Distributed transceiver design for the multi-antenna interference channel

In this thesis, we aim to optimize transmit and receive strategies in a network where there is little or no centralized resource management unit and nodes have limited knowledge of the channel states and limited backhaul communication among each other. In particular, the transmitters have mostly locally available channel state information (CSI) and we assume no data sharing or joint transmit strategies design among transmitters, thus prohibiting joint MIMO transmission. As transmitters must share the same system resources e.g. time and frequency, they generate interference in the process of communicating with the receivers making interference management essential. In a game theoretic perspective of the beamforming design problem over the interference channel, extreme egoistic and altruistic strategies can be defined. Egoistic transmitters act selfishly and maximize their own SINR despite the interference generated to the remaining of the network whereas altruistic transmitters exploit all resources to null out interference generated towards other receivers. It is intuitive to see that none of the above two strategies is generally sum rate optimal. A recent work shows that in the transmit beamforming vector design problem in the MISO-IC with single user decoding (SUD), balancing egoism and altruism brings the operating point on the Pareto boundary, which is the boundary of the achievable rate region assuming linear pre-processing. With this concept in mind, we investigate distributed transmit beamforming designs in the MISO-IC-SUD in Chapter 3. We develop an iterative algorithm that starts at the Nash equilibrium (egoistic extreme) and in each iteration moves towards the zero-forcing solution (altruistic extreme) with a fixed step size. The algorithm ends if one of the transmitters experiences a decrease of rates, thus mimicking the effects of bargaining. The proposed algorithm achieves an operating point close to the Pareto boundary and each user experiences a higher rate than the Nash equilibrium. We thus demonstrate that on the MISO-IC-SUD, players (transmit-receive pairs) can achieve higher rates by cooperating and maintaining a balance between egoism and altruism. As an extension of the beamforming problem on the MISO-IC-SUD, we design the transmit and receive strategies on the MIMO-IC-SUD in Chapter 4. Assuming mostly local CSIT, we model the problem as a Bayesian game which takes the unknown channel knowledge into consideration and where players maximize the expected utility function based on the statistics of the unknown channel. We derive the equilibria of the Bayesian games and revisit the sum rate maximization problem on the K users MIMO-IC-SUD. We observe that the sum rate maximization solution can be interpreted as a balance between the egoistic and altruistic equilibria. With this analysis, we provide an algorithm which allows the transmitters and receivers to optimize the transmit and receive beamformers iteratively. At convergence, the algorithm achieves interference alignment in high SNR regime which allows the sum rate to scale indefinitely with SNR, with the number of degrees of freedom (DOF) as slope. In low SNR regime, we outperform conventional interference alignment schemes as our proposed algorithm balances the egoistic and altruistic components of the metric. In particular, the proposed algorithm achieves close to optimal performances in asymmetric networks, in which some receivers experience stronger uncontrolled background noise. Then we proceed to allow the receivers to have interference decoding capability (IDC) in the MISO-IC in Chapter 5. This additional degree of freedom allows receivers to decode interference and subtract it from the received signal and thus enjoy interference free communication when the channel realizations allow it. However, the receivers' choices of action depend on the design of the transmit precoders. With each choice of the transmit beamformers, we form a new SISO-IC which has a different capacity region. Thus, with each MISO channel realization, we must choose the beamforming vector and transmit power such that the achievable sum rate is the highest after taking into account all possible receivers actions (decode interference or treat interference as noise). There are three design parameters: the receivers decoding structure, the transmit beamforming vector and the transmit power. However, the optimal choice of the three parameters is coupled with each other and its computation is shown to be NP-hard. Nevertheless, we simplify the analysis by first formulating the achievable rate region of a two-user MISO-IC-IDC as a union of regions with different decoding structures. Then, we characterize the boundaries of achievable rate regions of each decoding structure and thus the overall Pareto boundary. We parameterize the transmit power and beamforming vectors that attain the Pareto boundary. The Pareto optimal beamforming vectors are positive linear combination of two channel vectors with weights depending only on two real-valued scalars that range from zero to one. This refines the search space of potential Pareto boundary attaining solutions. As a direct application of the Pareto boundary characterization, we characterize the maximum sum rate point, whose solution set is a strict subset of that of the Pareto boundary, thus significantly reducing the search space of the originally NP-hard problem.