protocol: space-time hybrid ARQ (ST-HARQ) and a turbo space-time hybridARQ (TST-HARQ ) scheme. In the ST-HARQ scheme, the samecode as ST-AR Q is used but the previous erroneous packets arecombined with the current received packet to i rcrea se the di-versity gain. For the TST-HARQ schem e, the previous errorpackets and. curren t received packet are co de-co mbi ned and it-eratively decoded. This is possible by transmitting alternatelythe encode d packet and its interleaved version. [n addition, toallow for interleaver gain, space -time codes used m ust be recur-sive codes. We will compare the performance of the three AR Qprotocols by analyzing and simulating their thro ughp ut perfor-mances.The structure of this paper is as follows. A descri ption ofthe system and protocols used is described in Section 2. Per-formance analysis of the proposed protocols are: then given inSection 3. Numerical results will be shown and discussed inSection 4. Con clusio ns will be given in the final ;section.

1 1 . D E S C R I P T ~ O NF S Y S T E M SConsider a system with M transmit antennas and N receiveantennas as; shown in Fig ure 1. The baseband signal y i receivedby antenna j (1 5 j 5 N ) t time t is written as

M

i= lwhere E, is the symbol energy, c i is the symbol transmittedfrom antenna i, an d ni is the zero-mean additive white Gaus-sian noise (AWGN) with variance N 0 / 2 per dimension. Thecoefficient ai,j ( t ) s the path gain due to multipath fading fromtransmit antenna i to receive an ten na j. For fast fading channels,the coefficients ai,j ( t ) re independent of each other. And forquasi-static fading (or block fad ing), ai,j is constant for the du-ration of the transmitted block and in depen dent between blocks.We also assume that the path gains between anten nas are inde-pendent of each other. This can easily be satisfied if the an tennaspacing is adequate.

0-7803-7005-8/01/$10.000 2001 IEEE 2364

mailto:anguyen@ee.gatech.edumailto:mai@ee.gatech.eduhttp://www.yamacraw.org/http://www.yamacraw.org/mailto:mai@ee.gatech.edumailto:anguyen@ee.gatech.edu

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Consistent with the binary rank criterion by [ 3 ] , he space-time code considered in this paper is a rate 112 convolutionalcode with BPS K. Since any convolutional code can be convertedto an equivalent recursive convolutional code, the space-timecode used in this paper is recursive as shown in Figure 2. Thereason for using recursive space-time code is in the TST-HAR Qscheme. Th e transmission protocol of the TST-HAR Q schemeis shown in Figure 3. One can see that the structure is similarto a parallel concaten ated structure. Th erefo re, it is critical thatthe code be recursive so that interleaver gain is possible in theTST-HARQ protocol.A. Pure ARQ Protocol with Space-time Coding (ST- ARQ )

In this scheme , space-time codes are used along with the tra-ditional AR Q protocol. In a pure A RQ protocol, the informationbits are encoded with an error detection co de before transmis-sion. For this paper, we will assume that perfect error detec-tion is available so that it is not addr essed here. We will onlyaddress the transmission using spac e-tim e code s for transmit-ter diversity. The transmitter retransmits the packet when thereceiver detects errors in the received packet. At the receiver,all erroneous received packets are discarded. This protocol issimple and does not require much additional resources. As ex-pected, this system will have poor throughpu t when the channelis noisy. Its throughp ut perform ance for quasi-static Rayleighfading channels will be exam ined in Section 111.B. Hybrid AR Q Protocol with TransmitDiversity Combining

To overcom e the limitations of simple AR Q protocols, a hy -brid ARQ protocol with diversity co mbining called space-timehybrid AR Q (ST-HARQ) is prop osed . In this system, the previ-ous erroneous packets are saved and com bined with the currentreceived pa cket to increase the overall diversity order. Co mbi n-ing packets in this fashion is equivalent to increasing the num-ber of receiver anten nas with every retransmission. By increas-ing the diversity orde r with each retransmission, this system canadapt to the varying chann el conditions. Th is will decrease theaverage number of transmissions per pack et. In the deco dingprocess, maximum likelihood decoding of the space-time trel-lis code is carried out where the received packets are treatedas if they are from different antennas. This method is simplewith only minimal cost of extra memory in the receiver. A per-formance comparison between ST-HARQ and ST-ARQ will besimulated and an alyzed for quasi-static and fast fading channels.The bounds on the throug hput of TST-H ARQ in quasi-static flatfading channels will be given.C. Hybrid ARQ Protocol with Diversity and Code Combining

