Shahram Shahbazpanahi

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

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.

Convex Optimization-Based Beamforming

In this article, an overview of advanced convex optimization approaches to multisensor beamforming is presented, and connections are drawn between different types of optimization-based beamformers that apply to a broad class of receive, transmit, and network beamformer design problems. It is demonstrated that convex optimization provides an indispensable set of tools for beamforming, enabling rigorous formulation and effective solution of both long-standing and emerging design problems.

Multiple Peer-to-Peer Communications Using a Network of Relays

We consider an ad hoc wireless network consisting of d source-destination pairs communicating, in a pairwise manner, via R relaying nodes. The relay nodes wish to cooperate, through a decentralized beamforming algorithm, in order to establish all the communication links from each source to its respective destination. Our communication strategy consists of two steps. In the first step, all sources transmit their signals simultaneously. As a result, each relay receives a noisy faded mixture of all source signals. In the second step, each relay transmits an amplitude- and phase-adjusted version of its received signal. That is each relay multiply its received signal by a complex coefficient and retransmits the so-obtained signal. Our goal is to obtain these complex coefficients (beamforming weights) through minimization of the total relay transmit power while the signal-to-interference-plus-noise ratio (SINR) at the destinations are guaranteed to be above certain predefined thresholds. Although such a power minimization problem is not convex, we use semidefinite relaxation to turn this problem into a semidefinite programming (SDP) problem. Therefore, we can efficiently solve the SDP problem using interior point methods. Our numerical examples reveal that for high network data rates, our space division multiplexing scheme requires significantly less total relay transmit power compared to other orthogonal multiplexing schemes, such as time-division multiple access schemes.

Distributed source localization using ESPRIT algorithm

A new algorithm based on ESPRIT is proposed for the estimation of the central angle and angular extension of distributed sources. The central angles are estimated using TLS-ESPRIT for both incoherently distributed (ID) and coherently distributed (CD) sources. For CD sources, the extension width is estimated by constructing a one-dimensional (1-D) distributed source parameter estimator (DSPE) spectrum for each source. For ID sources, the extension widths are estimated using the central moments of the distribution. The algorithm can be used for sources with different angular distributions.

Filter-and-Forward Distributed Beamforming in Relay Networks With Frequency Selective Fading

A new approach to distributed cooperative beamforming in relay networks with frequency selective fading is proposed. It is assumed that all the relay nodes are equipped with finite impulse response (FIR) filters and use a filter-and-forward (FF) strategy to compensate for the transmitter-to-relay and relay-to-destination channels. Three relevant half-duplex distributed beamforming problems are considered. The first problem amounts to minimizing the total relay transmitted power subject to the destination quality-of-service (QoS) constraint. In the second and third problems, the destination QoS is maximized subject to the total and individual relay transmitted power constraints, respectively. For the first and second problems, closed-form solutions are obtained, whereas the third problem is solved using convex optimization. The latter convex optimization technique can be also directly extended to the case when the individual and total power constraints should be jointly taken into account. Simulation results demonstrate that in the frequency selective fading case, the proposed FF approach provides substantial performance improvements as compared to the commonly used amplify-and-forward (AF) relay beamforming strategy.

Robust Downlink Beamforming Based on Outage Probability Specifications

A new approach to multi-antenna downlink beam- forming is proposed that provides an improved robustness against uncertainty in the downlink channel covariance matrices caused by errors between the actual and estimated channel values. The proposed method uses the knowledge of the statistical distribution of such a covariance uncertainty to minimize the total downlink transmit power under the constraint that the outage probability does not exceed a certain threshold value. Although our approach initially leads to a non-convex optimization problem, it can be reformulated in a convex form using the semidefinite relaxation technique. The resulting convex optimization problem can be solved efficiently using the well-established interior point methods. Computer simulations verify performance improvements of the proposed technique as compared to the robust transmit beamforming method based on the worst-case performance optimization with judicious selection of the upper bounds on channel covariance errors.

Robust downlink power control in wireless cellular systems

A serious shortcoming of current downlink power control methods is that their performance may be severely degraded when the downlink channel information is known imprecisely at the transmitter. In this paper, a computationally and implementationally simple centralized downlink power control method is proposed for cellular wireless communication systems using code division multiple access (CDMA) or space division multiple access (SDMA). Our method provides a substantially improved robustness against imperfect knowledge of the wireless channel by means of maintaining the required quality of service for the worst-case channel uncertainty. In the SDMA case, the proposed technique can be straightforwardly combined with any of the existing transmit beamforming methods. Simulation results validate substantial robustness improvements achieved by our approach.

A generalized capon estimator for localization of multiple spread sources

In this correspondence, we develop a generalized Capon spatial spectrum estimator for localization of multiple incoherently distributed (spread) sources in sensor arrays. The proposed generalized Capon technique estimates the source central angles and angular spreads by means of a two-dimensional (2-D) parameter search. Simulation results show that the proposed method has a substantially improved performance compared with several popular spread source localization methods.

Minimum variance linear receivers for multiaccess MIMO wireless systems with space-time block coding

We consider the problem of joint space-time decoding and multiaccess interference (MAI) rejection in multiuser multiple-input multiple-output (MIMO) wireless communication systems. We address the case when both the receiver and multiple transmitters are equipped with multiple antennas and when space-time block codes (STBCs) are used to send the data simultaneously from each transmitter to the receiver. A new linear receiver structure is developed to decode the data sent from the transmitter-of-interest while rejecting MAI, self-interference, and noise. The proposed receivers are designed by minimizing the output power subject to constraints that zero-force self-interference and/or preserve a unity gain for all symbols of the transmitter-of-interest. Simulation results show that in multiaccess scenarios, the proposed techniques have substantially lower symbol error rates as compared with the matched filter (MF) receiver, which is equivalent to the maximum likelihood (ML) space-time decoder in the point-to-point MIMO communication case.

A covariance fitting approach to parametric localization of multiple incoherently distributed sources

In this paper, a new algorithm for parametric localization of multiple incoherently distributed sources is presented. This algorithm is based on an approximation of the array covariance matrix using central and noncentral moments of the source angular power densities. Based on this approximation, a new computationally simple covariance fitting-based technique is proposed to estimate these moments. Then, the source parameters are obtained from the moment estimates. Compared with earlier algorithms, our technique has lower computational cost and obtains the parameter estimates in a closed form. In addition, it can be applied to scenarios with multiple sources that may have different angular power densities, while other known methods are not applicable to such scenarios.