Pre- and Pot- Combining Space Receiver for Wideband Multi-Carrier Sytem Muhammad Imadur Rahman, Suvra Sekhar Da, Frank HP Fitzek, Ramjee Praad Center for TeleInFratruktur (CTiF), Aalborg Univerity, Denmark e-mail: {imr,d,ff,praad}@komaaudk; ph: +45 9635 8688 Abtract The baic receive pace diverity combining method, ie Maximum Ratio Combining (MRC), Equal Gain Combining (EGC) and Selection Combining (SC), are tudied in thi work for Pre- and Pot- combining wideband multi-carrier receiver A common ytem model for both thee cheme are devied The outage and mean capacity and Frame Error Rate (FER) imulation how that Pre- combining technique perform quite comparatively in indoor cenario, while Pot- combining perform far better in outdoor cenario Compared to Pre- combining cheme in indoor cenario, Pot- MRC and SC obtain an increment of 4 and 09 bp/hz repectively in term of 0% outage capacity At 0 3 of FER, Pot- MRC obtain a gain db and 4 db in required Signal to Noie Ratio (SNR) for indoor and outdoor cenario repectively In contrary to performance degradation, Pre- cheme require much le computational complexitie and they are impler to implement compared to Pot- cheme I INTRODUCTION One well-known way of improving the ytem performance in hotile wirele channel cenario i exploiting the patial diverity uing multiple receive antenna Traditionally receive diverity i ued in the Bae Station (BS) to obtain full diverity at the BS receiver In receive diverity ytem, multiple copie of originally ingle tranmitted ignal i received via eparate antenna Given that the antenna are ufficiently eparated in pace uch that the receive ignal do not experience any ignificant patial correlation, we can eaily ay that full diverity advantage can be achieved, ie the diverity order will be equal to the number of receive branche Thi can alo be achieved by uing tranmit diverity cheme, where multiple copie of tranmitted ignal are received at one ingle receive antenna imultaneouly and full diverity advantage are achieved The only difference between tranmit and receive diverity i that, when Channel State Information (CSI) i not available at the tranmitter, then array gain i not poible to obtain, wherea array gain i poible to obtain in the receive diverity ytem, a we aume that perfect CSI i alway available at the receiver [] While uing the pace diverity receiver, three kind of can be ued, namely Maximal Ratio Combining (MRC), Equal Gain Combining (EGC) and Selection Combining (SC) MRC being the mot complicated with the bet performance, while SC i the leat complicated with the wort performance among the three cheme In Orthogonal Frequency Diviion Multiplexing (OFDM) ytem, thee three technique can be applied either before the Dicrete Fourier Tranform () demodulation (ie in time-domain on received ample), or after the demodulation (ie in frequency-domain on each ub-carrier ymbol) We denote the cheme a Pre- and Pot- combining repectively In Pot- combining, all the ignal proceing i performed on ub-carrier bai, thu, bet cae performance i achieved While in Pre- combining, all the ignal proceing needed i performed in time domain, o the duplication of the operation for each receiving antenna branch i not a requirement any more, thu the receiver ha lower computational cot compared to Pot- technique [] When we implement the above mentioned combining technique after the operation, we can name the receive diverity technique a Pot- MRC, Pot- EGC and Pot- SC repectively Their three counterpart in Pre- operation can be called a Pre- Maximal Average Ratio Combining (MARC), Pre- Equal Average Gain Combining (EAGC) and Pre- Antenna Selection Combining (ASC) repectively In thi work, we have etablihed a ytem model for Pre- and Pot- receive diverity cheme in OFDM ytem Then we have obtained theoretical capacity curve to determine outage and mean capacity of the combining cheme