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1 Cooper, M. A., Armour, S. M. D., & McGeean, J. P. (2003). Downlink performance and complexity evaluation of equalisation strategies for an MC- CDMA 4G pysical layer candidate. Link to publication record in Explore Bristol Researc PDF-document University of Bristol - Explore Bristol Researc General rigts Tis document is made available in accordance wit publiser policies. Please cite only te publised version using te reference above. Full terms of use are available: ttp:// Take down policy Explore Bristol Researc is a digital arcive and te intention is tat deposited content sould not be removed. However, if you believe tat tis version of te work breaces copyrigt law please contact open-access@bristol.ac.uk and include te following information in your message: Your contact details Bibliograpic details for te item, including a URL An outline of te nature of te complaint On receipt of your message te Open Access Team will immediately investigate your claim, make an initial judgement of te validity of te claim and, were appropriate, witdraw te item in question from public view.

2 Downlink Performance and Complexity Evaluation of Equalisation Strategies for an MC-CDMA 4G Pysical Layer Candidate M. A. Cooper 1, S. M. D. Armour 1, J. P. McGeean 1,2 1 Centre for Communications Researc, University of Bristol, Woodland Road, Bristol, U.K. 2 Tosiba Researc Europe Ltd., 32 Queen Square, Bristol, BS1 4ND, U.K Tis paper focuses on te performance of equalisation strategies for a downlink MC-CDMA (Multi Carrier - Code Division Multiple Access) based system. MC-CDMA is a leading candidate modulation/multiple access sceme for so called 4 t Generation communications. Simulation results utilising Maximum Ratio Combining (MRC), Equal Gain Combining (EGC), Ortogonal Restoring Combining (ORC), and Minimum Mean-Squared Error Combining (MMSEC) for multi-user scenarios are presented. Performance is caracterised by bit error rate () for te downlink. A time domain least square cannel estimator was implemented along wit a frequency based pilot estimation sceme and comparisons made wit perfect cannel estimation. A complexity analysis of eac equalisation sceme is also undertaken. Performance results sow tat MMSEC provides te best performance for te multi-user scenario as MRC and ultimately EGC bot enter error floors as te number of users increase in a wideband cannel tereby reducing teir usefulness as multi user equalisation scemes. M I. INTRODUCTION ULTICARRIER Code Division Multiple Access (MC-CDMA) is igly regarded as a possible candidate for implementation in te Fourt Generation (4G) Pysical Layer (PHY) wic aims to bridge te gap between existing cellular mobile networks, and fully integrated self organising ad-oc networks. Tird Generation (3G) tecnology utilising CDMA as a PHY realises te implementation of efficient packet based operation wilst offering enanced data rates over current circuit switced 2G systems suc as GSM (Groupe Spécial Mobile). Existing 3G CDMA services offer data rates in te range of a few undred kb/s in macro- and micro-cell environments to a few Mb/s in pico-cellular environments [1]. Current WLAN standards suc as ETSI BRAN HIPERLAN/2 [2] as well as IEEE a [3] are capable of providing coverage up to 100m in indoor environments for data rates up to 54Mb/s troug te use of Coded Ortogonal Frequency Division Multiplexing (COFDM) [4]. Te support of macro-cellular as well as sorter range WLAN type services poses a unique set of design requirements in terms of mobility, traffic density, radio propagation environments, coverage and spectrum usage, wic must be accommodated by te 4G standard [5,6]. One vision of 4G tecnology aims to combine te PHY capabilities of CDMA and OFDM in a ybrid system known as MC-CDMA. Multipat effects ave been seen to provide a potential obstacle in te pat to acieving successful radio communication. Frequency selective fading [7] in a wideband cannel as been sown to result in a number of important and potentially catastropic effects on unsuitable modulation scemes. Excess delay spread traditionally leads to te spreading of