The Role of SNR in Achieving MIMO Rates in Cooperative Systems

Abstract

We compare the rate of a multiple-antenna relay channel, under different channel state information (CSI) and channel to the capacity of multiple-antenna systems to characpower allocation assumptions. It was shown that transmitter terize the cooperative capacity in different SNR regions. While it cooperation is more favorable with CSI at the transmitter is known that in the asymptotic regime, at a high SNR or with a cooperation is mrfvab wi C ate trmit large number of cooperating nodes, cooperative systems lack full (CSIT), while receiver cooperatIon is superor under opima multiplexing gain, in this paper we consider cooperative capacity power allocation without CSIT. gain at moderate SNR with a fixed number of cooperatingThe capacity of cooperative systems has been studied in the antennas. We show that up to a lower bound to an SNR threshold, asymptotic regime. In [16], it was shown that at asymptotically a cooperative system performs at least as well as a MIMO system high signal-to-noise ratio (SNR), the multiplexing gain of an with isotropic inputs; whereas beyond an upper bound to the SNR ' threshold, the cooperative system is limited by its coordination N-source-destnation-pair network is upper bounded by Nj2. costs, and the capacity is strictly less than that of a MIMO Thus cooperative systems do not enjoy full multiplexing gain. orthogonal channel. The SNR threshold depends on the network In fact, the N12 upper bound was believed to be loose and geometry (the power gain g between the source and relay) and the multiplexing gain was conjectured to be one. From another the number of cooperating antennas M; when the relay is close to perspective, the capacity of large Gaussian relay networks was the source (g > 1), the SNR threshold lower and upper bounds considered in [17]. In an N-node network, for asymptotically are approximately equal. As the cooperating nodes are closer, i.e., as g increases, the MIMO-gain region extends to a higher large N, capacity scales as 0(logN). Hence cooperative SNR. Whereas for a populous cluster, i.e., when M is large, the systems fail to achieve the linear capacity scaling order (in the coordination-limited region sets in at a lower SNR. number of antennas) found in multiple-input-multiple-output (MIMO) systems. Under what conditions, then, is cooperation of most value? In this paper, we consider cooperative capacity In wireless networks, node cooperation has been proposed gain at moderate SNR with a fixed number of cooperating as a strategy to improve communication reliability and system antennas. We show that up to an SNR threshold, which capacity. The idea of cooperative diversity was pioneered depends on the network geometry and the number of antennas, in [1], [2], where the transmitters cooperate to achieve a a cooperative system performs at least as well as a MIMO larger rate region by repeating detected symbols from each system with isotropic inputs. other. In [3] the transmitters forward parity bits to achieve The rest of the paper is organized as follows. Section II moc...

Multiple-Antenna Cooperative Wireless Systems: A Diversity–Multiplexing Tradeoff Perspective

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Transmit Signal and Bandwidth Optimization in Multiple-Antenna Relay Channels

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