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In this paper we study an intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) network where the direct link between the base station (BS) and one of the users is blocked and the IRS is deployed to serve the blocked user. The IRS designs under both the ideal IRS with continuous phase shifting and the non-ideal IRS with discrete phase shifting are considered. For both cases, by leveraging the isotropic random vector and the Laguerre series, we derive insightful results and closed-form expressions on the performance measures including the average required transmit power, the outage probability, and the diversity order. Our analytical results show that the transmit power scales down linearly with the BS antenna number and quadratically with the IRS element number. The diversity order equals the smaller of the BS antenna number and the IRS element number with a scaling coefficient. Our results also reveal the effect of the phase quantization resolution to the system performance when non-ideal IRS is used. Numerical results are provided to validate the accuracy of our analysis and the non-ideal IRS with four or more bits for quantization is shown to achieve nearly the same performance as the ideal IRS.

A popular technique of designing multiple-input multiple-output (MIMO) communication systems relies on optimizing the positive semidefinite covariance matrix at the source. In this paper, a unified MIMO optimization framework based on the Karush-Kuhn-Tucker (KKT) conditions is proposed. In this framework, with the aid of matrix optimization theory, Theorem 1 presents a generic optimal transmit covariance matrix for MIMO systems with diverse objective functions subject to various power constraints and different levels of channel state information (CSI). Specifically, Theorem 1 fundamentally reveals that for a diverse family of MIMO systems, the optimal transmit covariance matrices associated with different objective functions under various power constraints can be derived in a unified generic water-filling-like form. When applying Theorem 1 to the case of multiple general power constraints, we firstly equivalently transform multiple power constraints into a single counterpart by introducing multiple weighting factors based on Pareto optimization theory. The optimal weighting factors can be found by the proposed modified subgradient method. On the other hand, for the imperfect MIMO system with statistical CSI errors, we firstly address the non-convexity of the robust optimization problem by following the idea of alternating optimization. Finally, our numerical results verify the optimal solution structure in Theorem 1 and the global optimality of the proposed modified subgradient method, as well as demonstrate the performance advantages of the proposed alternating optimization algorithm.