Non-Orthogonal Pilot Sequence Design for Multi-Cells Interference Networks

TL;DR

This work tackles pilot design in dense multi-cell networks by introducing ETSC, a correlation metric that weights intra- and inter-cell interference through a matrix $\mathbf{B}$. It derives a new extended Welch bound via a Cross-inner Product Theorem, valid for general $J$, $K$, and $\tau$ with $\mathbf{B}$ positive definite, and identifies a necessary condition for equality (each cell’s set must be WBE). To address parameter regimes where bounds are not achievable or construction is unknown, the paper proposes ETSC-MM, a Majorization-Minimization algorithm that directly minimizes ETSC and can produce unimodular sequences, with favorable complexity and convergence properties. Numerical experiments show that ETSC-MM generates sequence sets with ETSC near or at the new bound, achieves low PAPR for unimodular designs, and delivers superior channel estimation performance in multi-cell settings compared to random or WBE baselines. The proposed framework thus provides a flexible, scalable approach to non-orthogonal pilot design in interference networks, with practical impact for improving cell-edge performance and pilot contamination control.

Abstract

In wireless communications, the performance of non-orthogonal sequence sets significantly affects the level of multi-user interference when the number of users surpasses the sequence length. The design of non-orthogonal sequences plays a crucial role in both the non-orthogonality of the pilots in multi-cell systems and the signature sequences in overloaded code-division multiple-access (CDMA) systems. In multi-cell systems, considering the strength disparity between channels originating from the home cell and the neighboring cells, the extended total squared correlation (ETSC) is proposed as a new sequence design criterion, which is defined as the sum of squares of the weighted correlations among sequences. In this paper, we derive a closed-form expression for the lower bound of ETSC for multi-cell systems with a given sequence length $τ$, where $τ\leq K$ and $K$ is the number of users per cell. This can be regarded as a generalization of the well-known Welch bound (Welch, 1974, IEEE TIT) and the extended Welch bound (Wang et al., 2021, IEEE TWC). Additionally, from the necessary conditions of the bound, the optimal sequence set can be easily obtained when the interference power factor matrix is positive definite. On the other hand, to address the lack of sequence generation methods under certain parameter conditions, we propose the ETSC-MM algorithm, which generates sequence sets with low ETSC based on a Majorization-Minimization (MM) optimization framework.

Figures (12)

• Figure 1: $J$-cell multi-user interference network.
• Figure 2: ETSC of sequence sets generated by Theorem\ref{['Theorem_NEWB']} and the WBE sequence set with $\tau=39$, $K=42,44,46,48$, $J=3$ and different $\mathbf{B}$.
• Figure 3: ETSC of non-unimodular sequence sets with $\tau=39$, $K=32$, $J=2$ and different $\mathbf{B}$.
• Figure 4: ETSC of unimodular sequence sets with $\tau=39$, $K=32$, $J=2$ and different $\mathbf{B}$.
• Figure 5: Comparison of PAPR with $\tau=39$, $K=32$, $J=2$ and different $\mathbf{B}$.

Theorems & Definitions (8)

• Theorem 1: Cross-inner Product Theorem
• Remark 1
• Theorem 2: The New Extended Welch Bound
• Remark 2
• Remark 3
• Lemma 1: song2015optimization
• Theorem 3
• Lemma 2: horn1994topics