Distributed Beamforming for Relay Networks Based on Second-Order Statistics of the Channel State Information

Abstract

Abstract-In this paper, the problem of distributed beamforming is considered for a wireless network which consists of a transmitter, a receiver, and relay nodes. For such a network, assuming that the second-order statistics of the channel coefficients are available, we study two different beamforming design approaches. As the first approach, we design the beamformer through minimization of the total transmit power subject to the receiver quality of service constraint. We show that this approach yields a closed-form solution. In the second approach, the beamforming weights are obtained through maximizing the receiver signal-to-noise ratio (SNR) subject to two different types of power constraints, namely the total transmit power constraint and individual relay power constraints. We show that the total power constraint leads to a closed-form solution while the individual relay power constraints result in a quadratic programming optimization problem. The later optimization problem does not have a closed-form solution. However, it is shown that using semidefinite relaxation, this problem can be turned into a convex feasibility semidefinite programming (SDP), and therefore, can be efficiently solved using interior point methods. Furthermore, we develop a simplified, thus suboptimal, technique which is computationally more efficient than the SDP approach. In fact, the simplified algorithm provides the beamforming weight vector in a closed form. Our numerical examples show that as the uncertainty in the channel state information is increased, satisfying the quality of service constraint becomes harder, i.e., it takes more power to satisfy these constraints. Also our simulation results show that when compared to the SDP-based method, our simplified technique suffers a 2-dB loss in SNR for low to moderate values of transmit power.Index Terms-Convex feasibility problem, distributed beamforming, distributed signal processing, relay networks, semidefinite programming.

Relay subset selection in cognitive networks with imperfect CSI and individual power constraints

“…1 are modeled as random values. In this paper, similar to [2]- [4], it is assumed that the joint Second-Order Statistics (SOS) of the channel gains are available at the SN. This approach allows us to consider uncertainty in the channel models through introducing the covariance matrices of the channels.…”

“…Total noise (2) where x (2) p is the signal transmitted by PU-TX during the second slot and n s is the zero-mean AWGN at SU-D which has a variance σ 2 s . Meanwhile, at the same time slot, PU-RX receives the signal transmitted by PU-TX and the interference from the secondary relays.…”

“…Bearing in mind (2) and assuming that the symbols transmitted by PU-TX and SU-D are zero-mean independent, it is possible to show, after some straightforward but tedious manipulations, that the SINR is given by…”

“…To address this issue, cooperative relaying among the secondary users has been considered as a potential solution to improve the QoS of the Secondary Network (SN) while respecting the interference threshold imposed by the PUs. In particular, distributed relay beamforming [2], is a powerful tool which has attracted especial interest in cognitive networks, e.g. in [3], [4], [5].…”

“…In all these works each relay either cooperates with full transmission power or does not cooperate at all. Nonetheless, this approach is not optimal because, as is well known, the optimal beamformer results in relay powers that are not necessarily at their maximum allowable values [2]. Moreover, the approaches in [6]- [9] are based on the knowledge of the instantaneous Channel State Information (CSI) of the channels of the primary and the secondary networks.…”