We propose a novel turbo space-time hybrid ARQ (TST-HARQ) scheme in which the previous erroneous packets andcurrent received packet are code and diversity comb ined. Thisis possible by tr ansm itting alternately the enco ded packet and itsinterleaved version. The transmission s chem e of this modifiedHAR Q can be seen in Figure 3 fo r a two transmit antenna sys-tem. F or the original tran smiss ion, the data packet is transmittedwith the recursive space-time code. In the event a retransmissionis requested, the same information bits are interleaved and en-coded with the sam e recursive space-time code. This the first

I"p&Bits

BPSKModulation

BPSKModulauon

Fig. 2 . Recursive Space-time Codes

Fig. 3. Turbo Space-time H ARQ transmission protocol.

retransmission. For the second, and other even-numbered re-transmissions, the non-interleaved version is sent. For the thirdand other odd numbered retransmissions, th e interleaved versionis sent. All similar versions (odd or even num bered packets)are combined, similar to ST-HARQ, before decoding. Using theturbo principle [6], terative decoding is done with the combinedeven and odd packets.

111. P ERF O RM ANCE ANALYSI SIn analyzing the throughput performance of these schem es, anideal retransmission protocol is assumed w here there is no delaybetween transmissions of packets and the feedback channel isideal. The through put is then a function of the cod e rate usedand the average number of transmissions, T,, that a packet issent until it is accepted. T he throug hpu t, I?, using a rate 1 space-time code can be written as r = &. This will s implify theanalysis where the results can be applied to a m ore sophisticatedretransmission protocol.

A. Performance of ST-ARQFor the pure ARQ protocol that uses space-time codes, thethroughput can be derived by finding the average number of

times a packet is transmitted until it is accepted. In the follow-ing, this average numb er will be analyzed for quas i-static fadingchannels. As will be seen, T, is a function of th e retransmissionprobability.Let D,, Dd, D, be the events that the received sequence con-tains undetected errors, the received sequence contains detectederrors, and the received sequence contains no errors, respec-

tively. The event that the decoded sequence contains detectederrors results in a retransmission request. It is then obviou s that

For this research, it can be safely assum ed that perfect error de-tection is available so that P(D,) is negligible and therefore,P(Dd)N 1- P(D,)

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The average numb er of transmissions in pure AR Q can easily bederived as [4]

The probability, P ( D d ) , equivalent to the frame error rate ofthe space- time code. Th is probability w ill discussed in Section111-D.B. Performance o ST-HARQ

Instead of discarding erroneous packets, these packets canbe com bined with subsequent received packets to increase thediversity order until the packet can be reliably decoded. Thisspace-time combin ing is equivalent to increasing the num ber ofreceive antennas w ith every retransmission, assuming a quasi-static channel.L et P ( D c ) ) ,P ( D y ) ) ,P(Di)) be the probabilities of acombined received sequence after j transmission contains un-detected errors, contains detected errors, and contains no errors,respectively. Again, assuming P ( D , ) is negligible, T, can beexpressed asT,. = 1+P ( D 2 ) )+ P (Dy ) ,Or ) + . . .

(3)The joint probability can be lower and upper bounded [121suchthat

m i 00

j=1 i= l j= 1

If P (D y ) ) s known exactly, the bounds of (4) can be found.On the other hand, if P( D y ) s upper bounded, then the upperbound of (4) (and therefore the lower bound of the throughput)can only be used. A discussion of P (D y ) )will be given insection 111-D.C. Performance of TST-HARQ

The performance of the previous scheme can be further en-hanced thr ough the use of the turbo principle. Usin g recursivespace-time codes, with both diversity and code com bining, theprobability of a retransmission for TST-HAR Q is less comparedto the ST-HA RQ scheme. Th e performance analysis, however,is comp licated by that fac t that the retransmission probabilitiesfor even and od d transmissions are needed. T his analysis is notcarried out in this paper becau se there are performance boundsfor parallel concatenated spac e-time codes. F or parallel concate-nated codes, the error performance upper bound is very weak,especially at low SNR. Therefore, applying such analysis to par-allel concatenated space-time codes will also result in a loosebound. Therefore, rather than use an excessively loose bound ,simulation results are used as evaluations of this schem es effi-ciency.D. Approximation of Retransmission Probabilities

