An Eigen Approach to Transmit Beamforming in Wireless Networks With Single Antenna Receivers

In this paper, we propose an eigen framework for transmit beamforming for single-hop and dual-hop network models with single antenna receivers. In cases where number of receivers is not more than three, the proposed Eigen approach is vastly superior in terms of ease of implementation and computational complexity compared with the existing convex-relaxation-based approaches. The essential premise is that the precoding problems can be posed as equivalent optimization problems of searching for an optimal vector in the joint numerical range of Hermitian matrices. We show that the latter problem has two convex approximations: the first one is a semi-definite program that yields a lower bound on the solution, and the second one is a linear matrix inequality that yields an upper bound on the solution. We study the performance of the proposed and existing techniques using numerical simulations.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

Sum Secrecy Rate in Multicarrier DF Relay Beamforming

In this paper, we study sum secrecy rate in multicarrier decode-and-forward relay beamforming. We obtain the optimal source power and relay weights on each subcarrier which maximize the sum secrecy rate. For a given total power on a given subcarrier k, P-0(k), we reformulate the optimization problem by relaxing the rank-1 constraint on the complex positive semidefinite relay weight matrix, and solve using semidefinite programming. We analytically prove that the solution to the relaxed optimization problem is indeed rank 1. We show that the subcarrier secrecy rate, R-s (P-0(k)), is a concave function in total power P-0(k) if R-s (P-0(k)) > 0 for any P-0(k) > 0. Numerical results show that the sum secrecy rate with optimal power allocation across subcarriers is more than the sum secrecy rate with equal power allocation. We also propose a low complexity suboptimal power allocation scheme which outperforms equal power allocation scheme.

Beamforming correction for dipole measurement using two-dimensional microphone arrays

In this paper, a beamforming correction for identifying dipole sources by means of phased microphone array measurements is presented and implemented numerically and experimentally. Conventional beamforming techniques, which are developed for monopole sources, can lead to significant errors when applied to reconstruct dipole sources. A previous correction technique to microphone signals is extended to account for both source location and source power for two-dimensional microphone arrays. The new dipole-beamforming algorithm is developed by modifying the basic source definition used for beamforming. This technique improves the previous signal correction method and yields a beamformer applicable to sources which are suspected to be dipole in nature. Numerical simulations are performed, which validate the capability of this beamformer to recover ideal dipole sources. The beamforming correction is applied to the identification of realistic aeolian-tone dipoles and shows an improvement of array performance on estimating dipole source powers. © 2008 Acoustical Society of America.