Adaptive Bit and Power Allocation for Rate and Margin Maximization in V-BLAST System

Transcription

1 Revista Científica Periódica - Teecomunicações ISSN Adaptive Bit and Power Aocation for Rate and argin aximization in V-BAST System Dror eiri and Irving Kaet Aeis Photonics, Netanya, Israe (emai: dmeiri@netvisionneti) Facuty of Eectrica Engineering, Technion Israe Institute of Technoogy, Haifa, Israe (emai: kaet@actcomcoi) Abstract This paper describes the "Water-Pouring" soution for wide-band mutitone version of the Vertica Be abs ayered Space-Time (V-BAST) architecture It is shown that the mutitone concept may be combined with the utipe-input-utipe- Output (IO) V-BAST concept for use on a frequency-seective channe We present an optima power and bit oading agorithm which attempts to optimize the system performance by enhancing either the data rate or the QoS (error rate), whie keeping the other fixed In both methods, a power constraint exists Simuation resuts of the proposed system and agorithm show that adaptive oading enabes efficient and reiabe communication even with ow SNRs It aso shows significant improvement in both methods as compared to a basic OFD V-BAST syste which has no a-priori knowedge of the channe characteristics For exampe, a system with four transmitters and receivers that uses a 56 mutitone symbo doubes the nomina bit rate at SNR of 33dB (for maximum bit rate) and achieves a gain of 9dB at BER of x0-4 (for maximum QoS) Index Terms fading channes, muti-input-mutioutput (IO) systems, orthogona frequency division mutipexing (OFD), wireess communications I INTRODUCTION The demand for high data rate communication systems, and the ack of avaiabe bandwidth has ed to much research effort into IO systems using mutipe transmit and receive antennas It was shown in [] that IO systems can improve the capacity of richscattering Rayeigh fading channes, by a factor which is ineary proportiona to the minimum of the number of the transmit and receive antennas The V-BAST [] architecture has been proposed for reaizing high spectra efficiencies over fat Rayeigh fading indoor wireess channes Turbo coding in V-BAST systems was proposed in [7] utitone transmission [3,4], or OFD, has been used in a number of wireine and wireess systems OFD eiminates the need of a compex equaizer (in wireess systems) for overcoming ISI caused by deay spread or frequency-seective fading However, in [3,4] it was shown that for a singe-input-singe-output (SISO) system which operates over a frequency-seective channe, if the transmitter knows the channe characteristics, the water-pouring mutitone (T) technique can be used to optimize the transmitted bit rate and approach the channe capacity Adaptive bit and power aocation agorithms [] were shown to achieve efficient use of the "waterpouring" soution in wireine ADS and VDS systems In [,,3,8], the channe capacity for the IO system has been anayzed and discussed Raeigh and Cioffi [7] have deveoped a coding structure that achieves the capacity and a technique that approaches this structure Few works have considered the usage of V-BAST in IO-OFD systems Adaptive moduation for such systems has been presented by Ng et a [4] This work assessed the maximum margin concept ony eiri and Kaet [8,5,6] have deveoped an adaptive oading agorithm for the Wide-Band utitone version of V- BAST for both maximum rate and maximum margin criteria In this paper we present adaptive oading agorithms that optimize either the data rate or the margin (known aso as Quaity of Service (QoS) maximization), whie keeping the other fixed In both methods, a power constraint exists Both optimization probems resut in (different) power and bit aocations, ie each sub-channe carries a different amount of data and transmitted with different power For the maximum margin approach, we show that for an equa number of antennas on both sides of the ink, this agorithm resuts in improvement of 3 severa dbs for BERs of 0 4 and 0 compared to a IO system with the best performance that has no channe knowedge at the transmitter, irrespective of the number of antennas For the maximum bit rate, we investigate