One major assumption in all orthogonal space-time block coding (O-STBC) schemes is that the channel remains static over the entire length of the codeword. However, time selective fading channels do exist, and in such case the conventional O-STBC detectors can suffer from a large error floor in the high signal-to-noise ratio (SNR) cases. This paper addresses such an issue by introducing a parallel interference cancellation (PIC) based detector for the G(i) coded systems (i = 3 and 4)

Burr, A G

Zheng, F C

English

White Rose Research Online

This is a repository copy of Signal detection for orthogonal space-time block coding over time-selective fading channels: A PIC approach for the G(i) systems.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/659/Article:Zheng, F C and Burr, A G orcid.org/0000-0001-6435-3962 (2005) Signal detection for orthogonal space-time block coding over time-selective fading channels: A PIC approach for the G(i) systems. IEEE Transactions on Communications. pp. 969-972. ISSN 0090-6778 https://doi.org/10.1109/TCOMM.2005.849990eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 6, JUNE 2005 969Signal Detection for Orthogonal Space-Time Block Coding Over Time-SelectiveFading Channels: A PIC Approach for the i SystemsF. -C. Zheng and A. G. BurrAbstract—One major assumption in all orthogonal space-timeblock coding (O-STBC) schemes is that the channel remains staticover the entire length of the codeword. However, time selectivefading channels do exist, and in such case the conventional O-STBCdetectors can suffer from a large error floor in the high signal-to-noise ratio (SNR) cases. This paper addresses such an issue by in-troducing a parallel interference cancellation (PIC) based detectorfor the coded systems ( = 3 and 4).Index Terms—Orthogonal space-time block coding (O-STBC),parallel interference cancellation (PIC), time selective fading chan-nels, wireless communications.I. INTRODUCTIONORTHOGONAL space-time block coding (O-STBC)technology has attracted enormous interest due to itshigh diversity order and low decoding complexity [2], [3].The low decoding complexity of O-STBC is directly due tothe linear maximum-likelihood (ML) decoder at the receiver.The linear ML decoder, however, relies on the so-called“quasi-static channel” assumption: the channel remains staticover the length of the entire codeword: for the two transmitantenna (2-Tx) STBC (i.e., – the Alamouti code [1]),for the systems, and for the systems ( for3-Tx, for 4-Tx, where is the symbol period. For thedefinition of and , see [3]). While such an assumption isreasonable in most cases, time selective or fast fading channelsdo exist in practice, even for the 2-Tx case (see [4]–[6] and thereferences therein). In these scenarios, the channel state variesfrom symbol to symbol. Clearly, the 3- and 4-Tx O-STBCcases (especially the systems) are much more vulnerable tochannel variation than the 2-Tx case due to the much longerSTBC codeword.The above channel variation will destroy the orthogonality ofthe channel matrix and therefore, cause inter element interfer-ence (IEI). The end effect of all this is an irreducible error floorin the bit error rate (BER) curves in the high signal-to-noise ratio(SNR) region. To suppress such an error floor in the 2-Tx case,Paper approved by A. F. Naguib, the Editor for Wireless Communication of theIEEE Communications Society. Manuscript received August 3, 2003; revisedNovember 22, 2004. This work was supported by the Engineering and PhysicalSciences Research Council (EPSRC), U.K., under Grant GR/R94428/01. Thispaper was presented in part at the 59th IEEE Vehicular Technology Conference,Milan, Italy, May 2004.F.-C. Zheng was with the Department of Electronics, University of York,York YO10 5DD, U.K. He is now with the School of Electrical Engineering,Victoria University of Technology, Melbourne, Vic. 8001, Australia (e-mail:fzheng@ieee.org).A. G. Burr is with the Department of Electronics, University of York, YorkYO10 5DD, U.K.Digital Object Identifier 10.1109/TCOMM.2005.849990an elegant decoder was presented in [4] and [5]. Since the de-coder structure in [4] and [5] cannot be used for the 3- or 4-Txcase, a simple zero forcing (ZF) scheme for the and sys-tems was proposed in [7] while a more effective version of theZF scheme was derived in [8].This paper proposes an alternative approach to the ZFdetector in [7] and [8]. Based on the principle of parallelinterference cancellation (PIC), the new detector (termed “PICdetector”) offers an even better performance than the ZF de-tector. The computational complexity of the PIC detector ishigher than that of the conventional and the ZF detector, butis still very affordable. Only the coded systems are consid-ered in this paper (the coded systems was addressed in [16]and [17]).II. MODEL FOR THE SYSTEMConsider a typical encoded 4-Tx O-STBC system with4 transmit (4-Tx) and 1 receive (1-Rx) antennas. A group offour complex symbols, , , , and , are passed through aencoder before transmitted over . The encoder output istherefore, a 8 4 matrix , where is , or(conjugate of ), and is transmitted by Tx at time . Also, byletting the channel gain from Tx to the Rx at time be ,the received signal at time is(1)where is a complex additive white Gaussian noise(AWGN) with zero mean and a variance of (there-fore, per dimension). Also, is subject toRayleigh fading but is normalized, i.e., , or ,.The “quasi-static channel” assumption in all O-STBCschemes requires that constant over the entirecodeword length. This, in the case of and systems,means that the channel remains static over . It has beenshown in [7], [8], [14] that even under normal vehicle speeds,the assumption of “quasi-static channel” may not hold for the4-Tx STBC (e.g., and ) systems. As such, this paperassumes that the channel is static over only and from oneto the next, it is time variant. Clearly, this is a much