Massive MIMO-OFDM Channel Acquisition with Multi-group Adjustable Phase Shift Pilots

Massive multiple-input multiple-output - orthogonal frequency division multiplexing (MIMO-OFDM) systems face the challenge of high channel acquisition overhead while providing significant spectral efficiency (SE). Adjustable phase shift pilots (APSPs) are an effective technique to acquire channels with low overhead by exploiting channel sparsity. In this paper, we extend it to multiple groups and propose multi-group adjustable phase shift pilots (MAPSPs) to improve SE further. We first introduce a massive MIMO-OFDM system model and transform the conventional channel model in the space-frequency domain to the angle-delay domain, obtaining a sparse channel matrix. Then, we propose a method of generating MAPSPs through multiple basic sequences and investigate channel estimation processes. By analyzing the components of pilot interference, we elucidate the underlying mechanism by which interference affects MMSE estimation. Building upon this foundation, we demonstrate the benefit of phase scheduling in MAPSP channel estimation and establish the optimal design condition tailored for scheduling. Furthermore, we propose an implementation scheme based on Zadoff-Chu sequences that includes received signal pre-processing and pilot scheduling methods to mitigate pilot interference. Simulation results indicate that the MAPSP method achieves a lower mean square error (MSE) of estimation than APSP and significantly enhances SE in mobility scenarios.

💡 Research Summary

This paper addresses the pressing problem of channel acquisition overhead in massive MIMO‑OFDM systems, which is a critical bottleneck for next‑generation 6G networks. The authors propose a novel multi‑group adjustable phase‑shift pilot (MAPSP) scheme that extends the previously introduced adjustable phase‑shift pilot (APSP) from a single‑group to multiple user groups, thereby enabling more efficient pilot reuse without sacrificing estimation accuracy.

The work begins by reformulating the conventional space‑frequency channel model into the angle‑delay domain using discrete Fourier transforms and array response matrices. This transformation reveals a highly sparse representation of the channel, where each element can be expressed as a product of a complex gain and a phase term. The phase term is modeled as a wrapped Gaussian distribution centered around the line‑of‑sight (LoS) component, reflecting the limited variance observed in realistic propagation environments.

Building on this sparsity, the MAPSP design employs several basic pilot sequences—specifically Zadoff‑Chu (ZC) sequences—assigned to distinct user groups. Each user within a group receives a unique phase‑shift factor, allowing the same basic sequence to be reused across groups. The authors analytically decompose pilot interference into intra‑group and inter‑group components, deriving explicit expressions for the corresponding angle‑delay domain cross‑correlation matrices. A fast DFT‑based algorithm is presented to compute these matrices efficiently, which is essential for evaluating the interference terms in the minimum‑mean‑square‑error (MMSE) channel estimator.

A key contribution is the derivation of optimal design conditions: the phase‑shift values should be chosen such that all cross‑correlation matrices become nearly diagonal, effectively minimizing mutual interference. Under these conditions, the MMSE estimator simplifies to a form identical to that of a single‑group APSP, but with substantially reduced overall interference.

Implementation details include a two‑layer scheduling algorithm. The first layer optimizes phase allocations across groups (inter‑group scheduling), while the second layer fine‑tunes phase differences among users within the same group (intra‑group scheduling). Prior to estimation, the base station performs a pre‑processing step that extracts intra‑group channel components from the received uplink signal, further simplifying the estimation problem.

Simulation results are based on the 3GPP 38.901 channel models for typical vehicular and high‑mobility scenarios. With 84 users at an SNR of 30 dB, MAPSP achieves spectral efficiency (SE) gains of approximately 17.2 %, 10.7 %, and 8.5 % over APSP for three representative configurations. When the number of users is increased to 126, the SE improvements rise dramatically to 25.3 %, 17.5 %, and 117.5 %, respectively. Correspondingly, the mean‑square‑error (MSE) of channel estimation is consistently lower for MAPSP across all tested SNRs.

In summary, the paper makes three major contributions: (1) a rigorous angle‑delay domain channel model that exposes sparsity and phase characteristics; (2) a multi‑group pilot framework with analytically derived interference mitigation conditions and a practical ZC‑based implementation; and (3) extensive performance validation showing that MAPSP can substantially reduce pilot overhead while delivering higher SE and more accurate channel estimates, especially in high‑mobility, dense‑user environments. The proposed MAPSP scheme thus offers a scalable and low‑complexity solution for future massive MIMO‑OFDM deployments.