two types of error constraints: (a) fixed error rate for a SNRs and (b) error rate figures of a typica OFD V-BAST system having the same system parameters (and that does not use adaptive oading) The first constraint resuts in a practica system that impements the uti-tone-uti-antenna (TA) technique [8] The second one maximizes the communication efficiency of any given system We show that for an equa number of antennas on both sides of the ink, and a fixed error rate constraint, using the adaptive oading agorithm enabes efficient and reiabe communication in ow SNRs, compared to IO systems with the best performance which has no channe knowedge at the transmitter For the case which there is a nomina error rate constraint, we show that at high SNR vaues the system more then doubes the bit rate The paper is organized as foows: Section describes the system and channe mode, Section 3 describes the V-BAST syste Section 4 presents the wideband 48 Teecomunicações - Voume 07 - Número 0 - Juho de 004

2 Revista Científica Periódica - Teecomunicações ISSN mutitone version of V-BAST incuding the adaptive bit and power aocation agorithm Section 5 gives the simuation resuts and Section 6 presents a summary and concusions II SYSTE AND CHANNE ODE A singe data stream is spit into mutipe sub-streams that are transmitted simutaneousy from an array of coocated antennas A the sub-streams occupy the same (and the entire) bandwidth, and have the same symbo duration The sum of the powers of a the transmitters is constrained There are N (N ) receiving antennas The compex term h (t) represents the independent channe impuse response (with a Rayeigh distributed ampitude) for the signa, s (t), transmitted from the ith antenna, and received by the th receiver antenna Accordingy, the compex vaued signa, r (t), received at receiver is given by = i= r ( t) hi ( t) si ( t) + n i i ( t) where * stands for convoution, i, N and n (t) is a zero-mean compex AWGN signa, with PSD of N 0 watts/hz The channe frequency response may be fat, or frequency-seective (if the channe suffers from ISI [5]) It is assumed that the receiver has perfect channe knowedge This may be the case for a sowy-changing mobie channe III V-BAST OVERVIEW The IO V-BAST system [] has been used in frequency-nonseective channes The received signas are sequentiay decoded using three steps: (a) Nuing the interference from the yet undetected symbos, (b) Symbo detection according to the optima detection rue, (c) Canceation of the previousy detected symbos The order of detection is significant and there is an optima ordering rue The Zero-Forcing V-BAST agorithm [] is described beow: a Initiaization b Recursion () i = (a) G = pinv( H ) (b) K = arg min ( G ) (c) w K = ( G i i ) Ki (d) T y K = w r i Ki i (e) s ˆK = sice( y ) i Ki (f) r ˆ ) i+ = ri sk i ( H K i (g) H K = H K = H K i = zeros(, N) (h) G i + = pinv( H ) (i) K i arg min ( Gi+ ) { K Ki} + = () i = i + (k) where H is the channe matrix of size xn, w is the nuing operator, r the received vector, y the receiver s estimate, i the index of the transmitted signa that is subect to the current detection, and K is a permutation of i and refers to the optima detection ordering Sice operation impements the maximum ikeihood () symbo decoding, zeros(,n) is a vector of ength N whose eements have zero vaue, and pinv is the pseudo inverse operator IV A WIDEBAND UTITONE VERSION OF V-BAST In the uti-carrier oduation (C) technique [3,4] a wideband signa is composed of many narrowband QA signas ( tones or "frequency-bins") Hence, each individua tone sees an essentiay frequency-nonseective channe, and a simpe one-tap equaizer can nuify the channe frequency distortion C can aso be used in the system defined in Section Two, and accordingy the many narrowband received IO signas can be decoded using V-BAST A base-band diagram of this system is shown in Figure Source Transmitter Destination Receiver Symbos Encoder Channe Information Symbos Decoder - IDFT - IDFT - IDFT - DFT - DFT - DFT CP i CP i CP i CP r CP r CP r i N Channe Fig Bock diagram of mutitone version of V-BAST Teecomunicações - Voume 07 - Número 0 - Juho de

