Joint Partial Relay Selection, Power Allocation and Cooperative Maximum Likelihood Detection for MIMO Relay Systems with Limited Feedback

Transcription

1 Joint Partial Relay Selection, Power Allocation an Cooperative Maximum Likelihoo Detection for MIMO Relay Systems with Limite Feeback Thomas Hesketh, Rorigo C. e Lamare, Stephen Wales Department of Electronics, University of York York, YO10 5DD, Unite Kingom Roke Manor Research Lt. Romsey, Hampshire, SO51 0ZN, Unite Kingom th524@york.ac.uk, rcl500@york.ac.uk, stephen.wales@roke.co.uk Abstract In this paper, joint partial relay selection (PRS) an power allocation methos are propose in conjunction with cooperative maximum likelihoo (ML) etectors. These methos are consiere for selecting relay noes that improve the bit error rate () performance of a two-phase multiple-input multiple-output (MIMO) half-uplex ecoe-an-forwar (DF) relay system with log-normal shaowing an power constraints, as compare to using all relays available regarless of whether the aitional relays will benefit the system. Limite feeback is applie to the joint PRS an power allocation techniques within the system, with results showing the effects of the propose relay selection methos on performance. I. INTRODUCTION The eployment of many low power relay noes to assist in the traitional user to base station communications scenario as in consumer mobile communications, has been theoretically shown to offer improvements in power consumption, outage rates an reuce error rates over the traitional single link, which is a result of the inherent spatial iversity present in the multiple routes in which the signals are transmitte [1],[2]. However, there is an extra complexity require to successfully reconstruct an etect the transmitte ata symbols from the multiple streams of information, which are often subject to ifferent environmental an transmission conitions, an then prouce a result with superior performance to the original noncooperative system transmission [3]. In a previous work by the authors [4], a two-phase relay system with multiple relays an a global power constraint was consiere an it was emonstrate how a cooperative maximum likelihoo (ML) etector coul be employe at the estination of the system, with a stochastic graient (SG) base antenna power allocation algorithm esigne to enhance the bit error rate () performance of the system. The propose techniques were seen to offer performance gains over the non cooperative system when the relays were within a close istance configuration of the source an estination noes, but when this istance was increase, the performance gains were seen to reuce, an in a single relay case with no SG power allocation, be worse than the non-cooperative case. In prior work by other authors, a scheme known as partial relay selection (PRS) was propose [5], where only the information local to the noe processing the relay selection was use in etermining the relay noes to cooperate with. Other works have use PRS as a metho in their works [6],[7],[8], but the basic principle of using the relays signal-to-noise ratio (SNR) in a maximising function remains unchange, an in the majority of works only single antenna amplify-an-forwar (AF) relay noes are consiere. In this work however, the problem of baly positione relays reucing the system performance in a ecoe-an-forwar (DF) MIMO relay system is consiere. Two PRS strategies to choose the relays that are most beneficial to the system performance are propose, one base on the channel power, another base on a combinatorial ML solution. A moel of a two-phase cooperative MIMO system with path loss an shaowing is presente, with a joint PRS, power allocation an cooperative etector scheme being propose. The PRS strategies o not require access to complete knowlege of the system, an thus can operate utilising only the information available at D, with limite feeback of the PRS an power allocation consiere. The PRS is mappe to the SG power allocation algorithm, an log normal shaowing, feeback quantisation, an errors are consiere in the system. The rest of the paper is organise as follows: Section II outlines the MIMO cooperative relay system an signal moels, Section III escribes the cooperative ML etector an the SG power allocation algorithm subject to relay selection. Section IV proposes the two PRS strategies, Section V presents simulation results of the propose strategies, an conclusions are rawn in Section VI. II. SYSTEM AND SIGNAL MODELS The two-phase transmission system uner consieration consists of three types of MIMO communication noes, a single source noe (S) that transmits the ata in the first phase, multiple relay noes (R) that retransmit the ata they receive from the source noe in the secon phase, an a single estination noe (D) which receives the source noe transmission in the first phase of the system, an the transmission of the relay noe in the secon phase of communication. The relays are assume to be DF relays, which means that they ecoe the receive signal into bits, an then re-encoe the bits into symbols for transmission in the secon phase. All noes are assume to have the same number of transmit an receive antennas (N t ), it is assume that all relays transmit simultaneously in the secon phase, D has perfect channel knowlege an the channels are assume to be static over a few ata packets, so that the elay-free feeback in the system is applicable to the subsequent environment.