under indoor and outdoor channel condition We have obtained FER performance of the Pre- and Pot- combining cheme under certain OFDM ytem parameter Finally, we have done a preliminary analyi of required ytem complexity for Pre- MARC and Pot- MRC cheme in term of number of multiplication required The ret of thi paper i organized a follow We have preented the ytem model for Pre- and Pot- combining cheme in Section II The analyi and imulation reult are placed in Section III Some initial concluion and the topic to be included in the final paper are dicued in Section IV II SYSTEM MODEL We adopt a ytem model that i originally etablihed in [3] The tranmitted ignal vector for the th OFDM ymbol,, i given by: = T cpf H d () where d i the data vector, F H i Invere Dicrete Fourier Tranform (I) matrix, and T cp i the Cyclic Prefix () addition matrix The element of d i taken from a complex contellation diagram Since only one antenna i ued at the tranmitter while multiple antenna are deployed at the receiver, the channel matrix become: G = ˆG, G, G T Q, with G q, i the Channel Impule Repone (CIR) convolution matrix between the tranmit antenna and the q th receive antenna Q denote number of receive antenna in the ytem and q denote receive antenna index In thi cae, the dimenion of the CIR convolution matrix will be G C [(N+Ng)Q (N+Ng)] N and N g denote number of OFDM ub-carrier and the length in ample repectively The received ignal vector r C [(N+Ng)Q ] may be expreed a: r = G + v (3) where v i the time-domain noie vector at the receiver At the receiver, the time-domain received ignal i down-converted and the i removed: y = T + cpr (4) ()
The time-domain OFDM ymbol vector after removal, y, can be decompoed into Q vector, each repreenting a diverity branch, or one received OFDM ymbol at a particular receiving antenna: y = ˆy y yq T At thi point, there are two method for combining the diverity branche to obtain the deired diverity gain, namely Pot- combining and Pre- combining The former perform OFDM demodulation before combining the diverity branche on ub-carrier bai, while the latter firt combine diverity branche over timedomain ample and then the OFDM demodulation i carried out Both of thee diverity combining technique will be explained in the following ection A Pot- Combining Fig z 0,0 z 0,N z,0 z,n z Q,0 z Q,N α 0,0 α,0 α Q,0 z 0 z N P/S Decoder Pot- combining technique (5) Outputed data tream Figure illutrate the diagram of an OFDM receiver uing Pot- combining method The received ignal at each antenna branch i demodulated eparately before combining Signal at the output of the demodulator can be expreed a: z = Fy = ˆz z z T Q where F i the -proce matrix, analogou to F H given in (), and z q i output ub-carrier vector at the q th antenna branch: z q = ˆz q, z q, z q,n T ; q =,,, Q (7) The ub-carrier at the output of the OFDM demodulator are combined eparately o a to maximize the intantaneou SNR on ub-carrier bai For each ub-carrier, the ignal from multiple antenna are linearly combined, ie: (6) z k = α,kz,k + α,kz,k + + α Q,kz Q,k (8) where z k i the k th combined ub-carrier, z q,k i defined a in (7) and α q,k i the weight factor aociated with the k th ub-carrier and the q th antenna (k =,,, N and q =,,, Q) The complex weight factor can be written a, α q,k = β q,ke jθ q,k, where β q,k and θ q,k are amplitude and phae of the weight factor repectively The linear combination operation can be expreed in matrix form: z = α z (9) with α C N NQ i the weight factor matrix for Q receive antenna at the th OFDM ymbol In cae of Pot- combining cheme, thi matrix i given by: α = ˆα α α Q (0) where α q i the diagonal weight matrix aociated with the q th antenna branch: α 3 q, 0 0 α 0 αq, 0 q = 6 4 7 () 5 0 0 αq,n For the k th ub-carrier, the choice of weight factor, {α,k, α,k,, αq,k}, depend on the combination technique ued at the diverity