3 Revista Científica Periódica - Teecomunicações ISSN This is an extension of the Discrete utitone (DT) impementation [] of the mutitone system used in ADS and VDS There are sub-channes in each - DFT and -IDFT The CP bocks at the transmitter and the receiver represent the introduction and remova of the cycic prefix, respectivey If the transmitter has no channe knowedge, the C technique becomes a simpe OFD system in which the same moduation is used at each transmitting antenna in each frequency The tota error rate is the same as that of V-BAST over a frequency-nonseective channe Knowedge of the channe characteristics at the transmitter(s) enabes the transmitter(s) to adapt the transmitted signa to the channe characteristics in such a way that the system performance wi be improved The improvement can be manifested by enhancing either the data rate or the QoS (error rate) whie keeping the other constant These are the soutions of the foowing probems: The maximum bit rate optimization probem: R = max b b D = m= under the tota power constraint: Pm, = m= P Tota The maximum QoS optimization probem: P Tota = min P b D = m= under the constant bit rate constraint: R = b m, = m= where b m, and P m, are the number of bits and the power aocated for the m-th antennas at the -th frequency-bin, respectivey D is the set of a possibe vaues of b, It is important to note that even though the ast probem is formuated to minimize the overa transmit power for a given QoS requirement, the same soution can be appied to maximize the QoS for a given overa transmit power This can simpy be achieved by increasing the power proportionay for a sub-carriers, whie using the same set of { b }, m, m=, = [6] In the foowing, we present an optima adaptive bit and power aocation agorithm It is a practica way to impement the TA technique [8] and to optimize the system performance under the two criterias given above et f(b) denote the singe sub-channe required received power (in energy per symbo time) needed for reiabe reception of b information bits per symbo with a unity channe gain For a square QA consteation, f(b), is given by [5]: pr ( e) ( ) N 0 f ( b) { Q ( )} (3) K 3 b m where (e) p r is the symbo error probabiity, K 4 and Q is the inverse of the Q-function De-Souza [9] proved that a given aocation is an optima soution to the probems above if and ony if any change in the aocation does not require ess transmitted energy ("Efficiency") and a resources (power for the maximum bit rate, and bit rate for the maximum QoS criterions) are expoited ("Tightness") For QA, f(b) is a convex, increasing function of b with f(0)=0 Hence, the oading agorithm that "puts every increment of the transmitted power where it is most effective" resuts in an efficient aocation [9] In V-BAST each symbo is decoded separatey: The symbos that have previousy been decoded are aready canceed, and the symbos that have not been detected yet are seen as interferers and are nued out This eaves us with a singe symbo, which is decoded The other symbos (out of symbos) are aso decoded, in their turn The concusion from the above is that the convexity of f(b) hods aso in the spatia dimension imposed by V- BAST, and hence an optima aocation can be reached as before In order to maintain the required error rate or QoS at the receiver, the transmit power aocated to the -th subcarrier of the m-th transmitting antenna must be equa to P = G H ) f ( b ) (4) ( m where G is a function of the channe and impements the reciproca of the corresponding channe energy gain Recaing the V-BAST, G can be given by: where ( H ) w G = (5) w m, for an arbitrary subcarrier index is given in (d) Note that for SISO system w, becomes m H As the power needed to transmit a certain number of bits in a singe sub-channe (out of the subchannes) is independent of the number of bits aocated to other sub-channes, assigning one bit one at a time to the sub-carrier that requires the east additiona power is "efficient" The bit aocation process wi be competed when a power is aocated, for the maximum bit rate approach, or when a R bits are assigned for the maximum QoS approach and hence the aocation is "tight" The suggested agorithm is given by: Step a Initiaization For every sub-carrier and every transmitter b m =, 0, P m, = 0 (6a) Step b Bit and Power Assignment Iterations Whie P m, PTota (for maximum bit rate) m= = or Whie b m, R (for maximum QoS) m= = For every sub-carrier and every transmitter antenna 50 Teecomunicações - Voume 07 - Número 0 - Juho de 004