symbol energy into subsequent data symbols leading to te undesirable effects of Inter-Symbol Interference (ISI). Besides te benefits described above, multicarrier tecniques (including MC-CDMA) ave been sown to limit tese undesirable effects troug te exploitation of te frequency selective nature of a cannel. Multi-Carrier CDMA, as described in [8-10], operates using two principles. Exploitation of te frequency selective nature of a wideband cannel troug COFDM implementation requires te transmission of coded data on narrowband carriers spanning a frequency selective cannel. Carriers are be overlapped to acieve good spectral efficiency wit ISI prevented by te insertion of a guard interval between eac symbol in te time domain. Doppler effects also give rise to Inter-Carrier Interference (ICI) wic cannot be compensated for in te receiver. Te utilisation of a spreading code in te frequency domain results in eac data bit being transmitted over a number of sub-carriers. Tis provides increased immunity to frequency selective fading troug te copying of multiple data symbols placed in te frequency domain. Spreading troug te use of ortogonal Hadamard codes provides a multi-user capability. However, frequency selective fading can destroy ortogonality between tese codes, tereby reducing performance as te number of users and delay spread increases. Tis paper is organised into sections as follows: In Section II te structure of a 4G candidate PHY specification based on MC-CDMA is outlined. Details Proceedings Symposium IEEE Benelux Capter on Communications and Veicular Tecnology, 2003, Eindoven

3 of te cannel models and software simulations used to evaluate tis PHY specification along wit te equalisation strategies are given in Section III. Te results of tese simulations are given in Section IV and te complexity analysis presented in Section V. Tese lead to te conclusions and comments on detailed in Section VI. II. SIMULATION STRUCTURE Multicarrier CDMA involves te concurrent transmission of identical data on multiple sub-carriers witin an OFDM symbol. Eac OFDM symbol consists of a summation of sub-carriers eac of wic is modulated to give a transmitted signal S were te elements of S [1-1] (for te case of BPSK modulation). Ortogonality of eac sub-carrier is acieved by making te carrier frequency spacing f, equal to te inverse of te active symbol period, T a. Te concept of ortogonality can be described by te matematical relationsip [11], were n and l form an ortogonal basis function set: t + t T a ϕ ( t ) ϕ n l * ( t ) dt n t carrier: ϕ ( t) = e n jnω t a 0 = T a n l n = l 2π ωa = 2 πf a = T a (1) Te MC-CDMA signal consisting of SC subcarriers is considered, were SC is defined by te product of te spreading code of lengt M, and te number of (coded) bits per OFDM symbol, P. Te following sections describe te MC-CDMA modem considered in tis paper wose arcitecture is sown in Fig. 1. A. FEC Coding and Decoding Forward Error Correction (FEC) coding troug te application of a ½ rate convolutional code wit constraint lengt K = 7, {133,171} octal, in te transmitter and te subsequent utilisation of soft decision Viterbi decoding in te receiver was considered. Te Viterbi algoritm utilises Minimum Likeliood Sequence Estimation (MLSE) metrics wic are computed from bot te received signal and te Cannel State Information (CSI). Te decoder adds log-likeliood ratios wic accumulate te likeliood of eac possible sequence, as opposed to dealing wit pure probability summations. Tese metrics are directly proportional to te distance to te decision boundary. It can normally be assumed tat te lengt of sequence taken into account for eac bit decision need be no longer tan 5K for an unpunctured code [12]. Longer sequences will provide only a negligible improvement in performance. B. Spreading Spreading is acieved troug te use of Wals- Hadamard codes. Te Hadamard matrix H containing i rows and j columns were i = j = M and is defined by:- H 2 1 = H M H ( M 2) H ( M 2) = H ( M 2) H ( M 2) Te elements of H are [1-1] and form a mutually ortogonal set despite te fact tat te auto-correlation and periodic cross-correlation properties are not optimal [13]. Te Wals-Hadamard matrix is a manipulation of H were te number of transitions between +1 and -1 for te i rows and j columns is denoted by R i and R j respectively. R i and R j are ordered sequentially were R R = 0 for[ i, j] = 0. i = j Fig. 1. MC-CDMA Simulation Arcitecture