The retransmission probability, or the frame error probability,of the space-time cod e used is needed fo r the throughput evalua-tion of these sche mes. We will discu ss the appro xima tion of this

probability by first showing the difficulty in evaluating it. Thefollowing analysis is for quasi-static fad ing chann els.The retransmission probability P(Dd) , conditioned on thechannel gains a = { a i j } , for a space-time code usingmaximum-likelihood decoding can be bounded [ 31 as(5)

where L is the number of BPSK symbols in the transmittedframe and P(Ela) s the probability of an error event in themaxim um likelihood dec oder. Averaging o ver the distributionof a,he retransmission probability is then

P(DdlLY) 5 1- (1- P(E1a))L

I ( D d ) 5 1- l ( 1 - P ( E l a ) ) L f ( a >a (6)where f(a:l s the Rayleigh density function.For maxim um likelihood decod ing, the error ev m t probabilitycan be union b ounded in term s of the pairwise erro r probabilityPe(c-+ e l a ) as

C e

The pairwise error probability is the probability that an erro-neous sequence e is chosen instead of the transmitted sequencec . This probability, conditioned on the channel values, is writtenas

/ , \

withN L I M l 2

an d Q(x )=: s & e- t z / 2 d t . The evaluation of (7) is no t triv-ial due to it$, ependen ce on the transmitted sequence. A dding tothis complexity, the integration in (6) is with respect to all chan-nel gains. This will beco me intractable when the re is a highorder of diversity. High diversity order results when the systemcontains a large number of antennas or when there is a largenumber of packets combined , as in the ST-HARQ scheme.A simpler probability can be used since the retransmissionprobability of an optim al space-tim e trellis code is equivalen t tothe retransmission probability when m aximum ratio combining(MRC ) of the same order is used. For MR C of order J , th eprobability of a retransmission or a block error is

(10)where p = xi=l:. The channel gains, ai, are Rayleigh dis-tributed which lead to p being a chi-square distr.,buted randomvariable [ 14.1 with 2J degrees of freedom . The density functionof /3 is

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- MR C Upper Bound(J = 6)A Sirnulalion(Tx.2 Rv=3)- - MR C Uppar Bound (J = 4)0 Simulation Tx=2 Rv=2)- RC Upper Bound (J = 2)

I 9 0 Stmulation (Tx=2 R v 4 )- - MR C Uppar Bound (J = 4)0 Simulation Tx=2 Rv=2)- RC Upper Bound (J = 2)

-4 -2 0 2 4 6 8 10 12EblNo (dB)

Fig. 4. Throughput of ST-ARQ scheme in quasi-static flat Rayleigh fadingchannels using MRC approximation and simulation results.

where p = E[a:].Assuming the space-time code achieves re-ceiver diversity, J = MN for each transmission in the ST-ARQscheme and J = j N M for the j-th transmission in the ST-HARQ scheme. Equation (10) is numerically calculated.IV. NUMERICALESULTS

In this section, we will first plot the throughput performa nceof the schemes, ST-ARQ and ST-HARQ, using the stated ap-proximation of the retransmission probabilities. Com parisonswill be made between these curves and simulation results. Next,the retransmission probabilities of the TST-HARQ scheme iscompared to ST-HARQ through simulations. And finally, sim-ulation results of the throughput of all these schemes are com-pared in quasi-static flat fading channels and fast fading chan-nels.To illustrate that the approximation of the retransmissionprobability using (10) is adeq uate, the calculated throug hput ofST-ARQ and ST-HA RQ are compared to simulation results. T heresults for different multiple antenna systems in ST-ARQ andST-HAR Q are plotted in Figures 4 an d 5, respectively. Only theupper bounds for the throughput using the MRC approximationare plotted because it was foun d that the bounds are very tight.For the simulations, the size of the each block is 256 bits andthe code used has a memory order of 4. As o ne can see, the sim-ulated results are very close to the approximations. For smallnumber of antennas, the simulated result has a lower through-put than the M RC approximations because the space-time codedused has an error performance a little worst than receiver diver-sity. If a more powerful code is used, its retransmission proba-

bility will be equivalent to that of MRC. For higher number ofantennas, the simulated results are slightly better than the ap-proximated results. Thi s is because higher num ber of receiveantennas will allow the spa ce-time code to have greater codinggain [ I ] . Overall, the throughput analysis using M RC frame er-ror rates is a good approximation for ST-ARQ and ST-HARQprotocols.For the remaining simulation results, the system consists oftwo transmit antennas and one receive antenna. T he size of the

o -4 -2EblNa Id01

Fig. 5 . Throughput of ST-HAR Q scheme in quasi-static flat Rayleigh fadingchannels using MRC bounds and simulation results100