moregeneral and realistic model with the quasi--static channel nowbecoming a special case. Perfect channel state information(CSI) is assumed in this paper. For the estimation of CSI, see[6] and [9]–[12].0090-6778/$20.00 © 2005 IEEE970 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 6, JUNE 2005III. CONVENTIONAL O-STBC DETECTORFOR THE SYSTEMFor symbol group , the code matrix foris [2], [3](2)From (1), the “manipulated received signal vector”can then be written as(3)where the channel matrix(4),, , 3, 5, 7, and.At the receiver end, the conventional O-STBC detector as-sumes that the channel is time invariant over the entire pe-riod. Regardless of any channel variation, the following expres-sion is effectively employed:(5)where is the estimated channel matrix for the “quasi-staticchannel”:(6)with , , and .It can be proved that the “linear maximum-likelihood (ML)”detector in [3] is equivalent to the following two-step proce-dure [7], [8]:[Step C1] Apply linear transform to the received signal:(7)[Step C2] Carry out the “linear ML” detection:(8)Here, , is the symbol alphabet, the th elementof , and (i.e., the th element of diagonal).In reality, however, the true physical process in Step C1 is(9)Note that in general in (9) is nondiagonal(10)The conventional 2-step linear detection procedure is truly MLif and only if the channel is truly static over , in which caseand thus for , and .For a time selective fading channel, however, andthus for . Physically, this leads to inter element in-terference (IEI). The value of the nondiagonal depends uponthe time-selectivity of the channel. When using the above con-ventional detector (thus the decoder in [3]) for a time selec-tive fading channel, these nonzero ’s are effectively ignored,resulting in extra detection errors in addition to those causedby the AWGN. These extra errors will form an irreducible errorfloor in the BER curves in the high SNR region.IV. PIC DETECTOR FOR THE SYSTEMAlthough (for ) in (10), it is also true thatnormally . This is because under normal vehiclespeeds or Doppler spread, the channel variation over stilltends to be relatively small. As an example, let us considerthe following popular AR(1) model for time-selective channels[4]–[11]:(11)where is another i.i.d. complex Gaussian random vari-able having zero mean and variance and being statisticallyindependent of . Also,, where is the Doppler frequency andis the 0th order Bessel function of the first kind. If the fadingpaths originate sufficiently far away from the receiver, canbe assumed to be the same for all the transmitter antennas. Toillustrate the dominance of , similarly to [14], we introducethe following “nondiagonal index”:(12)where denotes the Frobenius norm of , and matrixcomprises the nondiagonal elements of : .Clearly, the above index reflects the ratio of the squared mag-nitude of the nondiagonal elements to the squared magnitude ofthe diagonal elements in , and its value is dependent upon theDoppler spread of the channel. The relation between the non-diagonal index and is demonstrated in Fig. 1, which isobtained using 40 000 and realizations. It is easy to seethat for the normal range of Doppler spreads we always have.Based on the above observation, we can now apply the prin-ciple of parallel interference cancellation (PIC) to (9). As is wellIEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 6, JUNE 2005 971known, PIC (although suboptimum) is an effective yet simpleapproach in multiuser detection of CDMA (there is a rich lit-erature on PIC for CDMA. See e.g., [15] and all the referencestherein).A. Algorithm[Step P1] Initialization: Set iteration number , andobtain from the conventional O-STBC decoder via (7) and(8): .[Step P2] Iteration: For iteration number ,(13)The symbol detection for the current iteration can then beachieved via a simple least square approach(14)where is the symbol alphabet, and is the th elementof . Also, .As in a CDMA PIC detector, the above procedure comprisestwo components: tentative symbol estimation (TSE) and ten-tative interference subtraction (TIS). With the iterations pro-gressing, the TSE will contain fewer and fewer errors, makingthe TIS more and more accurate. Once the IEI related errorshave been eliminated, (14) becomes a linear ML procedure.This explains why the PIC detector potentially offers a muchbetter performance than the corresponding ZF detector. As tothe number of iterations, our simulations have shown thatiterations normally deliver most of the gain.B. Algorithm Discussion1) Quasi-Static Channels and Algorithm Evolution: Whenthe channel is indeed static over the entire period (i.e.,), the Initialization step (i.e., the conventional O-STBCdetector) will give the optimum solution. In such a special sit-uation, as and , the iterations in (13) and(14) will not alter the already optimum initial solution. To thisextent, the PIC detection algorithm represents an evolution ofthe conventional O-STBC detector.2) Algorithm Complexity: Compared with the conventionaldecoder, the main computation increase for the PIC detectoris from the calculation of matrix and the extra iterations in(13) and (14). It is easy to show that the total increase involves[ ] complex number (CN) multiplicationsand [ ] CN additions per symbol, where is themodulation level and is the number of iterations. This means,for and , 105 CN multiplications and 53 CN ad-ditions per symbol. On the other hand, the complexity increaseof the ZF scheme in [8] is 34 CN multiplications and 25 CNadditions (regardless of ). Therefore, the computational com-plexity of the PIC detector is higher than that of both the con-ventional and the ZF decoders [7], [8] (the surprisingly lowercomplexity of the ZF schemes is due to the special matrix al-gorithms in [7] and [8], which only involves the inversion of2 2 matrices). As is normally small ( ), however, theextra computation in the PIC detector is still moderate (com-pared with the full ML search over all 4 symbols, whose com-plexity is ), and can well be justified by the enormousperformance improvement.Fig. 1. Value of nondiagonal index  with respect to f T .Fig. 2. BER performance of the PIC G detector with respect to the numberof iterations (I).3) Encoded Systems: By setting in (1) and allthe other related equations, the above PIC detector can directlybe used in the encoded systems.V. SIMULATIONSThe system under 16-QAM (Gray encoded) modulationand the time selective fading channel in (11) are employed. Thesignal to noise ratio (SNR) at the receiver is defined as(since ), where is theTx power at each antenna, and (for the system).Also, the UMTS symbol rates are considered:with GHz, where SF is the spreading factor(in UMTS) but in our simulations is simply a parameter foradjustment.Five vehicle speeds are simulated: (quasi-staticchannels), 70, 100, 130, and 160 km/h (leading to differentvalues) for (or equivalently , 35, 50, 65,and 80 km/h for ). These correspond to thevalues of 0, 0.0043, 0.0062, 0.0080, and 0.0099 (see Fig. 1for the corresponding values of the nondiagonal index ). For972 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 6, JUNE 2005Fig. 3. BER performance of the PIC G detector for I = 3.Fig. 4. BER performance of the conventional G detector (i.e., I = 0).the case of , the BER details of the PIC for(i.e., the conventional decoder), 1, 2, and 3 are shownin Fig. 2. Clearly, two or three iterations deliver most of theperformance gain even for such a case of relatively high speed.For all the other speeds, only the BER results for areplotted in Fig. 3. For comparison, the results of the conven-tional detector are shown in Fig. 4. It is easy to see that thePIC detector exhibits no error floor while the conventionaldetector does. Most importantly, the BER degradation of thePIC caused by channel variation is very small indeed withinthe considered range. The penalty, however, is a relativelyhigher computational complexity.Our simulations (not shown here) have also indicated that theabove PIC detector works well right up to around 240 km/h (150miles/h) for (i.e., ). For the evenhigher speeds (or values), however, it may incur more than3 iterations or even a residual error floor. This obviously is notan issue for the ZF schemes in [7] and [8]. All the aboveobservations also apply to the coded 3-Tx systems.VI. CONCLUSIONSThis paper has presented a PIC based detector structure forthe O-STBC systems over time-selective fading channels.While the conventional detectors under such conditions tendto suffer from a considerable irreducible error floor in the highSNR cases, the PIC detector shows no error floor at all for thenormal speed range. The PIC’s relatively higher computationalcost can be justified by its enormous performance gain.REFERENCES[1] A. M. Alamouti, “A simple transmit diversity techniques for wirelesscommunications,” IEEE J. Sel. Areas Commun., vol. 16, no. 8, pp.1451–8, Oct. 1998.[2] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time blockcodes from orthogonal designs,” IEEE Trans. Inf. Theory, vol. 45, pp.1456–67, Jul. 1999.[3] , “Space-time block coding for wireless communications: Perfor-mance results,” IEEE J. Sel. Areas Commun., vol. 17, no. 3, pp. 451–460,Mar. 1999.[4] T. A. Tran and A. B. Sesay, “A generalized simplified ML decoder of or-thogonal space-time block code for wireless communications over time-selective fading channels,” in Proc. IEEE VTC 2002-F, May 2002, pp.1911–1915.[5] , “A generalized linear quasi-ML decoder of OSTBC’s for wire-less communications over time-selective fading channels,” IEEE Trans.Wireless Commun., vol. 3, no. 3, pp. 855–864, May 2004.[6] Z. Liu, X. Ma, and G. B. Giannakis, “Space-time coding and Kalmanfiltering for time-selective fading channels,” IEEE Trans. Commun., vol.50, no. 2, pp. 183–6, Feb. 2002.[7] F.-C. Zheng and A. G. Burr, “Receiver design for orthogonal space-timeblock coding for four transmit antennas over time-selective fading chan-nels,” in Proc. IEEE GLOBECOM, vol. 1, San Francisco, CA, Dec.2003, pp. 128–132.[8] , “Double diagonalization: an improved zero-forcing detector fororthogonal stbc over time-selective fading channels,” in Proc. IEEE VTC2005-F, Dallas, TX, Sep. 2005.[9] R. A. Iltis, “Joint estimation of PN code delay and multipath using theextended Kalman filter,” IEEE Trans. Commun., vol. 38, no. 10, pp.1677–1685, Oct. 1990.[10] A. W. Fuxjaeger and R. A. Iltis, “Adaptive parameter estimationusing parallel Kalman filtering for spread spectrum code and Dopplertracking,” IEEE Trans. Commun., vol. 42, no. 6, pp. 2227–2230, Jun.1994.[11] M. K. Tastsanis, G. B. Ginannakis, and G. Zhou, “Estimation of fadingchannels with random coefficients,” Signal Process., vol. 53, no. 2/3, pp.211–229, 1996.[12] M. Enescu and V. Koivunen, “Time-varying channel tracking for space-time block coding,” in Proc. IEEE VTC 2002-S, vol. 1, Birmingham, AL,May 2002, pp. 294–297.[13] O. Tirkkonen, A. Boariu, and A. Hottinen, “Minimal nonorthogonal rate1 space-time block code for 3+ Tx antennas,” in Proc. 6th IEEE ISSSTA,Sep. 2000, pp. 429–432.[14] F.-C. Zheng and A. G. Burr, “Space-time block coding for four transmitantennas over time-selective fading channels: Orthogonal or nonorthog-onal design?,” in Proc. IEEE VTC 2003-F, vol. 1, Orlando, FL, Oct.2003, pp. 513–517.[15] D. Divsalar, M. K. Simon, and D. Raphaeli, “Improved parallel interfer-ence cancellation for CDMA,” IEEE Trans. Commun., vol. 46, no. 2, pp.258–268, Feb. 1998.[16] F.-C. Zheng and A. G. Burr, “Orthogonal space-time block coding overtime-selective fading channels: A PIC detector for the H systems,” inProc. IEEE ICC 2004, vol. 2, Paris, France, Jun. 2004, pp. 687–691.[17] F.-C. Zheng and A. G. Burr, “Signal detection for orthogonal space-timeblock coding over time-selective fading channels: The H systems,”IEEE Trans. Wireless Commun., to be published.