4 TABLE I PILOT AND ZERO LOCATIONS FOR FD AND TDLS CSI Pilot Locations 1 Z 17 Z (w 1) (w - 17) C. Bit and Pilot Location Along wit te inclusion of training sequences at te start of a packet (as detailed below), pilots were inserted in te frequency domain at regular spacings. Te number of pilot symbols is given by (FFT size * 1 / 16 ). Zeros are inserted in te baseband signal at bot te upper and lower edges of te frequency symbol. Tis is to avoid te effects of frequency aliasing wic may occur in te receiver. Te carrier at ((FFT size / 2) + 1) wic represents te carrier at DC is likewise avoided for transmission, to avoid te effects of carrier feed-troug and DC offsets. Te total number of zeros is given by (FFT size * 3 / 16 ) wit all oter locations (FFT size * ¾) in te frequency domain containing coded data. Table I details te pilot and zero locations were p w is te sub-carrier index for pilot number w. D. IFFT Ortogonal Modulation was acieved using a 512- point Inverse Fast Fourier Transform (IFFT). Subsequent addition of a cyclic prefix (or guard interval) to prevent ISI is also required. Te requirement to prevent ISI is tat te guard interval duration, T g, must be longer tan te excess delay spread of te cannel. Te total symbol duration T symbol is defined in (2) were T u is te duration of te useful (unextended) symbol period. T = T + T (2) symbol A summary of Pysical Layer Parameters for te system considered are specified in Table II. Parameter TABLE II SIMULATION PARAMETERS u g Value Modulation BPSK Total Sub-carriers N 512 Spreading Factor, SC 32 Coding Rate ½ Useful Symbol Duration T u V Sub-carrier Spacingà I 8kHz Guard Interval Duration T g 19.5 V Total Symbol Duration T symbol V OFDM Symbols per second V No. of COFDM Symbols in Packet 100 Operating Frequency 2GHz Bandwidt B 4.096MHz Coded Bits per Sub-carrier (N BPSC) 1 Coded Bits per OFDM Symbol (N CBPS) 384 Data Bits per OFDM Symbol (N DBPS) 192 Coded Data Rate (Mb/s) Nominal Data Rate (Mb/s) Zero Locations 1,, 48, 256, 466,, 512 E. Training Sequence Insertion In order to facilitate cannel estimation in te receiver using coerent detection, known data sequences were inserted in to te transmitted sequence. Tese facilitate CSI derivation in te receiver. Te packet consists of 100 OFDM symbols and 2 pilot symbols leading to a total packet duration of 14.7ms. It is assumed tat te system operates witin te coerence time of te cannel. F. Cannel Estimation Perfect CSI was assumed for a comparative investigation into tese equalisation scemes. In addition, a time domain least squares (TDLS) metod as described in [14,15] was implemented in order to provide a more realistic cannel estimation based on te training sequences and pilots inserted into te transmitted sequence. Likewise a frequency domain (FD) pilot estimation metod was also compared. Fig. 2. Revised cannel estimation utilising a time domain cannel metod wereby te impulse cannel response is limited before subsequent application in te equaliser. Te two pilot symbols located at te start of te packet were utilised for tis estimation. Subsequent to te IFFT in Fig. 2, te resulting cannel impulse response was windowed in time to te corresponding number of filter taps in te cannel as sown in Fig. 3. Impulse response values falling outside tis window (i.e. occurring after te cut-off boundary) were discarded and replaced wit zeros. Te revised signal was ten converted back into te frequency domain and applied to te data packet. For te case of an unknown cannel order, te window lengt could be specified to be equal to te guard interval duration or could be calculated by using a tresold level calculated from a sent impulse delta function. Fig. 3. Power Delay Profile sowing te extraction and discarding of values exceeding te defined cut-off condition. In practice tis corresponds to te number of taps in te wideband cannel.