2 In [4], the system moel mae the assumption that the relays were all at the same istance from the S an D noes in a symmetric layout. In this paper, the assumption that the relays are at the same istance away is relaxe, which requires that the system moel be altere. A more realistic propagation moelling that takes into account path loss an shaowing effects is incorporate into the system. The first phase (S R an S D) can be represente as follows: y s = α s β s H s A s x s +n (1) (1) y srm = α srm β srm H srm A s x s +n (1) r m,m = 1,...,M (2) an the secon phase of communication (R D) by: y r = M (α rm β rm H rm A rm x rm )+n (2) (3) m=1 whereh s,h srm anh rm aren t N t matrices enoting the S D, S R an R D channels, respectively, where the m subscript enotes the relay number that the value is associate with up to M relays, x s an x rm are vectors of length N t that enote the ata symbols that are transmitte from the source an relays, respectively. The matrices A s an A rm are N t N t iagonal matrices enoting the S an R power allocations, respectively, where each iagonal element correspons to an antenna on that evice. The scalars α s, α srm an α rm represent the istance epenent path loss in the channel, the scalarsβ s, β srm anβ rm are the log-normal shaow faing channel losses, the vectors y s, y srm an y r are N t length vectors that represent the receive signal in the S D, S R an R D links, respectively, an the noise at each receiver is represente by a vector of length N t, with n r the noise at the relay, an n the noise at the estination. The superscript (1) or (2) enotes which phase of transmission the noise is applie to. The vector y r can be thought of as a sum of the relay transmissions in the secon phase. S α sr1 β sr1 H sr1 A s α srm β srm H srm α s β s H s R 1 A r1 BSC Feeback Channel R M A rm α r1 β r1 H r1 α rm β rm H rm Fig. 1: MIMO cooperative multiple relay system moel with power allocation an relay selection feeback channel. Fig. 1 gives a representation of this system in a block iagram. It is assume that the channels in the system are moelle as a Rayleigh complex istribution with block faing. The istance epenent path loss variable α for the relay links is efine by the relative istances of R from S an D [9], an so relative to the path loss of the S to D link, as follows: α s = L, (4) D α srm = α rm = α s = 1,...,M (5) (srm ) γ,m α s = 1,...,M (6) (rm ) γ,m where L is the power path loss of the S to D link, srm an rm is the relative istances of each R from the S an D as compare to the S to D link an γ is the path loss exponent, usually between 2 an 4 epening on the environment. The log-normal shaowing [10], [11] is moelle as a log-normal ranom variable, that is prouce from a normal istribution with a stanar eviation of σ s, which is known as the shaowing sprea in B given by: ( ) σs N(0,1) β = 10 where N(0,1) represents a normal istribution with mean 0 an variance 1, an it is assume that each channel has log normal shaowing with the same shaowing sprea. 10 The elements of the noise vectors n (1) r m, n (1) an n (2) are comprise of circular complex aitive white Gaussian noise (AWGN) samples with a variance in proportion to that of the SNR at D, as given by: n = (7) ( σn 2 )CN(0,1), (8) where CN(0, 1) represents a complex normal istribution with mean 0 an variance 1, an σ n is the variance of the noise at that receiver, given by: 1 σ n = (9) SNR L It is assume that all receive antennas on all noes are subject to the same average noise power. The feeback channel in which the relay selection an power allocation information is transmitte to S an all R is moelle as a binary symmetric channel (BSC), which can be efine as having an error probability ρ e of inverting a bit transmitte through it. III. JOINT PARTIAL RELAY SELECTION, COOPERATIVE ML DETECTION AND POWER ALLOCATION Here a joint PRS, cooperative ML etection scheme an power allocation scheme is presente. Unlike the previous work on joint cooperative ML etection an power allocation reporte in [4], PRS techniques are incorporate in orer to mitigate the effects of links associate with poorly positione relays, thereby improving the overall performance of the system. A. Joint Relay Selection an Cooperative ML Detector The cooperative ML etector operates on a moifie ML rule, which is create by combining the two ML rules from each communication phase of the system to the estination (S to D an R to D), into an equivalent single ML rule that is moifie to use available information in the system. For convenience, the scalar terms α an β will be groupe into a

