Local Partial RZF in Cell-Free Massive MIMO: A Deterministic Equivalent Analysis

We consider a cell-free massive multiple-input and multiple-output (CF-mMIMO) system, where we derive a deterministic equivalent (DE)-form of the ergodic sum spectral efficiency (SE) based on local partial regularized zero-forcing (LP-RZF) precoding with statistical channel state information (S-CSI) by leveraging large-dimensional random matrix theory. Thanks to this derivation, the previously challenging issue of precoding design based on S-CSI is now resolved, particularly in scenarios where CSI is limited to local information at each access point (AP). Moreover, as the central processing unit (CPU) now only needs to transmit an optimized regularization parameter to the APs, the computational overhead can be reduced, which naturally enhances the system scalability. Driven by these advantages, we then introduce a joint user association, power allocation, and precoding design (i.e., regularization parameter optimization) scheme aimed at maximizing the ergodic sum SE and minimizing the sum power consumption. This is achieved through two optimization problems: one for the ergodic sum SE maximization using weighted minimum mean square error (WMMSE)-based processing and another for the sum power consumption minimization employing a block coordinate descent (BCD)-based algorithm. Numerical results demonstrate the superior performance of the proposed PRO-LPRZF scheme.