4 Revista Científica Periódica - Teecomunicações ISSN P w Step c Finish ( b + ) = *[ f ( b + ) f ( b m arg min Pm, )] (6b) { ˆ, ˆ} = (6c) b ˆ = b ˆ (6d) + mˆ, mˆ, P mˆ,ˆ b = { b }, m, m=, = and P = aocation soution = P + P (6e) mˆ,ˆ mˆ, ˆ { P }, m, m, = = are the bit and power For the maximum QoS approach, after aocation is finished, the tota power shoud be normaized to accommodate the power budget, as expained before Aso note that for the maximum QoS, the cacuation in (6b), can be repaced with a more convenient expression: ~ P ( b + ) = w *[ b + b where w m, is the m-th row of the pseudo-inverse of the - th sub-channe matrix As in the V-BAST reception scheme, the order of the cacuation of m ] (7) w, for a given sub-channe is of importance In the V-BAST receiver the component with the smaest post-detection signa to noise ratio (PDSNR) dominates the error performance of the syste and thus choosing the symbo with best PDSNR at each stage in the detection process eads to the gobay optima ordering [] Athough the aocation agorithm aims to acheive the same PDSNR for a received sub-channes, optima ordering at the aocation process shoud be done in a simiar manner to that of the V-BAST receiver because the integer constraints resut in different PDSNR for two sub-channes aocated with the same number of bits Summarizing, the agorithm for cacuating the weight vector w, for the th sub-carrier is a sub-section m of V-BAST agorith obtained by using equations (a),(b),(c),(d),(h),(i),() and (k) One of the properties of the V-BAST system is that it expoits the reception diversity in IO systems where N to achieve high QoS performance Note that the agorithm wi inherenty achieve resuts that are equa or better than any reception diversity system with N, since this soution is a subset of the soution space of the agorithm we propose The agorithm is optima aso for bit and power aocation in a IO system in which < N Note, however, that the cacuation of f(b) changes since the required energy for receiving b bits gets smaer because of the diversity enhancement Naturay, as the ratio between N and gets arger, the improvement achieved by the oading wi get smaer, because of the channe averaging effect The agorithm is optima aso for V-BAST systems that operate over frequency non-seective fading channe In this case there is a singe carrier, accordingy = in a equations If we take ony one transmitter and receiver (=), the agorithm becomes the we known "greedy agorithm" [9] The oading agorithm described so far handes IO systems that operate over time invariant channes Ceary, the same mechanism can be used over timevarying channes But considering the compexity of the oading agorith such a system might be impractica However, assuming that (a) the time variant channe can be divided into time sots in which the channe can be considered as constant or time invariant, and (b) that the channes corresponding to adacent time sots have partia correation, it wi be usefu taking advantage of the extended "Efficientize" agorithm given in [8] and to use the previous aocation as an initiaization for the current channe Accordingy the bits aocated in every subchanne wi be increased or decreased at every iteration, rather than increased ony when the initia aocation is zero V SIUATION RESUTS The foowing exampes shows performance gain of three systems: The first is required to transmit a maximum number of bits, with the symbo error rate constrained to be smaer or equa to x0-3 (maximum bit rate criterion) The second system is required to transmit 4096 bits per symbo with the best error rate (maximum QoS criterion) The third system is required to transmit maximum number of bits, with the symbo error rate constrained to be smaer or equa to the symbo error rate of the