Abstract
In this paper, we propose closed-form precoding schemes with optimal performance for constructive interference (CI) exploitation in the multiuser multiple-input single-output downlink, where the cases of both strict and non-strict phase rotation are considered. For optimization with strict phase rotation, we mathematically derive the optimal precoding structure with Lagrangian and Karush–Kuhn–Tucker conditions. By formulating its dual problem, the optimization problem is further shown to be equivalent to a quadratic programming over a simplex, which can be solved more efficiently. We then extend our analysis to the case of non-strict phase rotation, where it is mathematically shown that a $K$ -dimensional optimization for non-strict phase rotation is equivalent to a $2K$ -dimensional optimization for strict phase rotation in terms of the problem formulation. The connection with the conventional zero-forcing precoding is also discussed. Based on the above-mentioned analysis, we further propose an iterative closed-form scheme to obtain the optimal precoding matrix, where within each iteration a closed-form solution can be obtained. Numerical results validate our analysis and the optimality of the proposed iterative closed-form algorithm, and further show that the proposed iterative closed-form scheme offers a flexible performance-complexity tradeoff by limiting the maximum number of iterations, which motivates the use of CI precoding in practical wireless systems.
Highlights
M ULTIPLE-input multiple-output (MIMO) systems have been widely acknowledged as a promising technology in the field of wireless communications, due to the significant gains over single-antenna systems [1]
By following a similar approach for the case of strict phase rotation, we analytically show that the optimal precoding matrix for theses two scenarios shares a similar closed-form expression, and a K-dimensional optimization for non-strict phase rotation is equivalent to a 2K-dimensional optimization for strict phase rotation in terms of the problem formulation
We summarize the contributions of this paper as: 1) We formulate the optimization problem for constructive interference (CI)-based precoding, where we maximize the distance between the constructive region and the detection thresholds
Summary
M ULTIPLE-input multiple-output (MIMO) systems have been widely acknowledged as a promising technology in the field of wireless communications, due to the significant gains over single-antenna systems [1]. As for the SINR balancing problem, it is proven to be an inverse problem to the power minimization optimization, based on which schemes via bisection search [7] and iterative algorithms [10] have been proposed Both the closed-form and optimization-based precoding designs mentioned above have ignored the fact that interference can be beneficial and further exploited on on a symbol level [14], [15]. Symbol-level precoding schemes based on convex optimization for CI has been proposed in [19], [20], where the concept of constructive region is introduced to relax the strict phase rotation constraint in [18] and achieve an improved performance. 5) We further propose an iterative closed-form algorithm to obtain the optimal precoding matrix for both the strict and non-strict phase rotation cases, where within each iteration a closed-form solution can be derived. Cn×n represents an n × n matrix in the complex set, and I denotes the identity matrix. (·) and (·) denote the real and imaginary part of a complex number, respectively. card (·) denotes the cardinality of a set
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