module, namely MRC, EGC and SC Thee technique will be dicued in the following ection ) Pot- MRC: In MRC, the output i a weighted um of all diverity branche, ie αq,k 0; q & k Thi multiplication i performed uch that each of the ignal branche are co-phaed (ie all branche have zero phae) The gain factor αq,k are elected o that P Q q= β q,k =, which implie that the noie power after diverity combining i not modified βq,k i aigned baed on the intantaneou power or the SNR from each received ignal branch If the power i mall in any particular branch, then it will be aigned a mall gain factor, and vice vera ) Pot- EGC: The EGC technique i imilar to MRC becaue the diverity branche are co-phaed, and all of them contribute to the output of the However, it i different from MRC that the diverity branche are not weighted correponding to their intantaneou SNR Thi reduce the complexity of obtaining the SNR for each diverity branch Equal value are elected for all gain factor, iee βq,k = Q ; q For example, in cae of dual antenna ytem, β,k = β,k = 05; k 3) Pot- SC: The principle of SC method i to deliver to the detector the diverity branch which yield the highet SNR In other word, the SC algorithm need to monitor the SNR level of all branche, and elect the i th branch with the highet SNR value The weight factor αi,k aociated with that branch will be, and all other weight factor, αq,k (q = 0,,, Q; q i), are zero [4] In practice, it i difficult to meaure the SNR level of diverity branche Therefore, the intantaneou ignal plu noie value i uually ued intead of the SNR, with the aumption that the noie power (N 0) i contant for all branche The elected diverity branch can be ued for a duration of everal OFDM ymbol, provided that the duration i le than the channel coherence time [4] B Pre- Combining Fig y 0 y y Q α 0 α α Q y P/S Decoder Outputed data tream An OFDM receiver employing Pre- combining technique The pre- combining technique combine the time-domain OFDM ample from multiple receive antenna and deliver the combined ample to the demodulator [5] The proce i hown in Figure Clearly, the computational complexity i dramatically reduced for pre- combining technique: only one OFDM demodulator and one diverity are required After the
pre- diverity combining module, the receiver architecture i identical to that of the Orthogonal Frequency Diviion Multiple Acce (OFDMA) receiver dicued in [6] The output of the pre- combining module i y C N, and it can be expreed a: y = α y () where y i the time-domain OFDM ymbol vector after removal in (4) and α C N QN i the weight factor matrix ued for linear combination operation on Q antenna α = ˆα 0 α α Q (3) where α q i the diagonal weight matrix aociated with the q antenna branch: α 3 q 0 0 α 0 αq 0 q = 6 4 7 q = 0,,, Q 5 0 0 αq (4) It i important to note that the ame weight factor αq i applied for all time-domain ample of an OFDM ymbol on the q th antenna branch Thi make the cheme different from the above mentioned pot- combining technique Analogouly to pot- combining, there are three option for electing the weight factor for pre- combining cheme, namely Antenna Selection Combining (ASC), Equal Average Gain Combining (EAGC), Maximal Average Ratio Combining (MARC) and Orthogonal Combining (OC) ) Pre- MARC: The Pre- Maximal Average Ratio Combining (MARC) elect the optimal et of weight factor for Q receive antenna, ie {α0, α,, αq}, o a to maximize the SNR of the ignal after combining In [5], [7], it i proven that the optimal weight factor are the firt column of left ingular matrix of the CIR matrix, correponding to the highet Eigenvalue of CIR matrix, λ H In thi cae, the receive SNR i equal to E N 0 λ H, The Pre- MARC require the etimation of CIR on all receive antenna The computational complexity in thi cae i comparable to pot- cheme, a each antenna branch require a proceor for frequency-domain channel