5 III. SIMULATION MODEL A software simulation of te above system was designed to investigate te performance of te equalisation scemes detailed in Table IV for te case of te downlink. Simulations were conducted for a quasi-stationary Rayleig fading wideband cannel were it could be assumed tat a number of OFDM symbols representing a packet of data are transmitted witin te coerence time of te cannel. Te cannels utilised in tese simulations are based on te European Telecommunication Standards Institute (ETSI) UMTS Terrestrial Radio Access (UTRA) standard [16] for use in te veicular environment, as detailed in Table III. A wideband cannel model is assumed based on a tapped delay line model wic provides a statistical approac assuming Wide Sense Stationary Uncorrelated Scattering (WSSUS). Tis as te advantage over oter tecniques suc as ray tracing of being computationally efficient [17]. A Rayleig distributed function wit zero mean and variance as defined by te mean power delay profile of te cannel is generated for eac tap suc tat te amplitude at eac tap for eac sub-carrier is an independent and identically distributed (iid) random variable. Te pase is assumed to take random iid eac sub-carrier. Te cannel impulse response (CIR) over a multipat cannel assuming L pats is given as IROORZV ZKHUH DQG n are te time delay and SURSDJDWLRQ GHOD\ UHSUHVHQWV WKH DPSOLWXGH variation, and represents te pase variation. Effective equalisation strategies are critical in ensuring te maximisation of te inerent benefits of MC-CDMA in a multipat fading environment in wic te frequency selective fading will cause different cips (transmitted on different sub-carriers) to be subject to different gains and attenuations. Tis results in different cips aving different SNRs. It may also compromise te ortogonality of spreading codes assigned to different users. MC-CDMA based scemes utilising coerent detection tecniques can employ te equalisation tecniques of Maximal Ratio Combining (MRC), Equal Gain Combining (EGC), Ortogonality Restoring Combining (ORC), and Minimum Mean Square Error Combining (MMSEC) wit teir inerent strengts and weaknesses in tandem wit an appropriate cannel estimation tecnique. Te compensation vectors are given in Table IV wic are applied to y k to give z k, were z k = G * yk. For MMSEC J denotes te number of active users. TABLE IV EQUALISATION COEFFICIENT FORMULAE Equalisation Tecnique Compensation Vector MRC G MRC = * ( τ, t) L 1 = l= 0 α ( t). e l jφl t) ( τ τ ) (. δ (3) n EGC * G EGC = Te received signal y k at a given sub-carrier k, is represented as follows, were H k is te frequency response of te cannel for sub-carrier k, x k te transmitted signal for sub-carrier k, and n k te complex noise vector wic is assumed to be mutually statistically independent wit identical autocorrelation functions for eac sub-carrier [12]. Perfect sub-carrier syncronisation and zero pase offset are assumed. ORC G ORC = 2 MMSEC G MMSEC = 2 + * J ( E N ) SC b * o y = H x + n (4) k k k k Model No. Description TABLE III CHANNEL MODELS RMS Delay Spread (ns) Max. Delay Spread (ns) No. of taps Maximum Relative Velocity of Tx/Rx (km/) Maximum Doppler at 2GHz (Hz) 1 Indoor A Indoor B Outdoor Indoor Pedestrian A Outdoor Indoor Pedestrian B Veicular A Veicular B

6 IV. RESULTS A performance comparison of te UTRA defined cannel models for COFDM are sown in Fig. 4 using perfect CSI, and clearly sow te extent to wic delay spread contributes to give increased performance troug increased frequency diversity of a cannel. MC-CDMA downlink transmission simulation results for UTRA cannel model 4 assuming a quasistationary cannel are presented in Figs. 5-8 were perfect CSI is assumed. Cannel Model 1 Cannel Model 2 Cannel Model 3 Cannel Model 4 Cannel Model 5 Cannel Model 6 interference wit a penalty paid for te noise enancement effects wilst avoiding an error floor. Users = 1 Users = 8 Users = 16 Users = 24 Users = Fig. 5. MRC multi-user performance comparison. Results sow te presence of an error floor at ig Eb/No for large numbers of users due to te loss of ortogonality between users Users = 1 Users = 8 Users = 16 Users = 24 Users = 32 Fig. 4. COFDM performance comparison of UTRA defined cannel models. For te single user scenario it is sown tat MRC sligtly outperforms EGC due to te pre-detection weigting of eac sub-carrier wit respect to its SNR. Tis is in contrast to EGC wic provides equal weigting regardless of SNR. Under conditions of a large number of concurrent users, MRC can be seen to enter an error floor at ig E b /N o values at te value of interest. Tis is due to tis loss of ortogonality between codes and terefore users in a frequency selective cannel. A more frequency selective cannel will compound te problem of ortogonality loss between codes at tese E b /N o values raising te error floor. EGC would also be expected to exibit an error floor but te extent to wic tis exists is lower tan for MRC. Te performance results for ORC are displayed in Fig. 7, and sow te effects of severe noise amplification in sub-carriers wit a low SNR leading to an overall poor performance. Tis occurs as ORC provides cannel inversion equalisation coefficients leading to ig