2011 International Conference on Advanced Technologies for Communications (ATC 2011) Outage Probability Analysis of Cooperative Diversity DF Relaying under Rayleigh Fading D.T Nguyen, Universit of Teehnology Sydney, Australia Quoe Tuan Nguyen, Vietnam National University Hanoi, Vietnam Trang Cong Chung, Vietnam National University Hanoi, Vietnam Abstract: the focuses on delay-limited and non-ergodic scenarios, and evaluates In this paper, we present exact analytical expressions for outage probability of cooperative diversity wireless networks operating in various decode-and-forward (DF) relay performance of cooperative relaying protocols in terms of outage protocols probability (fixed, adaptive, and incremental relaying) under Rayleigh fading In this paper, in view of ever lowering cost, flexibility and conditions Current works only analyze the asymptotic behavior of these protocols, either under high signal-to-noise ratios (SNR) or robustness in noise resistance of digital detection, we concentrate under low SNR-Iow rate conditions Our analytical results are only on decode-and-forward (DF) relaying protocols and ignore presented in such a way that they can be used for both asymptotic the noise propagating amplify-and-forward (AF) relaying Fixed conditions relaying Index Terms: Multiple relay channel, achievable rate, decode-and continuously active and are normally used when channel state forward, partial decoding, linear relaying information (CSI) is not available to the transmitter Selection or adaptive INTRODUCTION message coding is no longer proved to dramatically effective improve in improving the performance of (NACK) cooperative diversity wastage of bound for the outage capacity of the relay channel The focus of this paper, however, is the exact formulas for the outage probability of the above three forms of DF relaying protocols As was pointed out in the previous paragraph, the information blockwise-sense, and the strict Shannon capacity of the channel is capacity of relaying networks using incremental DF protocols is a However, when the system is random variable depending on the number of sub-blocks being constrained by the message decoding delay T and the bandwidth used for transmission W is also limited, the requirement WI» cannot be met and The relationship between outage capacity and outage probability is, therefore, also a statistical relationship or [6] A simple comparison of the performance of the three DF asymptotically mean stationary random variables and the strict Shannon capacity is zero [5] avoiding 4, 6] resort to the max-flow min-cut theorem [2] to fmd an upper length of the message block, i.e the channel is memoryless in the ergodic thus In order to calculate the outage capacity, because of the slowly fading channels, the fading is assumed constant over the as destination, complexity of the probabilistic analysis involved, most authors [3, cope with low-SNR transmission under heavy fade conditions In modeled the (i.e when the direct link is not in outage) or two sub-blocks combining to achieve spatial diversity gain, and source and relay be from (when the direct link is in outage) terminals can use repetition code or other more powerful codes to cannot better using DF protocol is a random variable [6] depending on how protocols, relay terminals can process the received signal in parameters for is many times the transmission requires either only one sub-block different ways, the destination terminals can use different types of channel designed relay bandwidth at high SNRs The information rate of an IR network relaying protocols for ease of potential implementation In these well defmed and achievable the those in which the relay only transmits upon a negative feedback today In this paper, we deal only with the classical three-terminal low-complexity are which transmission to the destination using repetition coding or other theoretical foundation of most reseach work on relay networks using protocols in more powerful codes Incremental relaying (IR) protocols are relay channel were first studied in [1] and this work forms the network (SR) those When the measured SNR falls below a threshold, the relay stops transmission Upper and lower bounds of the capacity of a general relay relaying are its relaying function and the source simply continues its direct transmission reliability, and cooperative diversity transmission has protocols efficiency in low SNR conditions and CSI is available at the relay In the slow-fading environment, once a channel is in deep fade, (FR) protocols based on outage capacity is outside the scope of this In most practical situations, the paper channel is non-ergodic and capacity is a random