Transceiver design and interference alignment in wireless networks: complexity and solvability

University of Minnesota M.S. thesis. November 2013. Major: Mathematics. Advisor: Gennady Lyubeznik. 1 computer file (PDF); vi, 58 pages.This thesis aims to theoretically study a modern linear transceiver design strategy, namely interference alignment, in wireless networks. We consider an interference channel whereby each transmitter and receiver are equipped with multiple antennas. The basic problem is to design optimal linear transceivers (or beamformers) that can maximize the system throughput. The recent work [1] suggests that optimal beamformers should maximize the total degrees of freedom through the interference alignment equations. In this thesis, we first state the interference alignment equations and study the computational complexity of solving these equations. In particular, we prove that the problem of maximizing the total degrees of freedom for a given interference channel is NP-hard. Moreover, it is shown that even checking the achievability of a given tuple of degrees of freedom is NP-hard when each receiver is equipped with at least three antennas. Interestingly, the same problem becomes polynomial time solvable when each transmit/receive node is equipped with no more than two antennas.The second part of this thesis answers an open theoretical question about interference alignment on generic channels: What degrees of freedom tuples (d1, d2, ..., dK) are achievable through linear interference alignment for generic channels? We partially answer this question by establishing a general condition that must be satisfied by any degrees of freedom tuple (d1, d2, ..., dK) achievable through linear interference alignment. For a symmetric system with dk = d for all k, this condition implies that the total achievable DoF cannot grow linearly with K, and is in fact no more than K(M + N)/(K + 1), where M and N are the number of transmit and receive antennas, respectively. We also show that this bound is tight when the number of antennas at each transceiver is divisible by the number of data streams

Resource allocation and feedback in wireless multiuser networks

This thesis focuses on the design of algorithms for resource allocation and feedback in wireless multiuser and heterogeneous networks. In particular, three key design challenges expected to have a major impact on future wireless networks are considered: cross-layer scheduling; structured quantization codebook design for MU-MIMO networks with limited feedback; and resource allocation to provide physical layer security. The first design challenge is cross-layer scheduling, where policies are proposed for two network architectures: user scheduling in single-cell multiuser networks aided by a relay; and base station (BS) scheduling in CoMP. These scheduling policies are then analyzed to guarantee satisfaction of three performance metrics: SEP; packet delay; and packet loss probability (PLP) due to buffer overflow. The concept of the τ-achievable PLP region is also introduced to explicitly describe the tradeoff in PLP between different users. The second design challenge is structured quantization codebook design in wireless networks with limited feedback, for both MU-MIMO and CoMP. In the MU-MIMO network, two codebook constructions are proposed, which are based on structured transformations of a base codebook. In the CoMP network, a low-complexity construction is proposed to solve the problem of variable codebook dimensions due to changes in the number of coordinated BSs. The proposed construction is shown to have comparable performance with the standard approach based on a random search, while only requiring linear instead of exponential complexity. The final design challenge is resource allocation for physical layer security in MU-MIMO. To guarantee physical layer security, the achievable secrecy sum-rate is explicitly derived for the regularized channel inversion (RCI) precoder. To improve performance, power allocation and precoder design are jointly optimized using a new algorithm based on convex optimization techniques

Efficient Globally Optimal Resource Allocation in Wireless Interference Networks

Radio resource allocation in communication networks is essential to achieve optimal performance and resource utilization. In modern interference networks the corresponding optimization problems are often nonconvex and their solution requires significant computational resources. Hence, practical systems usually use algorithms with no or only weak optimality guarantees for complexity reasons. Nevertheless, asserting the quality of these methods requires the knowledge of the globally optimal solution. State-of-the-art global optimization approaches mostly employ Tuy's monotonic optimization framework which has some major drawbacks, especially when dealing with fractional objectives or complicated feasible sets. In this thesis, two novel global optimization frameworks are developed. The first is based on the successive incumbent transcending (SIT) scheme to avoid numerical problems with complicated feasible sets. It inherently differentiates between convex and nonconvex variables, preserving the low computational complexity in the number of convex variables without the need for cumbersome decomposition methods. It also treats fractional objectives directly without the need of Dinkelbach's algorithm. Benchmarks show that it is several orders of magnitude faster than state-of-the-art algorithms. The second optimization framework is named mixed monotonic programming (MMP) and generalizes monotonic optimization. At its core is a novel bounding mechanism accompanied by an efficient BB implementation that helps exploit partial monotonicity without requiring a reformulation in terms of difference of increasing (DI) functions. While this often leads to better bounds and faster convergence, the main benefit is its versatility. Numerical experiments show that MMP can outperform monotonic programming by a few orders of magnitude, both in run time and memory consumption. Both frameworks are applied to maximize throughput and energy efficiency (EE) in wireless interference networks. In the first application scenario, MMP is applied to evaluate the EE gain rate splitting might provide over point-to-point codes in Gaussian interference channels. In the second scenario, the SIT based algorithm is applied to study throughput and EE for multi-way relay channels with amplify-and-forward relaying. In both cases, rate splitting gains of up to 4.5% are observed, even though some limiting assumptions have been made