noise amplification. In cases were te maximum number of users is supported ten ORC is seen to produce superior performance over MRC due to its inerent ability to maintain ortogonality between users even in a frequency selective environment, and ence will never enter an error floor. Compreensive simulations carried out wic concur wit tose given in [9] ave revealed tat ORC is able to eliminate multi-user Fig. 6. EGC multi-user performance comparison. Single user results sow a comparative performance to MRC, but a superior performance to MRC as te number of users increase. EGC will tend to an error floor at iger Eb/No as well as in a more frequency selective cannel. For te low multi-user scenario MMSEC provides similar performance to MRC and EGC. However for te ig multi-user scenario MMSEC provides te best performance over te oter scemes due to its ability to avoid severe noise amplification at low SNRs, and to maintain ortogonality at ig SNRs. Investigation results into te frequency domain (FD) training sequence cannel estimation and te time domain least squares (TDLS) metod are sown in Fig. 9. Tese two metods provide a cannel estimate derived from te transmission and subsequent averaging of two OFDM pilot symbols sent at te start of te data packet. Te FD cannel estimation led to a degradation in performance of 1.6dB. However te TDLS metod improves tis performance by providing a noise limited cannel estimation and resulted in only a negligible degradation in performance over te assumed perfect CSI case.

7 Users = 1 Users = 8 Users = 16 Users = 24 Users = Fig. 7. ORC multi-user performance comparison sowing te ability of tis equalisation tecnique to maintain ortogonality between many concurrent users, tereby outperforming MRC and EGC at ig Eb/No values. Poor performance at low Eb/No values is due to te noise amplification of tese sub-carriers. Users = 1 Users = 8 Users = 16 Users = 24 Users = Fig. 8. MMSEC multi-user performance comparison. Results sow te ability of MMSEC to avoid severe noise amplification at low Eb/No values in te ig user case, wilst maintaining ortogonality at ig Eb/No values. Perfect CSI TDLS CSI FD CSI Fig. 9. performance comparison utilising perfect CSI, a frequency domain (FD) training sequence and te time domain least squares (TDLS) metod of cannel estimation for single user MMSEC equalisation. V. COMPLEXITY In order to undertake a fair comparison of te equalisation strategies and cannel estimation strategies it is necessary to consider teir complexity as well as teir performance. Te complexity requirements of eac of tese tecniques sould also be considered in te context of te overall baseband processing requirement. Tis is done below, initially in terms of te number of operations required per OFDM symbol and subsequently translated in terms of Millions of Instructions per Second (MIPS) requirements. Te FFT as been te subject of considerable researc aimed at optimising its implementation in digital ardware. For te 512-point FFT considered ere for te multi-carrier demodulation, split radix implementations can yield a computation requirement as low as 3,076 Real Multiplications and 12,292 real additions [18]. P less real additions tan te number of data bearing sub-carriers are required in order to despread te data. Cannel estimation in its basic form nominally requires 1 complex division per sub-carrier to be performed. However, if suitable pilot symbols are employed in te training sequence (i.e. wit unit amplitude and zero pase) tese divisions can be rendered trivial. If two training sequences are transmitted sequentially to improve performance in additive noise, as is te case considered ere, one complex addition per active (data or pilot) sub-carrier is required in order to average te received symbols (division by two is considered a trivial operation). Te time domain least squares cannel estimation metod adds a requirement for an additional FFT and IFFT pair besides tat used in te demodulation process. It sould be noted tat as stated in [15] te requirements of tese operations are not strictly tose of full FFT/IFFT operations. However, tis metod as not been subjected to te same toroug optimisation as te conventional FFT algoritm and so te complexity requirements given above will be considered ere as a worst case. MRC and EGC require a complex multiplication to be performed for eac data bearing sub-carrier. ORC and MMSEC require additional real operations to accommodate te necessary real divisions. Wilst te estimation of signal to noise ratio for MMSEC is not a trivial undertaking, a single estimate may be obtained for eac received OFDM symbol and scaled according to te CSI to produce te relevant value. Tis parameter is also only subject to slow fading and will not require update on a symbol by symbol basis. According to [19], a complex multiplication may be implemented as 3 real multiplications and 5 real additions. A complex addition requires 2 real additions. On te basis of tis and OFDM symbol period, te number of operations required for eac possible combination of cannel estimation and equalisation can be evaluated in terms of te required MIPS. Tis information is given in Table V.