variable, thus no transmission rate is reliable In this case, the outage probability is In practical wireless sensor networks, power is limited and defined as the probability that the instantaneous random capacity SNR is usually very low, and the performance of relaying falls networks in terms of energy efficiency in the low SNR regime below a probability is measure [5] given threshold, and capacity versus outage performance becomes essential However, in the low SNR regime, the Shannon Consequently, as with many authors, this paper capacity is theoretically zero as SNR -+O and is no longer a useful the natural information theoretic 978-1-4577-1207-4/11/$26.00 ©2011 IEEE 116 measure Therefore in [5], a more appropriate metric called outage capacity is defined as the maximal transmission rate for which the outage probability does not exceed We expect that some level of synchronization between the terminals is required for cooperative diversity to be effective When CSI is unavailable to the transmitters as in most simple implementations in practice, coherent transmission cannot be exploited, hence even full-duplex cooperation, i.e where terminals can transmit and receive simultaneously, cannot improve the total Shannon capacity of the network Therefore, in this paper we focus on half duplex operation where E(lxI2) x, y, n, = P and are the normalized transmit signal, i.e I, the corresponding received signal, the additive noise which is modeled as a circularly symmetric complex Gaussian random variable with zero mean and variance ri at the receiver, i.e n 11th) Pr({lhsr 12 + = _11 th II" = = 1-e - [1 - I'sd -I'Td { ( /lsd - e The result in the last line of _ !! l!l IIsd (7) ) - 3.3 Outage Probability ofIR-DF Relaying As pointed out in the Introduction, the information capacity 2} > 11th) Ihrd ( of relaying using incremental DF protocols is a random variable /lTd - e _ !! l!l IIrd )}] depending By using the first order approximation e-x;:::;l-x, the number of sub-blocks being used for outage probability, therefore, cannot be simply defined based on a (7) capacity threshold Instead, we calculate outage probability of an can be obtained from (A1), (A3) and (A5) of the Appendix on transmission Its information capacity is difficult to defme and its IR-DF realying network directly from the defmition of outage condition The system is in outage either when the source it can be shown that destination and the source-relay links are both in outage, or when the source-relay link is not in outage, i.e able to decode-and forward, but the accumulation of 118 SNR at the destination of signals from the source and the relay is not enough to exceed the outage threshold Thus under exponential fading the outage probability of an IR-DF relaying wireless network is P/}IU�-DFCl1th) PrClhlR_DF12 :::; 11th) PrClhsdl2 0 vol 25, no 5, T.M Cover and J.A Thomas, information Theory John Wiley & Sons, 1991 e -x "" 1- x FU(J1) II J1u [3] A Host-Madsen and J Zhang (June, 2005) "Capacity bounds and , we have { }=_ power allocation for the wireless relay channel"] Theory 51 (A2) v are iEEE Trans Inform (6), pp 2020-2040, June 2005 http://www.it.iitb.ac.in/�subbu/pdf ps/relay channell.pdf [4] IN Laneman et aI., "Cooperative Diversity in Wireless Networks: A1.2 Sum of two independent exponential random variables Let s=u+v, where u, IEEE Transactions on Information Theory, pp.572-584, September 1979 (AI) II" T.M Cover and AA EI Gamal, "Capacity theorems for relay channel," Efficient Protocols and Outage Behavior," IEEE Trans Inform Theory, 50 (12), pp 3062-3080, December 2004 two independent exponential r.v's with mean J1u and J1v, respectively, then from the convolution [5] L.H Ozarow et aI., "Information theoretic considerations for cellular theorem mobile radio," I fs(J1)= (fu @ fv ) p = J1"J1v e-Jli)J" _e-Jli)Ju IEEE Trans on Vehicular Technology, vol 43, no 2, pp.359-377, May 1994 S: e-x1""e-(P-X)/" , dx [6] T Renk et aI., "Outage Capacity of Incremental Relaying at Low Signal-to-Noise Ratios," VTC 2009-Sep J1v - J1u 120 iEEE 70lh Vehicular Technology Conference ... expressions for the outage probability of various versions of DF protocols Figure shows the curves of outage probability as a function of channel gain threshold I'th of two decode-and-forward relaying protocols:... destination of signals from the source and the relay is not enough to exceed the outage threshold Thus under exponential fading the outage probability of an IR -DF relaying wireless network is P/}IU�-DFCl1th)... performance of a fixed DF relay to that of the link between the source and the relay, i.e no diversity gain can be achieved (6) From the corresponding probability of outage under exponential fading