Relay Scheduling and Cooperative Diversity for Delay-Sensitive and Bursty Traffic

This paper considers a problem of scheduling and cluster size with N i.i. d. source nodes trying to transmit data to a common destination node (e.g. a gateway or a processing center), with the help of some subset of nodes in the form of relays. The source nodes share the network in a TDM manner, using a round-robin scheduling scheme. There are two causes of bit errors in the system: channel decoding and delay violati on. We are interested in the optimal negative SNR exponent, i.e. , the asymptotic decay rate, of the total probability of bit error. In finding the SNR exponent, we optimize the channel transmissi on rate as well as the number of cooperative relay nodes. I. I NTRODUCTION We consider a cooperative wireless network consisting of multiple nodes, each with an independent information source, and a common destination-node. We are interested in a cross-layer queue-channel optimization problem for bursty and delay-sensitive information sources. Each node is a bursty source of information bits concatenated with an infinite buffer and a constant-rate quasi-static relay chan nel to the common destination. More specifically, we consider a network where, at any particular time, one node’s bits are transmitted to the destination, with the help of other nodes in the form of relays. The cross-layer performance metric of interest is the total bit loss probability where loss can be d u to decoding errors as well as delay violation. It is well-known that cooperation among nodes in a slowfading wireless network can substantially improve the reli ability of communication [2], [3]. Although there are many ways to cooperate in the network with multiple sources (see e.g. [4], [5]), we consider a simple time-sharing cooperati on scheme among the information-source nodes. At each time, only one node is an information source and some of the other (pre-assigned) nodes act as relays to help transmission of t he source node. We call this set of an information source and its relay nodes as a cooperative cluster . The choice of which information source (and its cooperative cluster) is active at any particular time is determined by a scheduler. In this paper, we consider a simple round-robin scheduler where each node periodically becomes the information source. In each cooperative cluster, the improvement due to cooperation among the source and relays, known as cooperative diversitygain [2], is a result of encoding across independent spatial channels. It is important to note that the cooperative diversity gain is fully achieved only with coding the The authors are with the ECE Department, University of Calif ornia San Diego, La Jolla, CA, 92093. This research is supported in part by the Center for Wireless Communications, UCSD and UC Discovery G rant No. Com04-10176, ARO-MURI Grant No. W911NF-04-1-0224, NSF CAR EER Award No. CNS-0533035, and AFOSR Grant No. FA9550-05-01-04 30. information over some minimum number of channel uses. This required coding time is a monotone increasing function of the number of cooperative relay nodes. In cases where delay requirements (in units of channel uses) are much large r than the total number of relays, the cooperative diversity gain improves the system performance by decreasing the probability of channel outage. On the other hand, when the bit-arrival processes are stochastic and bursty and the bit s have a strict delay requirement which is of the same order as the size of the network, the required coding time results in a n increase in the end-end delay any bit faces. This potentiall y can increase the probability of delay violation. In such a setting, increasing cooperative diversity might or might n o be desirable. In this paper we are interested in finding the optimal values of the cooperative cluster size, as well as th e transmission rate of the relay channels, so that the total bi loss probability is minimized. Since it is difficult to derive the exact relationship betwee n the interested parameters and the probabilities of channel outage and the delay violation, we choose to study an asymptotic approximation when the signal-to-noise ratio (SNR) is asymptotically high. The first advantage of this choice is that there exists an asymptotic high-SNR analysis for the channel outage probability, known as the diversitymultiplexing-tradeoff(DMT) analysis [1]. Another advantage of a high SNR analysis is that, with a proper scaling of the source statistics with SNR, we can derive an asymptotic approximation of the delay violation probability that is valid even when the delay requirement is finite. 1 Having the asymptotic expressions for the probabilities of channe l outage and delay violation enables the main contribution of this paper: the formulation of a cross-layer optimal operat ing point for cooperative wireless network with multiple burst y sources and delay constraints under the static round-robin scheduler. This paper is a part of an on-going research in jointly considering channels and queues for delay-sensitive data o ver wireless channels (see [13] for references). This paper is a n extension of our previous work in [12], where we studied a cooperative network with a single source at high-SNR. The high-SNR approximation in this work was motivated by a cross-layer study in [9], where the DMT result [1] was first used for a study of joint source-channel optimization. The remainder of the paper is organized as follows. In Section II, we provide mathematical models for the bit-arrival 1 This derivation is based on the many-flow large-deviationsresults (see e.g. [6]–[8]). process, the cooperative communication with an amplifyand-forward protocol, and the round-robin scheduler. Section III describes the asymptotic performance measures of t he system and provides the existing high-SNR asymptotic resul t, also known as DMT, for the channel outage in cooperative relay channel. Section IV gives the asymptotic probability of delay violation under the round-robin scheduler. Section V presents the main result of the paper where we derive the optimal transmission rate and the cooperative cluster size that minimize the asymptotic total bit loss probabilit y. A discussion of the results is also provided. Section VI concludes the paper. The proofs are given in the appendices. For the rest of the paper, we use the notation =̇ corresponding to the exponential equality, i.e. y =̇ ρ is equivalent to lim ρ→∞ log(y) log(ρ) = x. We refer to the set {1, 2, . , N} as S and use[q]ba := min{max{a, q}, b} whena < b. II. SYSTEM MODEL AND PROBLEM FORMULATION We consider a cooperative (uplink) network consists of N nodes, denoted by 1 to N , and a common destination node E, shown in Figure 1. The system is time-slotted into discrete timeslots, for which all nodes’ transmissions are assumed to be synchronized. At each timeslot, each source-node receiv es information according to a stochastic process and stores th e bits that cannot be sent immediately in a buffer which is assumed to be infinite. The delay requirement asks that each bit of information be decoded at the destination-node E within a maximum allowable delayof D time-slots from the time it arrives at its source-node. Otherwise, the bit will be obsolete, discarde d, and counted as erroneous. We assume no retransmission of unsuccessful transmissions. Next we provide more details and notations for a particular cooperative communication scheme of interest, as well as the arrival processes. In addition, we define the performanc e measure. A. Cooperative Communication with OAF Protocol and Relay Scheduling Communication takes place in the presence of additive receiver noise, and in the presence of spatially independen t and identically distributed quasi-static fading. We assum e complete knowledge of the fading channels at the receiver of the final destination, and no knowledge of the fading at the receivers of the assisting relays. Each node has a single receive and transmit antenna, operating in half-duplex. We assume, without loss of generality, that a timeslot contain s one channel use. The nodes cooperate within units of T consecutive timeslots, calledcooperation frame[5]. Without loss of generality, we assume cooperation frames start at time T , m ∈ Z. Within any cooperation frame, we have a relay channel, where only one node is an information source and the other n − 1 nodes (out ofN − 1 nodes) are relays. The assignment of relays to source is fixed. We denote the set of an information source and its relays as a cooperative cluster. Every cooperative cluster has a fixed size of n. g2 Node 2