8 TABLE V COMPLEXITY ANALYSIS MIPS % for Cannel Estimation % for Equalisation Basic TDLS Basic TDLS Basic TDLS MRC, EGC ORC MMSEC From Table V it can be seen tat te coice of equalisation strategy does not ave a uge impact on te overall complexity requirement of te receiver. Given its superior performance and relatively low additional computation requirement, MMSEC would appear te strongest equalisation option. All te equalisation strategies require a relatively small fraction of te overall computation due to te large computational requirement of oter parts of te receiver; particularly te FFT. Tis is exacerbated wen TDLS cannel estimation is used. Tis cannel estimation metod would appear to add significant computational overead altoug te value considered ere is most likely a worst case and tis sould be evaluated against te performance benefit tat it offers over oter tecniques. VI. CONCLUSIONS Simulations conducted in to te performance of a coded BPSK modulated multi carrier CDMA system sow tat a frequency selective cannel can be exploited to acieve increased performance. Results sow tat bot MRC and EGC equalised signals exibit an increasingly ig error floor as te number of concurrent users increases. Tis is due to a loss of ortogonality between users utilising Wals- Hadamard codes caused due to a non-flat cannel spectrum. Te loss of ortogonality effects are more pronounced in MRC tan EGC. ORC is able to avoid tis error floor by maintaining ortogonality of te codes, and as suc an increase in user numbers does not ave any effect on performance. MMSEC is also able to avoid tese problems as te algoritm successfully maintains ortogonality at te of interest. performance in te single user case sows tat MRC is able to provide te best performance of all te scemes due to its ability to feed weigted values into te bit decision variable. ORC provides te worst performance in tis case due to noise amplification issues. For te single user case, te Eb/No required to acieve a of are 9.6dB, 9.8dB 16.5dB and 9.8dB for MRC, EGC, ORC and MMSEC respectively. At te maximum user scenario, te E b /N o required to acieve a performance of was 12.2dB, 10.4dB, 16.5dB and 10.2dB for MRC, EGC, ORC and MMSEC. As te number of users increase, it can be seen tat MMSEC provides te best performance, significantly exceeding tat of ORC. Te training sequence approac to cannel estimation sowed a degradation in performance of 1.6dB compared to te assume perfect CSI results. Te time domain least squares metod is able to provide a good estimation wic sows only a negligible degradation over te perfect CSI case ACKNOWLEDGMENTS M.A. Cooper would like to tank Tosiba Researc Europe Limited (TREL) for teir financial and academic support, and in particular te academic support given by Dr. D. McNamara. Tanks are also due to te Engineering and Pysical Sciences Researc Council (EPSRC) for teir financial support. REFERENCES [1] K. W. Ricardson, UMTS Overview, IEE Electronics & Communications Engineering Journal, June 2000, pp [2] HIPERLAN Type 2 Tecnical Specification; Pysical (PHY) Layer, October <DTS/BRAN > V0.k [3] IEEE Std a-1999, Part11: Wireless LAN Medium Access Control (MAC) and Pysical Layer (PHY) specifications. Hig Speed Pysical Layer in te 5GHz Band. [4] A. Doufexi, S. Armour, P. Karlsson, M. Butler, A. Nix, D. Bull, J. McGeean, A Comparison of te HIPERLAN/2 and IEEE a Wireless LAN Standards, IEEE Communications Magazine, May 2002, Vol. 40, No. 5. [5] J. M. Pereira, Fourt Generation: Now it is Personal! PIMRC 2000, Vol. 2, pp [6] P. Maonen, G.C. Polyzos, European R&D on Fourt Generation Mobile and Wireless IP Networks, IEEE Personal Communications, December 2001, Vol. 8, No. 6. [7] B. 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