Fractional Programming for Stochastic Precoding over Generalized Fading Channels

This paper seeks an efficient algorithm for stochastic precoding to maximize the long-term average weighted sum rates throughout a multiple-input multiple-output (MIMO) network. Unlike many existing works that assume a particular probability distribution model for fading channels (which is typically Gaussian), our approach merely relies on the first and second moments of fading channels. For the stochastic precoding problem, a naive idea is to directly apply the fractional programming (FP) method to the data rate inside the expectation; it does not work well because the auxiliary variables introduced by FP are then difficult to decide. To address the above issue, we propose using a lower bound to approximate the expectation of data rate. This lower bound stems from a nontrivial use of the matrix FP, and outperforms the existing lower bounds in that it accounts for generalized fading channels whose first and second moments are known. The resulting approximate problem can be efficiently solved in closed form in an iterative fashion. Furthermore, for large-scale MIMO, we improve the efficiency of the proposed algorithm by eliminating the large matrix inverse. Simulations show that the proposed stochastic precoding method outperforms the benchmark methods in both Gaussian and non-Gaussian fading channel cases.

💡 Research Summary

This paper addresses the problem of designing stochastic precoders for a multi‑cell, multi‑user MIMO downlink system with the objective of maximizing the long‑term weighted sum‑rate under per‑base‑station power constraints. Unlike most prior works that assume a specific probability distribution for the fading channels (typically Gaussian), the authors only require knowledge of the first‑order (mean) and second‑order (covariance) statistics of each channel matrix. This “moment‑based” model is attractive because the required statistics can be estimated reliably using long‑term measurements, machine‑learning predictors, or digital twins, while the exact distribution is often unavailable or too complex to model.

The system model consists of L cells, each with a base station equipped with M_t transmit antennas, serving K users each having M_r receive antennas. The block‑fading channel from BS ℓ to user (j,k) is denoted H_{jk,ℓ} ∈ ℂ^{M_r×M_t}. Only the mean C_{jk}=E