OFD V-BAST system A the three systems use a 56 mutitone symbo, and there are four transmitting and four receiving antennas The symbos are chosen from square QA consteation and thus an even number of bits are Gray mapped onto the symbos Each simuation run assumes that the channe parameters for that run are known at the receiver and at the transmitter (when reevant) These parameters are samped from the Rayeigh distribution pertinent to the deay profie The profie we use for these exampes is the DVB-T [0] portabe channe The SNR figures at the abscissa, are reative, and are arbitrariy defined as foows: Each receiving antenna receives the superimposed signa from a transmitters This signa has a power of P rx per received symbo Accordingy the received SNR (at each antenna) is defined as SNR = 0og 0 Prx N0 The reation between the tota transmitted energy and the received energy is given by P P E(r), where r is a tx = Rayeigh distributed random variabe P tx is divided between the transmitters over the frequency-bins The graphs beow were obtained by averaging the resuts over many channe reaizations Figure refers to the first exampe (maximum rate at constant error rate constraint) and shows two curves: The first is for equa bit and power aocation and the fixed error rate constraint The second shows resuts for our adaptive oading agorithm In this case the number of bits per antenna per tone varies from zero to eight, and the energy per tone is aso variabe The optimized resuts rx Teecomunicações - Voume 07 - Número 0 - Juho de 004 5

5 Revista Científica Periódica - Teecomunicações ISSN show significant improvement, compared to the first case As expected from the water-pouring soution properties, the smaer the SNR is, the greater the gain As can be seen, at SNR beow 5 db the system with no oading coapses Adaptive oading, however, enabes communication in such conditions Note aso that for SNR of 30 db the bit rate gain is approximatey 75 BITS PER TRANSITTER PER TONE =N=4 without adaptive oading =N=4 with adaptive oading SNR [db] Fig Bits per transmitter per tone vs, SNR with and without adaptive oading, with 56 mutitone symbo over 3 a DVB-T channe, =N=4, P r ( e) = x0 Figure 3 refers to the second exampe (maximum QoS) and aso shows two curves The first is for a V- BAST OFD system with an equa bit and power aocation: four bits per antenna per tone The second shows resuts for our adaptive oading agorithm In this case the number of bits per antenna per tone varies from zero to eight, and the energy per tone is aso variabe The optimized resuts show significant improvement, compared to the first case For exampe there are gains of 3 and 9 db, respectivey, at BERs of 0-3 and x0-4 Note aso that the higher the SNR is, the greater the gain BER =N=4 without adaptive oading =N=4 adaptive oading without adaptive oading is 30 db This system's performance can be improved by our agorithm in two senses: (a) owering the required SNR by approximatey 0 db (as demonstrated in Figure 3) or aternativey (b) enhancing the bit-rate by approximatey 75 times the origina rate (as aso shown in Figure 4) oreover, at SNR of 33dB one can have the same system performance as an equivaent system with 8 transmitters and 8 receivers that does not use adaptive oading It is important to note that a the resuts of this section are achieved without coding BIT RATE GAIN SNR [db] Fig 4 Potentia bit rate gain vs, SNR with adaptive oading compared to OFD V-BAST with 4096 bits per 56 mutitone symbo over a DVB-T channe, =N=4 VI SUARY AND CONCUSIONS We have presented an agorithm for adaptive bit and power aocation in V-BAST systems operating in any sow fading channe The oading agorithm is optima for a maximum bit rate criterion and for maximum QoS (maximum margin) criterion Simuations of this system show significant improvement for both criteria: By adopting the maximum rate approach it is possibe either to achieve efficient and reiabe communication with ow SNRs (which is not achievabe in the origina V-BAST system), or to increase the bit rate By adopting the maximum QoS approach the power margin is improved with the SNR ACKNOWEDGENT 0-4 