10-1

F!l i

10-2

0 5 10 15 20104-5 Eb/No (dB)

Fig.6. Frame Error Rate of ST-HARQ and TST-HARQ for the different numberof transmissions.

frames is 1024 bits and the cod e used has memory order 3. T heperformance enhancement of the TST-HARQ protocol over ST-HA RQ protocol is first demonstrated by comp aring their frameerror rates after various number of retransmissions. As shownin Figure 6, there is a 3dB gain in SNR between the frame errorrate (retransmission probability) of TST-HARQ and ST-HARQafter the 2nd transmission. Thi s gain increases slightly for the4th transmission. One can see that TST-H ARQ achieved thesame diversity but with additional cod ing gain du e the parallelconcatenated structure.The throughput of the three protocols are simulated and theresults are shown in Figure 7. In the range of SNR where ST-ARQ completely collapses, ST-HARQ and TST-HARQ proto-cols still have significant throughput. A s expected, the through -put of TST-HARQ protocol is highest among the three schemes.This shows that the proposed T ST-HARQ has a lower averagenumber of transmissions per packet compared to the other twoprotocols.In the last simulation result, the performance of the three pro-tocols in fast lat Rayleigh fading channels is shown in Figure

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1

09

0 8

0 7

0 6az 0 5r

0 4

I

5 10 15Eb/No (dB1-5

Fig. 7. Throughput of Turbo Space-time HARQ , Space-time HARQ, and Space-time ARQ in quasi-static Rayleigh fading channels.1 _ - - -

Fig. 8. Throughput of Turbo Space-time HARQi, Space-time HARQ, andSpace-time ARQ in fast Rayleigh fading channels

8. For fast fading, the throughput of the S T-ARQ protocol isdegraded compared to quasi-static channels. This is because asingle symbo l error is mor e likely. Ov erall there is a wider gap inthe throughput performan ce between the AR Q protocol and theHA RQ protocols in fast fading because the errors are uncorre-lated. This allows th e parallel structure of TST-HARQ transmis-sion to correct more errors. Therefore, the combining method ofTST-HARQ make the m ost of the uncorrelated errors.V. CONCLUSIONS

In this paper, the use of space-time codes in ARQ protocolshas been investigated. ST -ARQ uses space-tim e cod es in a pureARQ protocol. Two hybrid ARQ protocols were proposed toprovide additional efficiency over the pure ARQ protocol. Thefirst, ST-H ARQ , is a diversity combining sc heme that uses mul-tiple copies of the packet to increase the overall diversity. Thesecond, TST-HARQ, uses both diversity combining and codecombining to increase the diversity gain and coding gain witheach retransmission.A simple performance analysis of ST-ARQ and ST-HARQ

was derived that provides a good approximation of theirthroughp ut perform ance in quasi-static fading channels. Byequating the frame error rate of space-time co des to the fram eerror rate of maximum ratio combining of the sa.me diversityorder, an expression fo r the retransmission probability is given.Thi s expression is then used in the throu ghput analy sis and hasbeen shown I:O agree well with simu lated results.Simulations have shown that TST-HA RQ provides superiorperformance over ST-ARQ and ST-HAR Q scheraes. For theSNR range where the throughput of ST-AR Q collapses to zero,the two hybrid schemes still provide some throughput. Thesimulation results were presented for quasi-static and fast flatRayleigh facling channels.

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[ I O ] S. Sayeed, Throughput analysis and design of fixed and adaptivearq/diversity systems for slow fading channels, in froc. o f the IEEEGLOBECOM 1998, Syndney, Aust, 1998, pp. 368 636 91.[1 ] D. Chase, Code combining- a maximum likelihood decoding approachfor combining an arbitrary number of noise packets, E E E Trunsuctionson Comr;?unicutions,vol. COM -33, pp. 385-393, May 198.5.[I21 S. Kallel, Analysis of a type ii hybrid arq scheme with code combining,IEEE Trunsuctions on Communicutions, vol. COM-38, pp. 1133-1 137,August 1990.1131 E. Malkamaki and H. Leib, Evaluating the performanc - of convolutionalcodes oyer block fading channels: IEEE Trunsuction.son Communicu-tions, vol. 45, no. 5, pp. 1643-1646, July 1999.[141 John G. Proakis, Digirul Comm unicufions, McGraw-Hi.1, Inc., New York,NY, 1996.

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