etimation In order to reduce the complexity, the correlation matrix of received ignal i ued intead of CIR matrix [5] The performance of Pre- MARC cheme depend on type of channel model it i operating on If channel repone i flat over the OFDM pectrum, the Pre- MARC performed equivalently to pot- MRC, but with le complexity However, if the channel i frequency-elective, the performance of Pre- MARC i degraded and le diverity gain i achieved compared to pot- MRC [5] ) Pre- EAGC: All Q weight factor for Q receive antenna, {α0, α,, αq}, are et to one in the Pre- Equal Average Gain Combining (EAGC) cheme A a reult, the output ignal i the um of all time-domain ignal at different receive antenna In order to achieve diverity gain in the Pre- EAGC cheme, the branche mut be co-phaed before umming Thi operation often require eparate channel etimator and equalizer for each receive antenna branch, which increae computational complexity at the receiver, epecially when the channel i frequency-elective However, if the channel coherence time i much longer than the OFDM ymbol duration, uch requirement could be negligible 3) Pre- ASC: In the Pre- Antenna Selection Combining (ASC) cheme, only the diverity branch with the highet average SNR i elected and delivered to the OFDM demodulator In other word, the weight factor for the q th diverity branch, whoe average SNR i the highet, i and all other weight factor are zero In [7], it i hown that the performance of the Pre- ASC cheme i alway wore than that of the Pre- MARC cheme, E and the receive SNR i equal to max q N 0 H q F The H q F i the quared Frobeniu norm of the channel matrix aociated with the q th antenna, and, in thi cae, can be interpreted a the total power gain of the Single Input Single Output (SISO) channel between the tranmit antenna and the q th receive antenna [] III ANALYSIS, SIMULATIONS AND DISCUSSIONS A Simulation Parameter We have ued two imulation cenario a explained in Table I For all our analyi and imulation, we have confined ourelve to the cae of dual antenna receiver diverity (ie Q = ) We aume that perfect time and frequency ynchronization i etablihed We alo aume that perfect channel etimation value for each ubcarrier for both the patial channel are available at the receiver We ue exponential channel model to generate correponding CIR and Channel Tranfer Function (CTF) of the channel In our exponential model, channel impule repone in exponentially ditributed with decay between the firt and lat impule a -40dB TABLE I OFDM SIMULATION PARAMETERS FOR INDOOR AND OUTDOOR SCENARIO Parameter Indoor Outdoor OFDM ub-carrier, N 64 5 Data ub-carrier, N data 48 388 Pilot ub-carrier, N pilot 4 60 Null ub-carrier, N null 64 length, N 6 00 OFDM Symbol Duration, T 4µ 306µ Ueful data period, T data 3µ 56µ period, T 08µ 5µ Data Symbol mapping QPSK Pilot Symbol mapping BPSK Channel coding cheme -rate Convolutional coding Sytem bandwidth 0MHz Carrier frequency 54GHz B Sytem Capacity Analyi The theoretical outage capacity of Pot- MRC, Pot- SC, Pre- MARC and Pre- EAGC are evaluated in thi ection via a emi-analytical monte-carlo imulation approach Thi i done for both indoor and outdoor environment Firt, the channel i imulated uing the model mentioned above Then the intantaneou channel capacity i obtained uing the imulated CTF baed on the following equation: C = N N X k=0 log ( + ρh k h k) (5) where ρ i the tranmit SNR and h k i the equivalent CTF of k th ub-carrier Equivalent CTF mean the CTF at the particular ub-carrier after the diverity combining The above intantaneou capacity i derived for each channel realization and then Cumulative Ditribution Function (CDF) of intantaneou channel capacity i