The authors woud ike to thank the anonymous reviewers for the hepfu comments and feedback SNR [db] Fig 3 BER vs SNR with and without adaptive oading for 4096 bits per 56 mutitone symbo (constant bit rate) at s IO system with =N=4 Figure 4 refers to the third exampe (maximum rate at OFD V-BAST error rate constraint) and we present the potentia bit rate gain vs SNR The system is required to have at any SNR the same symbo error rate as that of a system that uses no adaptive oading (OFD V-BAST) For exampe at BER=x0-3, the required SNR in system REFERENCES [] G J Foschini and J Gans, On imits of wireess communication in a fading environment when using mutipe antennas, Wireess Persona Comm (6), Kuwer Academic Pubishers, ar 998, pp [] PW Woniansky, GJ Foschini, GD Goden and RA Vaenzuea, V-BAST: An architecture for reaizing very high data rates over the rich-scattering wireess channe, Proc URSI ISSSE `98, Pisa, Itay, 998, pp Teecomunicações - Voume 07 - Número 0 - Juho de 004

6 Revista Científica Periódica - Teecomunicações ISSN [3] I Kaet, The mutitone channe, IEEE Trans Communication, vo37, pp 9-4, Feb 989 [4] JAC Bingha uticarrier moduation for data transmission: An idea whose time has come, IEEE Communication agazine, pp 5-4, ay 990 [5] J G Proakis, Digita Communication New York: cgraw-hi, 00 [6] CY Wong et a, utiuser OFD with adaptive subcarrier, bit and power aocation, IEEE J Seect Areas Comm Vo 7, Oct 999, pp [7] GG Raeigh, J Cioffi, Spatio-tempora coding for wireess communication, IEEE Trans Communication, Vo46, No3, ar 998, pp [8] D eiri, "Wide Band utitone Version of V- BAST", Sc Thesis, Department of Eectrica Engineering, Technion, Haifa, Israe, September 00 [9] JC De Souza, "Discrete Bit oading For uticarrier oduation Systems", Phd Thesis, Department of Eectrica Engineering, Stanford University, ay 999 [0] ETSI, "Digita Video Broadcasting (DVB); Framing structure, channe coding and moduation for digita terrestria teevision (DVB-T)",ETS , arch 997 [] PS Chow, et a "A discrete mutitone transceiver for HDS appications", IEEE J Seect Areas Comm Vo 9, Aug 99, pp [] E Teatar, "Capacity of muti-antenna gaussian channes", Eur Trans Teecomm, Vo 0, No 6, November-December 999, pp [3] Chen-Nee Chuah, Capacity of uti-antenna Array Systems, Sc Thesis, University of Caifornia, Berkey CA, January 5, 000 [4] K-W Ng, et a Iterative bit and power aocation for V-Bast based OFD IO system in frequency seective channes, WCNC '0, ar 00, pp7-75 [5] D eiri, I Kaet "Wideband utitone version of V- BAST", 7th internationa workshop on OFD, September 00, Hamburg, Germany [6] D eiri, I Kaet "Adaptive oading for utitone version of V-BAST", nd ISRAE IEEE Conference, December 00, Te-Aviv, Israe [7] Seathurai and S Haykin, "TURBO BAST for high speed wireess communication", WCNC '00, September 000 [8] H Bockei et a "On the capacity of OFD-based spatia mutipexing systems", IEEE Trans Communication, vo50, pp 5-34, Feb 00 Dror eiri (S 00 03) was born in Haifa, Israe in 97 He received BSc and Sc in eectrica engineering from the Technion, Israe Institute of Technoogy in 996 and 003, respectivey He has been a system engineer and technica proect manager at Oren Semiconductors from 996 to 999 and R&D team eader at Surf Communication Soutions from 999 to 00 On 00 he oined Aeis photonics, Netanya, Israe as manager of signa processing His interests incude digita communications, adaptive signa processing and IO systems Irving Kaet was born in The Bronx, NY He received the BEE degree from the City Coege of New York, New York, in 96, and the S and DrEngSc degrees from Coumbia University, New York, in 964 and 969, respectivey He taught at the City Coege of New York from 964 to 967 He has been iving in Israe since 970 He was a consutant at Be aboratories for many years in the fieds of HDS, ADS, mobie wireess communications, and on the 56 kbit/s modem He is a Visiting Associate Professor at the Technion,in Israe, for the past six years He is presenty interested in the fied of moduation for wireess communications Dr Kaet is a member of Sigma Xi, Tau Beta Pi, and Eta Kappa Nu Teecomunicações - Voume 07 - Número 0 - Juho de