Signal detection for orthogonal space-time block coding over time-selective fading channels: A PIC approach for the G(i) systems

One major assumption in all orthogonal space-time block coding (O-STBC) schemes is that the channel remains static over the entire length of the codeword. However, time selective fading channels do exist, and in such case the conventional O-STBC detectors can suffer from a large error floor in the high signal-to-noise ratio (SNR) cases. This paper addresses such an issue by introducing a parallel interference cancellation (PIC) based detector for the Gi coded systems (i=3 and 4)

Zheng, F.-C.

Burr, A. G.

Central Archive at the University of Reading

Signal detection for orthogonal space-time block coding over time-selective fading channels: a PIC approach for the Gi Systems

Abstract—One major assumption in all orthogonal space-time block coding (O-STBC) schemes is that the channel remains static over the entire length of the codeword. However, time selective fading channels do exist, and in such case the conventional O-STBC detectors can suffer from a large error floor in the high signal-to-noise ratio (SNR) cases. This paper addresses such an issue by in-troducing a parallel interference cancellation (PIC) based detector for the coded systems (  = 3 and 4). Index Terms—Orthogonal space-time block coding (O-STBC), parallel interference cancellation (PIC), time selective fading chan-nels, wireless communications. I

F. -c. Zheng

A. G. Burr

CiteSeerX

Signal detection for orthogonal space-time block coding over time-selective fading channels: a PIC approach for the Z3 systems

F.-C. Zheng

A.G. Burr

Crossref

Signal Detection for Orthogonal Space-Time Block Coding Over Time-Selective Fading Channels: A PIC Approach for the&lt;tex&gt;$ cal G_i$&lt;/tex&gt;Systems

https://eprints.whiterose.ac.uk/659/1/burrag1.pdf

Signal detection for orthogonal space-time block coding over time-selective fading channels: A PIC approach for the G(i) systems

Abstract

Similar works

Full text

Available Versions

White Rose Research Online

Central Archive at the University of Reading

CiteSeerX

Crossref