Outage Probability and SER of Multi-antenna Fixed Gain Relaying in Cooperative MIMO Networks Phee Lep Yeoh ∗† , Maged Elkashlan † , and Iain B. Collings † ∗ School of Electrical and Information Engineering, University of Sydney, Sydney, Australia † Wireless Networking and Technologies Laboratory, CSIRO ICT Centre, Sydney, Australia Email: pyeoh@ee.usyd.edu.au, maged.elkashlan@csiro.au, iain.collings@csiro.au Abstract—This paper proposes multiple-input multiple-output (MIMO) transmission in fixed gain amplify-and-forward relaying to allow for high data rate coverage in wireless distributed net- works. We consider a hierarchical network architecture in which the relay is a multiple antenna static node assisting single antenna mobile nodes. We derive new exact closed-form expressions for the outage probability and the symbol error rate (SER) valid for arbitrary N antennas at the relay under independent but not necessarily identically distributed (i.n.d.) Rayleigh fading. Our solutions apply to general operating scenarios with distinct average received signal-to-noise ratios (SNRs) throughout the network. Based on these, we derive new concise asymptotic expressions which accurately characterizes the outage probability and the SER in the high SNR regime. In our asymptotic solutions, we present an exact expression for the array gain in terms of the average received SNRs and the number of antennas N . We further show that the maximum achievable diversity order is N +1. I. I NTRODUCTION Hierarchical network architectures have become increas- ingly popular in practical deployments of wireless distributed networks such as ad-hoc and sensor networks [1]. We con- sider a hierarchical network in which the mobile nodes are typically small low-power devices with single antennas while infrastructure-based relays are higher power forwarding nodes with greater capabilities allowing for multiple antenna pro- cessing. This network architecture has many important appli- cations. One such example is in livestock production where it is important to separate bulls in a field and monitor cow move- ments [2, 3]. The cattle are fitted with single antenna sensor devices while more capable multi-antenna solar powered nodes are installed on fence posts. Such a hierarchical architecture can be viewed within the framework of cooperative MIMO networks. Cooperative MIMO networks have been considered from an information theoretic perspective (e.g., see [4, 5] and citations therein). These works have provided insights into the ergodic capacity. Other important metrics such as the outage probabil- ity and the symbol error rate (SER) require more attention to support effective network design. Existing solutions for cooperative MIMO networks with amplify-and-forward (AF) relaying have focused on cellular infrastructures with a single antenna at the relay. Among them, [6] considered the scenario where the source is a multiple antenna base station and the destination is a single antenna mobile terminal. In [7, 8], the source and the destination are multiple antenna base stations communicating via a single relay. The more general scenario of having multiple relays assisting a base station was addressed in [9]. It was shown that the diversity order is a sum of the number of relays and the number of antennas at the base station. Here, in contrast to [6–9], we examine a hierarchical wire- less sensor network where the relay is equipped with multiple antennas as discussed above. We focus on fixed gain MIMO relaying which does not require full channel state information in the relay scaling gain. In such networks, we derive new exact closed-form expressions for the outage probability and SER which are valid for arbitrary N antennas at the relay with independent but not necessarily identically distributed (i.n.d.) Rayleigh fading. This allows us to address general operating scenarios with distinct average received signal-to-noise ratios (SNRs) in the direct link and the two-hop relay link. Our exact solutions are further analyzed in the high SNR regime, leading to new design insights. Our asymptotic expressions are explicitly characterized by two important network parameters: the diversity order and the array gain. We highlight that increasing the average received SNRs in the relay link brings an increase in the array gain of the network. Furthermore, we reveal that having a multi-antenna relay in the hierarchical network achieves a maximum diversity order of N +1. II. FIXED GAIN MIMO RELAYING The cooperative MIMO network under consideration is presented in Fig. 1, where the source transmits information to the destination either directly or indirectly via a fixed gain MIMO relay. The source and the relay transmit to the destination in orthogonal channels. For example, with time- division relaying, the source transmits in the first time slot to both the relay and the destination. In the second time slot, the relay applies a fixed scaling gain to the received signal and forwards it to the destination. We adopt the principles of selection diversity to identify the link with the highest instantaneous received SNR between the direct link and the MIMO relay link. Specifically, let x be the transmitted scalar symbol from the source with zero mean and unit variance. The received signal at the destination from the source is expressed as y SD = h SD  E s x + n D , (1) 978-1-61284-231-8/11/$26.00 ©2011 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings