Block-Level MU-MISO Interference Exploitation Precoding: Optimal Structure and Explicit Duality

TL;DR

This work tackles block-level interference-exploitation precoding for MU-MISO downlink, introducing slot-variant and slot-invariant designs for both power minimization and SINR balancing. It derives optimal structures via Lagrangian duality, reveals explicit dual relationships between PM and SB, and between block-level and symbol-level schemes, enabling decomposition into smaller subproblems and substantial complexity reductions. A novel linear IE precoder is proposed, with existence guaranteed when the number of symbol slots does not exceed the number of users, linking IE gains to a linear transformation of data symbols. Numerical results demonstrate that the proposed block-level approaches achieve notable performance with reduced complexity compared to symbol-level methods, validating the theoretical dualities and optimal structures.

Abstract

This paper investigates block-level interference exploitation (IE) precoding for multi-user multiple-input single-output (MU-MISO) downlink systems. To overcome the need for symbol-level IE precoding to frequently update the precoding matrix, we propose to jointly optimize all the precoders or transmit signals within a transmission block. The resultant precoders only need to be updated once per block, and while not necessarily constant over all the symbol slots, we refer to the technique as block-level slot-variant IE precoding. Through a careful examination of the optimal structure and the explicit duality inherent in block-level power minimization (PM) and signal-to-interference-plus-noise ratio (SINR) balancing (SB) problems, we discover that the joint optimization can be decomposed into subproblems with smaller variable sizes. As a step further, we propose block-level slot-invariant IE precoding by adding a structural constraint on the slot-variant IE precoding to maintain a constant precoder throughout the block. A novel linear precoder for IE is further presented, and we prove that the proposed slot-variant and slot-invariant IE precoding share an identical solution when the number of symbol slots does not exceed the number of users. Numerical simulations demonstrate that the proposed precoders achieve a significant complexity reduction compared against benchmark schemes, without sacrificing performance.

Figures (9)

• Figure 1: Geometric interpretation of IE for a generic $\mathcal{M}$-PSK constellation.
• Figure 2: Average transmit power per frame versus SINR threshold, $N_c=100$, $N_s=20$, QPSK.
• Figure 3: Average transmit power per frame versus subblock length, $\gamma = 12 ~\text{dB}$, $Nc=2000$, $N_s=30$, QPSK.
• Figure 4: Average transmit power versus average execution time per block, $N_c=2000$, $\gamma=12 ~\text{dB}$, $N_s=\left\{6, 12, 18, 24, 30, 36, 42\right\}$, QPSK.
• Figure 5: BER versus SNR, $N_c=500$, $N_s=20$, QPSK.