3 single term given by δ = αβ. The cooperative ML etection problem can be escribe as the following optimisation: [ˆx,Âs,Âr 1...Âr M ] = argmin( y s δ s H s A s x 2 x n Z, A s,a rm C N t N t + mǫω s y rm δ rm H rm A rm x m 2 ) (10) where Z represents the constellation set for the moulation scheme use, Ω s is the selecte relay set which is selecte by a relay selection metho, which will be etaile later on, an x n is the nth element of x. By efining the relation S = mǫω s δ rm H rm A rm, (11) an equivalent ML rule can be erive: [ˆx,Âe] = argmin y e H e A e x 2, (12) x n S, A e C N t N t H e A e = (A H s HH s δh s δ sh s A s +S H S) 1/2 (13) y e = (H e A e ) 1 (A H s H H sδ H sy s +S H y r ) (14) B. Power Allocation A power allocation algorithm is evelope base on an SG recursion. The SG power allocation works on the antennas of both the S an all R, an so moifies the power allocation matricesa. For ease of manipulation, the iagonalamatrices an the ata vectors x are rearrange into equivalent iagonal ata matrices X an power allocation vectors a. Also, the signals with the two phases of transmission can be stacke to prouce a single set of equations to work with the SG algorithm as escribe by: [ ] [ ] [ ] ys δ y t = = s H s X s a s n (1) y r mǫω S (δ rm H rm X rm a rm ) + n (2) = H t X t a t +n t (15) A generic SG recursion can be escribe as: Q[i+1] = Q[i]+µ C, (16) where µ is a fixe step size, typically very small, i is a time inex, Q is the variable to be optimise an C is the instantaneous graient of the cost function use to evaluate the variable. If the ML equation is use as the cost function C = E[ y t H t X t a t 2 ], an a t as the variable to be calculate, applying the SG algorithm to (15) prouces: a t [i+1] = a t [i]+µx H t [i]hh t [i]e t[i], (17) e t [i] = y t [i] H t [i]x t [i]a t [i], (18) with the efinition of H t [i] altere to [ ] δs H H t [i] = s [i] 0 Nt N t 0 Nt N t 0 Nt N t δ rm H r1 [i] δ rωs H rωs [i] (19) in orer to compensate for the fact that only the summe receive relay vectory r is available, not each iniviual relay transmissiony rm. The vectora t is then normalise to comply with the system power constraint: P t = tr(a t [i]a H t [i]), (20) where P t is the total system power allowe, an tr() represents the trace operator. Thus, a t [i] is normalise as follows: a n t [i] = a t [i] P t tr(at [i]a H t [i]), (21) a n t [i] can then be separate into the ifferent noe power allocations by unstacking, then re-iagonalising it into a matrix. IV. PROPOSED PARTIAL RELAY SELECTION STRATEGIES In this section, two PRS strategies will be consiere, one scheme base on channel link power (CP-PRS), an another technique that utilises the ML rule (ML-PRS). Both selection strategies assume that the number of relays to be selecte in the system is known, an use only the information foun at D, i.e. no knowlege of the S to R link. A. Propose CP-PRS Given the number of relays to be selecte (R L ), D etermines the sum power of each channel s MIMO paths (p Hrm ) for each R to D link with path losses, an chooses the relay set associate with the R L largest sum channel path powers (ˆΩ s ), accoring to: p Hrm = j=n t j=0 k=n t k=0 (δ rm H rm H H r m δ H r m ) j,k,m = 1,...,M (22) ˆΩ s = arg max p Hrm (23) ˆΩ sc R L This selection criterion is not subject to noise given that it is assume that D has perfect knowlege of all δ rm H rm, an can be performe once before each packet, assuming that δ rm H rm is static over one packet. It is similar to the PRS- D in [6], but instea of instantaneous SNR, our scheme relies on the channel power alone. This relay selection metho is a simple search an compare problem, which in conjunction with only having to perform the metho once per packet, meaning that the complexity is quite low for etermining ˆΩ s, as only a matrix multiplication an some summing operations are require. B. Propose ML-PRS Utilising the ML rule for the secon phase of transmission, a combinatorial partial relay selection is given by ˆΩ s = arg min Ω sǫω r y r lǫω s δ rl H rl A rl x l 2 (24) where Ω r represents all possible unique combination sets of any number of selecte relays an ˆΩ s is the selecte relay set that gives the minimum error between the receive relay transmissions an the estimate relay transmissions. In orer to choose the relay set to minimise Eq. (24), an exhaustive search on all possible Ω s set combinations can be performe, if x l is assume to be retransmitte as the pilot ata x. Since y r is subject to noise n (2), the instantaneous caniate set estimate ˆΩ s may not be the true optimum, an