Probability that quantity < abcia 09 08 07 06 05 04 03 0 0 CDF of the correponding capacity of X SIMO Sytem at 0 db SNR Pot MRC Pot SC Pre MARC Pre EAGC 0 0 3 4 5 6 7 8 Capacity in bp/hz Fig 3 CDF of the correponding capacity of SIMO Sytem at 0 db SNR in indoor cenario Probability that quantity < abcia 09 08 07 06 05 04 03 0 0 CDF of the correponding capacity of X SIMO Sytem at 0 db SNR Pot MRC Pot SC Pre MARC Pre EAGC 0 0 3 4 5 6 7 Capacity in bp/hz Fig 4 CDF of the correponding capacity of SIMO Sytem at 0 db SNR in outdoor cenario plotted in Figure 3 and 4 for indoor and outdoor cenario repectively For a large number of random channel, the outage and mean capacity can be determined from thee two figure In our cae, we have imulated 0,000 random channel and obtained the CDF A we ee from the figure, Pot- cheme alway give better outage capacity value and better mean capacity than Pre- cheme Pot- MRC and Pot- SC depict a 0% outage capacity capacity of 7 and bp/hz repectively, where a both Pre- cheme how 3 bp/hz only One poible reaon for thi i, Pot- cheme exploit the available diverity in much efficient way than the Pre- cheme The mean capacity of Pot- MRC and Pre- MARC are 4575 and 3770 bp/hz repectively Higher mean capacity in Pot- MRC mean a teeper CDF, which obviouly come from more diverity exploitation The difference in outage ituation i more evident in outdoor cenario Now the mean capacity value are 40605 bp/hz and 3305 bp/hz for Pot- MRC and Pre- MARC repectively The difference in 0% outage capacity follow the ame trend a it i experienced in indoor cenario A the combining in done in timedomain in Pre- cheme, the average gain determination doe not capture the effect of all the multipath A we have done ub-carrier by ub-carrier combining for Pot- cheme, the diverity order i fully achieved in thoe cheme Thi i the reaon that Pot- cheme alway perform better in term of outage and mean capacity FEP Fig 5 0 0 0 0 FEP of x Pre & Pot combining SIMO cheme MRC, indoor 0 3 MARC, indoor SC, indoor SC, outdoor MRC, outdoor MARC, outdoor 0 4 0 5 0 5 0 SNR, db FER of different Pre- and Pot- Combining receiver diverity C FER Performance in Indoor and Outdoor Scenario Figure 5 how the Frame Error Rate (FER) performance of the combining cheme in indoor and outdoor cenario repectively In indoor cenario, a frame conit of 64 6 05 = 04 ource bit, while in outdoor cenario, it i 5 6 05 = 89 ource bit in one frame In indoor cenario, Pot- MRC, Pre- MARC and Pot- SC perform almot imilar At 0 3 of FER, Pre- MRC obtain a gain db in required SNR in thi cenario While in outdoor cenario, both Pot- cheme perform better than Pre- MARC cheme Thi i becaue of the averaging effect of Pre- MARC cheme Compared to indoor cenario, here Pre- MRC perform even better with repect to 0 3 of FER, the gain now become 4 db It i intereting to note that even Pot- SC perform better than Pre- MARC in outdoor frequency elective cenario by nearly db at 0 3 of FER While indoor cenario depict much le evere frequencyelectivity, the Pre- MARC cheme can till perform on par with Pot- cheme But, in outdoor cenario, the frequency electivity i very evere (5µ of maximum delay pread in our cae), and thu, the average gain at the time-domain ample in Pre- MARC cheme doe not provide enough SNR enhancement, in other word, the time-domain averaging doe not exploit full patial diverity available in the ytem D Implementation Complexity We compared the complexity of the cheme in term of number of multiplication required Conidering that we have a channel which i time-invariant for coniderable amount of time, o that N pkt number of OFDM ymbol can be put in one OFDM packet, then the number of multiplication required for one OFDM ymbol are Q(Q )No X pre = + N pkt N pkt «QN X pot = N pkt logn + QN N logn + QN «(6) (7) where N logn multiplication are required for FFT module per OFDM ymbol [8] N o i the number of time-domain data ample that need to be acquired to obtain the correlation matrix The computational complexity aociated with Eigen analyi for gain factor i not taken into account, a it only required only once for complete OFDM packet [5]
