<p>We examine the robust downlink beamforming design from the point of outage probability constraint. We further reason that since the estimated downlink channel correlation (DCC) matrices form a manifold in the signal space, the estimation error should be measured in terms of Riemannian distance (RD) instead of the commonly used Euclidean distance (ED). Applying this concept of measure to our design constraint, we establish approximated outage probability constraints using multidimensional ball set and multidimensional cube set. We transform the design problem into a convex optimization problem which can be solved efficiently by standard methods. Our proposed methods apply to both Gaussian distribution assumption and uniform distribution assumption. Simulation results show that the performance of our design is superior to those of other robust beamformers recently developed.</p> / Master of Applied Science (MASc)

This thesis studies a two-way relay network (TWRN), which consists of two single antenna source nodes and a multi-antenna relay node. The source nodes exchange information via the assistance of the relay node in the middle. The relay scheme in this TWRN is amplify-and-forward (AF) based analog network coding (ANC). A robust beamforming matrix optimization algorithm is presented here with the objective to minimize the transmit power at the relay node under given signal to interference and noise ratio (SINR) requirements of source nodes. This problem is first formulated as a non-convex optimization problem, and it is next relaxed to a semi-definite programming (SDP) problem by utilizing the S-procedure and rank-one relaxation. This robust beamforming optimization algorithm is further validated in a MATLAB-based orthogonal frequency-division multiplexing (OFDM) MIMO two-way relay simulation system. To better investigate the performance of this beamforming algorithm in practical systems, synchronization issues such as standard timing offset (STO) and carrier frequency offset (CFO) are considered in simulation. The transmission channel is modeled as a frequency selective fading channel, and the source nodes utilize training symbols to perform minimum mean-square error (MMSE) channel estimation. BER curves under perfect and imperfect synchronization are presented to show the performance of TWRN with ANC. It is shown that the outage probability of robust beamforming algorithm is tightly related to the SINR requirements at the source nodes, and the outage probability increases significantly when the SINR requirements are high.

In wireless communication systems, relays are widely used to extend coverage. Over the past years, relays have evolved from simple repeaters to more sophisticated units that perform signal processing to improve signal to interference plus noise ratio (SINR) or throughput (or both) at the destination receiver. There are various types of relays such as amplify and forward (AF), decode and forward (DF), and compress and forward (CF) (or estimate and forward (EF)) relays. In addition, recently there has been a growing interest in two-way relays (TWR). By utilizing the concept of analog network coding (ANC), TWRs can improve the throughput of a wireless sys- tem by reducing the number of time slots needed to complete a bi-directional message exchange between two destination nodes. It’s well known that the performance of a TWR system greatly depends on its ability to apply signal processing techniques to effectively mitigate the self-interference and noise accumulation, thereby improving the SINR. We study a TWR system that is equipped with multiple antennas at the relay node and a single antenna at the two destination nodes. Different from traditional work on TWR, we focus on the case with imperfect knowledge of channel state information (CSI). For such a TWR, we formulate a robust optimization problem that takes into ac- count norm-bounded estimation errors in CSI and designs an optimal beamforming matrix. Realizing the fact that this problem is extremely hard to solve globally, we derive two different methods to obtain either optimal or efficient suboptimal beam- forming matrix solutions. The first method involves solving the robust optimization problem using the S-procedure and semidefinite programming (SDP) with rank-one relaxation. This method provides an optimal solution when the rank-one relaxation condition for the SDP is satisfied. In cases where the rank-one condition cannot be satisfied, it’s necessary to resort to sub-optimal techniques. The second approach presented here reformulates the robust non-convex quadratically constrained quadratic programming (QCQP) into a robust linear programming (LP) problem by using first-order perturbation of the optimal non-robust beamforming solution (which assumes no channel estimation error). Finally, we view the TWR robust beamforming problem from a practical standpoint and develop a set of iterative algorithms based on Newton’s method or the steepest descent method that are practical for hardware implementation.