Power Minimizer Symbol-Level Precoding: A Closed-Form Sub-Optimal Solution

In this letter, we study the optimal solution of the multiuser symbol-level precoding (SLP) for minimization of the total transmit power under given signal-to-interference-plus-noise ratio (SINR) constraints. Adopting the distance preserving constructive interference regions (DPCIR), we first derive a simplified reformulation of the problem. Then, we analyze the structure of the optimal solution using the Karush-Kuhn-Tucker (KKT) optimality conditions, thereby we obtain the necessary and sufficient condition under which the power minimizer SLP is equivalent to the conventional zero-forcing beamforming (ZFBF). This further leads us to a closed-form sub-optimal SLP solution (CF-SLP) for the original problem. Simulation results show that CF-SLP provides significant gains over ZFBF, while performing quite close to the optimal SLP in scenarios with rather small number of users. The results further indicate that the CF-SLP method has a reduction of order $10^3$ in computational time compared to the optimal solution.Comment: 7 pages, 1 figure, 1 table, submitted to IEEE signal processing letter

Joint Power Allocation and User Association Optimization for Massive MIMO Systems

This paper investigates the joint power allocation and user association problem in multi-cell Massive MIMO (multiple-input multiple-output) downlink (DL) systems. The target is to minimize the total transmit power consumption when each user is served by an optimized subset of the base stations (BSs), using non-coherent joint transmission. We first derive a lower bound on the ergodic spectral efficiency (SE), which is applicable for any channel distribution and precoding scheme. Closed-form expressions are obtained for Rayleigh fading channels with either maximum ratio transmission (MRT) or zero forcing (ZF) precoding. From these bounds, we further formulate the DL power minimization problems with fixed SE constraints for the users. These problems are proved to be solvable as linear programs, giving the optimal power allocation and BS-user association with low complexity. Furthermore, we formulate a max-min fairness problem which maximizes the worst SE among the users, and we show that it can be solved as a quasi-linear program. Simulations manifest that the proposed methods provide good SE for the users using less transmit power than in small-scale systems and the optimal user association can effectively balance the load between BSs when needed. Even though our framework allows the joint transmission from multiple BSs, there is an overwhelming probability that only one BS is associated with each user at the optimal solution.Comment: 16 pages, 12 figures, Accepted by IEEE Trans. Wireless Commu

Low-Complexity OFDM Spectral Precoding

This paper proposes a new large-scale mask-compliant spectral precoder (LS-MSP) for orthogonal frequency division multiplexing systems. In this paper, we first consider a previously proposed mask-compliant spectral precoding scheme that utilizes a generic convex optimization solver which suffers from high computational complexity, notably in large-scale systems. To mitigate the complexity of computing the LS-MSP, we propose a divide-and-conquer approach that breaks the original problem into smaller rank 1 quadratic-constraint problems and each small problem yields closed-form solution. Based on these solutions, we develop three specialized first-order low-complexity algorithms, based on 1) projection on convex sets and 2) the alternating direction method of multipliers. We also develop an algorithm that capitalizes on the closed-form solutions for the rank 1 quadratic constraints, which is referred to as 3) semi-analytical spectral precoding. Numerical results show that the proposed LS-MSP techniques outperform previously proposed techniques in terms of the computational burden while complying with the spectrum mask. The results also indicate that 3) typically needs 3 iterations to achieve similar results as 1) and 2) at the expense of a slightly increased computational complexity.Comment: Accepted in IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 201

Symbol-Level Precoding Design for Max-Min SINR in Multiuser MISO Broadcast Channels

In this paper, we address the symbol level precoding (SLP) design problem under max-min SINR criterion in the downlink of multiuser multiple-input single-output (MISO) channels. First, we show that the distance preserving constructive interference regions (DPCIR) are always polyhedral angles (shifted pointed cones) for any given constellation point with unbounded decision region. Then we prove that any signal in a given unbounded DPCIR has a norm larger than the norm of the corresponding vertex if and only if the convex hull of the constellation contains the origin. Using these properties, we show that the power of the noiseless received signal lying on an unbounded DPCIR is an strictly increasing function of two parameters. This allows us to reformulate the originally non-convex SLP max-min SINR as a convex optimization problem. We discuss the loss due to our proposed convex reformulation and provide some simulation results.Comment: Submitted to SPAWC 2018, 7 pages, 2 figure

A Tutorial on Interference Exploitation via Symbol-Level Precoding: Overview, State-of-the-Art and Future Directions

IEEE Interference is traditionally viewed as a performance limiting factor in wireless communication systems, which is to be minimized or mitigated. Nevertheless, a recent line of work has shown that by manipulating the interfering signals such that they add up constructively at the receiver side, known interference can be made beneficial and further improve the system performance in a variety of wireless scenarios, achieved by symbol-level precoding (SLP). This paper aims to provide a tutorial on interference exploitation techniques from the perspective of precoding design in a multi-antenna wireless communication system, by beginning with the classification of constructive interference (CI) and destructive interference (DI). The definition for CI is presented and the corresponding mathematical characterization is formulated for popular modulation types, based on which optimization-based precoding techniques are discussed. In addition, the extension of CI precoding to other application scenarios as well as for hardware efficiency is also described. Proof-of-concept testbeds are demonstrated for the potential practical implementation of CI precoding, and finally a list of open problems and practical challenges are presented to inspire and motivate further research directions in this area

Interference Exploitation-based Hybrid Precoding with Robustness Against Phase Errors

Hybrid analog-digital precoding significantly reduces the hardware costs in massive MIMO transceivers when compared to fully-digital precoding at the expense of increased transmit power. In order to mitigate the above shortfall, we use the concept of constructive interference-based precoding, which has been shown to offer significant transmit power savings when compared with the conventional interference suppression-based precoding in fully-digital multiuser MIMO systems. Moreover, in order to circumvent the potential quality-of-service degradation at the users due to the hardware impairments in the transmitters, we judiciously incorporate robustness against such vulnerabilities in the precoder design. Since the undertaken constructive interference-based robust hybrid precoding problem is nonconvex with infinite constraints and thus difficult to solve optimally, we decompose the problem into two subtasks, namely, analog precoding and digital precoding. In this paper, we propose an algorithm to compute the optimal constructive interference-based robust digital precoders. Furthermore, we devise a scheme to facilitate the implementation of the proposed algorithm in a low-complexity and distributed manner. We also discuss block-level analog precoding techniques. Simulation results demonstrate the superiority of the proposed algorithm and its implementation scheme over the state-of-the-art methods