Figure 6 and 7 how the relative proceing cot between Pre- MARC and Pot- MRC in comparion to N and N pkt repectively for different value of Q The relative proceing cot i defined a X pot X pre from (7) and (6) In both figure, we can ee that the proceing cot i dratically reduced in Pre- MARC cheme when N or N pkt or Q increae For N = 56, Pot- MRC with Q = and 8 require 7 and 33 time more proceing capabilitie repectively compared to Pre- MARC cheme The ame trend i een when the complexitie are alo compared in term of number of ymbol per OFDM packet Relative Proceing Cot 35 3 5 5 Relative Proceing Cot V N; N pkt = 50, N o = 50 M = M = 4 M = 6 M = 8 50 00 50 00 50 300 350 400 450 500 Number of Subcarrier, N Fig 6 Relative Proceing cot for Pre- MARC and Pot- MRC in comparion to number of OFDM ub-carrier; N pkt = 50 and N o = 50 Relative Proceing Cot 3 5 5 Relative Proceing Cot V N pkt ; N = 64, N o = 50 are very high compared to their counterpart To end, the deciion between Pre- and Pot- combining reception hould be taken baed particular ytem environment, ytem parameter and expected ytem performance In the current work, the combining cheme are tudied when no patial correlation due to antenna pacing, preence of Line of Sight (LOS) component etc are conidered in the channel model Thee can be tudied a a next tep The effect of channel correlation can be tudied for outage and mean capacity Some innovative technique to extract more patial diverity in Pre- technique can be invetigated to reduce the performance gap between Pre- and Pot- combining technique ACKNOWLEDGEMENT The author would like to thank Daniel VP Figueiredo, Huan C Nguyen and Nicola Marchetti of WINGlab, CTIF, Aalborg Univerity, Denmark for the ueful dicuion and cooperation in performing thi work REFERENCES [] AJ Paulraj, R Nabar & D Gore, Introduction to Space-Time Wirele Communication, t ed Cambridge Univerity Pre, September 003 [] M I Rahman et al, Optimum Pre- Combining with Cyclic Delay for OFDM Baed WLAN Sytem, in proc VTC Spring, Milan, Italy, May 004 [3], Multi-antenna Technique in Multi-uer OFDM Sytem, Aalborg Univerity, Denmark, JADE project Deliverable, D3[], September 004 [4] G L Stuber, Principle of Mobile Communication Kluwer Academic Publiher, January 996 [5] M Okada and S Komaki, Pre- Combining Space Aited COFDM, IEEE Tran Veh Tech, vol 50, no, March 00 [6] M I Rahman et al, Comparion of Variou Modulation and Acce Scheme under Ideal Channel Condition, Aalborg Univerity, Denmark, JADE project Deliverable, D3[], July 004 [7] S Sandhu and M Ho, Analog Combining of Multiple Receive Antenna with OFDM, in IEEE ICC, vol 5, May 003, pp 348 343 [8] RV Nee & R Praad, OFDM for Wirele Multimedia Communication Artech Houe Publiher, January 000 M = M = 4 M = 6 M = 8 05 0 50 00 50 00 50 300 OFDM ymbol/packet, N pkt Fig 7 Relative Proceing cot for Pre- MARC and Pot- MRC in comparion to number of OFDM ymbol/packet; N = 64 and N o = 50 IV CONCLUSION In thi paper, we have briefly dicued the merit and demerit of Pre- and Pot- combining diverity receiver for wideband OFDM ytem We have found that Pot- cheme are alway uperior to Pre- cheme In indoor cenario, thi i not o evident, but thi i very evident in outdoor cenario The advantage that Pre- cheme offer i impler implementation and leer computational requirement Thi become very evident when the number of ub-carrier i very large and when the number of received branche are alo high Thu, the choice between thee two type of receive diverity combining cheme are a trade-off problem between performance and ytem complexity In our opinion, the advantage of Pre- cheme in term of ytem complexity compared to performance lo with regard to Pot- cheme i acceptable in indoor cenario Where a, in outdoor cenario, the ytem performance degradation in Pre- cheme