4 so the search must be performe repeately for ifferent samples (time inices). Then the R L relays which are most often members of the instantaneous caniate set estimates are chosen for ˆΩ s. The ML combination partial relay selection algorithm is escribe below. 1) Select relay set Ω s from a possible combination set Ω r 2) Calculate the error (Eq. (24)) if Ω s relays are selecte 3) If the error is less than that previous teste Ω s, store the error an Ω s 4) Compute steps 1 to 3 for all possible Ω s 5) Compute steps 1 to 4 for a number of time inex samples 6) From the selecte Ω s for each time inex, fin the R L most commonly selecte relays As the metho involve requires an exhaustive set search over 2 M 1 possible unique relay combinations, an multiple iterations are require per packet, the complexity of this algorithm is much higher than the channel power partial relay selection metho. V. SIMULATION RESULTS In the simulations, it is assume that pilot signals transmitte from S for the purposes of PRS an power allocation, that sphere ecoers (SD) [12] are use at all R an D, an that D has perfect channel state information (CSI) knowlege, which inclues the packet-wise path loss an log-normal shaowing losses. The values for the parameters use in the simulations are shown in Table I. Using these values, we can calculate the number of feeback bits require per packet for the relay selection with an without SG power allocation, which can be calculate as an overhea of 0.075% for equal power allocation, an 1.475% with SG power allocation. The authors note however, that the number of power allocation bits coul be reuce by compression or by binary power ajustment strategies. TABLE I: Simulation Parameters. Parameter Value Trials 2000 Packet Length 2000 symbol vectors P t 1 µ 0.05 N t 2 a t[0] Half S, Half equally between all R γ 4 R L 2 M 6 L 0.01 σ s 6B Feeback Quantisation 4 Bits for each R an I Moulation QPSK For PRS, the ML-PRS algorithm is compute for 10 ifferent time inex samples with all relays active, before relay selection takes place. It is assume that D has channel knowlege before the packet is transmitte, an so the channel base relay selection can be compute before the packet is transmitte. In a real system, it is also likely that the CSI of the previous packet will be similar to the next packet, an so this CSI coul be use for the PRS. The relays are assume to be able to reject power allocation feeback packets, if the number of relays selecte an the number of power allocation values receive are mismatche, the relays will use the last known acceptable feeback packet. The SNR values use are etermine as the SNR of thes to D link with no cooperation, in orer to ensure a fair comparison with the non-cooperative case. Fig. 2 shows the structure of the feeback packet, with the relay selection portion comprising of M bits, each bit corresponing to a relay s state, 0 for off, 1 for on. The power allocation ata bits A are split into the real (R) an imaginary (I) parts, with each part being quantise into 4 bits in this scenario. If SG power allocation is not use, then only the relay selection bits (RS) are transmitte after the chosen relay selection strategy has complete. If power allocation is use, once the relay selection has been etermine, the feeback bits are transmitte after every symbol vector is receive at D, comprising the relay selection an then the power allocation. PRS A s A rωs1 PRS = 0,1, RL A = R, I 1 2.Quantisation Bits A rωsrl Fig. 2: Packet structure for PRS an power allocation feeback. The position of the relays consiere is set up such that two relays are positione close to S an D, two are further away such that they might contribute to the system performance, an two are much further away, generally not being beneficial for the system performance. Fig. 3 represents this network setup. S R = 1.5 R = 1 R 5+6 R 3+4 S = 1 R = 1 R = 1.5 R = 0.5 R 1+2 R = 0.5 D Fig. 3: Positioning of relays in the system consiere. Fig. 4 shows the versus SNR plot of the relay selection strategies propose as compare to a non-cooperative case, an the cooperative case without PRS, with no SG power allocation or limite feeback applie. It can be seen that the ML combinatorial metho gives the best performance of the two relay selection methos with up to 5B over no relay selection an 10B over the non-cooperative case. The CP- PRS scheme performs on a similar level as the ML-PRS at low SNR values, but at higher SNR values, has a ecrease performance gain. It is worth consiering though, that the CP- PRS scheme has a much lower complexity cost than the ML- PRS metho. Fig. 5 shows the versus SNR plot of the PRS strategies with an without ynamic power allocation, as compare to the non-cooperative case, without limite feeback. For both PRS strategies, the ynamic power allocation can be seen to give up to 6-7B of gain over the equal power allocation scenario, an 12B over the non-cooperative case. Fig. 6 shows the versus SNR plot of the PRS schemes with power allocation uner limite feeback. It can be seen that introucing feeback errors results in the introuction

5 No Cooperation No PRS CP PRS ML PRS pfe = 0.01 pfe = pfe = pfe = 0 SNR(B) Fig. 4: vs S D SNR for the 2x2 MIMO relay system, comparing the non-cooperative case with the cooperative with no PRS case, an the two propose PRS schemes with equal power allocation SNR(B) (a) CP-PRS pfe = 0.01 pfe = pfe = pfe = 0 of an error floor, with the level of the error floor highly epenent on the probability of feeback error, although it can be assume that the feeback error percentage coul be reuce ramatically with the application of error correction techniques. VI. CONCLUSIONS In this paper, a joint PRS, power allocation an cooperative ML etector has been propose, along with two relay selection strategies, a CP-PRS scheme, an an ML-PRS algorithm. It is seen that the system gives large gains over a noncooperative case, with the PRS schemes offering gains over using all relays available in the scenario, an the aition of ynamic SG base power allocation further improving performance. The ML-PRS scheme is shown to have the best performance of the two propose PRS schemes, but at the cost of a much higher complexity than the CP-PRS. It is also seen that with quantisation an limite feeback with errors results in the presence of an error floor as the SNR increases, which coul potentially be counteracte with error correction coing. ACKNOWLEDGMENT This work is jointly supporte by the University of York an Roke Manor Research Lt. No Cooperation Equal PA CP PRS SG PA CP PRS Equal PA ML PRS 10 5 SG PA ML PRS SNR(B) Fig. 5: vs S D SNR for the 2x2 MIMO relay system, comparing the non-cooperative case with the two propose PRS schemes, with an without the power allocation metho. SNR(B) (b) ML-PRS Fig. 6: vs S D SNR for the 2x2 MIMO relay system with power allocation, for ifferent feeback error probabilities, for both propose PRS schemes. REFERENCES [1] A. Nosratinia, T. E. Hunter, an A. Heayat, Cooperative communication in wireless networks, Communications Magazine, IEEE, vol. 42, no. 10, p , [2] J. Laneman, D. Tse, an G. Wornell, Cooperative iversity in wireless networks: Efficient protocols an outage behavior, IEEE Transactions on Information Theory, vol. 50, no. 12, pp , Dec [3] P. Clarke an R. C. e Lamare, Joint transmit iversity optimization an relay selection for Multi-Relay cooperative MIMO systems using iscrete stochastic algorithms, IEEE Communications Letters, vol. 15, no. 10, pp , [4] T. Hesketh, P. Clarke, R. C. e Lamare, an S. Wales, Joint maximum likelihoo etection an power allocation in cooperative MIMO relay systems, in Smart Antennas (WSA), 2012 International ITG Workshop on. IEEE, Mar. 2012, pp [5] I. Krikiis, J. Thompson, S. Mclaughlin, an N. Goertz, Amplify-anforwar with partial relay selection, IEEE Communications Letters, vol. 12, no. 4, pp , Apr [6] I. Ahme, A. Nasri, D. S. Michalopoulos, R. Schober, an R. K. Mallik, Relay subset selection an fair power allocation for best an partial relay selection in generic noise an interference, IEEE Transactions on Wireless Communications, vol. 11, no. 5, pp , May [7] H. Ding, J. Ge, D. B. a Costa, an Z. Jiang, Diversity an coing gains of Fixe-Gain Amplify-an-Forwar with partial relay selection in nakagami-m faing, IEEE Communications Letters, vol. 14, no. 8, pp , Aug [8] L. Sun, T. Zhang, H. Niu, an J. Wang, Effect of multiple antennas at the estination on the iversity performance of Amplify-an-Forwar systems with partial relay selection, IEEE Signal Processing Letters, vol. 17, no. 7, pp , Jul [9] Y. Fan an J. Thompson, MIMO configurations for relay channels: Theory an practice, IEEE Transactions on Wireless Communications, vol. 6, no. 5, pp , May [10] M. Zorzi, Power control an iversity in mobile raio cellular systems in the presence of ricean faing an log-normal shaowing, IEEE Trans. on Vehicular Technology, vol. 45, no. 2, pp , May [11] P. Agrawal an N. Patwari, Correlate link shaow faing in multi-hop wireless networks, IEEE Transactions on Wireless Communications, vol. 8, no. 8, pp , Aug [12] C. Liu, A new approach for fast generalize complex sphere ecoing algorithm in MIMO systems, in 2007 International Conference on Wireless Communications, Networking an Mobile Computing, Shanghai, China, Sep. 2007, pp