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Smart Pilot Assignment for Massive MIMO
Xudong Zhu, Zhaocheng Wang, Linglong Dai, Chen Qian
TL;DR
Pilot contamination from inter-cell pilot reuse limits massive MIMO performance, especially for poorly served users. SPA measures pilot-specific interference using large-scale fading and assigns the least-interfered pilots sequentially to the weakest-channel users. Simulations show gains over conventional assignment and convergence toward the optimal solution as BS antennas increase.
Problem
Pilot contamination remains a bottleneck because inter-cell interference from reused pilots does not vanish as the number of BS antennas increases.
Method
SPA measures each pilot sequence’s inter-cell interference and assigns the least-interfered sequence sequentially to the user with the worst channel quality.
Results
At M = 32, SPA outperforms conventional schemes by about 2 dB minimum uplink SINR; at M = 128, it improves minimum-user capacity by about 0.6 bps/Hz.
Takeaways & Limitations
SPA approaches exhaustive-search performance as the number of BS antennas grows while improving the weakest users’ uplink performance.
Abstract
from arXiv · showhide
A massive multiple-input multiple-output (MIMO) system, which utilizes a large number of antennas at the base station (BS) to serve multiple users, suffers from pilot contamination due to inter-cell interference. A smart pilot assignment (SPA) scheme is proposed in this letter to improve the performance of users with severe pilot contamination. Specifically, by exploiting the large-scale characteristics of fading channels, the BS firstly measures the inter-cell interference of each pilot sequence caused by the users with the same pilot sequence in other adjacent cells. Then, in contrast to the conventional schemes which assign the pilot sequences to the users randomly, the proposed SPA method assigns the pilot sequence with the smallest inter-cell interference to the user having the worst channel quality in a sequential way to improve its performance. Simulation results verify the performance gain of the proposed scheme in typical massive MIMO systems.
I. INTRODUCTION
Pilot contamination remains a performance bottleneck in massive MIMO because reused pilots create inter-cell interference. SPA addresses limitations of existing approaches by matching pilot-interference severity with users’ channel qualities.
- Pilot contamination persists as inter-cell interference increases, unlike intra-cell interference and uncorrelated noise, which can diminish with more BS antennas.
- Existing remedies trade off interference reduction against data-pilot interference, computational complexity, or spectral-efficiency loss from coordination overhead.
- Conventional assignments overlook both users’ different channel qualities and the varying contamination severity of pilot sequences.
- SPA measures each pilot’s inter-cell interference and sequentially assigns the least-interfered pilot to the user with the worst channel quality.
II. SYSTEM MODEL
The system uses orthogonal pilots reused across cells, so correlating received pilots produces channel estimates contaminated by same-pilot users in other cells. As antennas grow, noise and small-scale fading diminish, but pilot contamination limits uplink capacity.
- Each of L hexagonal cells has an M-antenna BS serving K single-antenna users, with channel vectors modeled using large- and small-scale fading.
- Orthogonal pilot sequences are reused across cells because pilot resources are limited, while conventional methods assign them without considering users’ channel-quality differences.
- Correlating received pilots yields an estimate that combines channels from same-pilot users in all cells, creating pilot contamination.
- The matched-filter detector uses the contaminated channel estimate, while intra-cell interference and uncorrelated noise can be reduced by increasing BS antennas.
- Uplink capacity is limited by pilot contamination and cannot be improved by increasing either uplink or pilot transmit power.
III. PROPOSED SCHEME
The proposed scheme formulates pilot assignment as an optimization problem, develops SPA as a greedy approximation, and analyzes its performance.
- Pilot assignment is formulated as an optimization problem for a target cell.
- SPA approaches the optimization solution using a greedy sequential procedure.
- Performance analysis is provided to verify the effectiveness of the proposed scheme.
A. Problem Formulation
The assignment objective prioritizes the weakest users by maximizing the target cell’s minimum uplink SINR. Because exhaustive search is impractical, SPA uses trackable large-scale fading coefficients to approximate the original problem greedily.
- A. Problem Formulation: The target cell has K! possible one-to-one assignments between K users and K pilot sequences.
- A. Problem Formulation: The optimization objective is to maximize the minimum uplink SINR among all users because severely contaminated users become the performance bottleneck.
- A. Problem Formulation: Exhaustive optimization is difficult because accurate channel estimates are unavailable under pilot contamination.
- A. Problem Formulation: Large-scale fading coefficients provide a slowly changing, easily tracked basis for approximating the original assignment problem.
- A. Problem Formulation: SPA solves the simplified optimization problem P′ through a greedy procedure.
B. Pilot Assignment
The SPA scheme reduces pilot-assignment complexity by sorting pilot sequences by inter-cell interference and users by channel quality, then pairing them sequentially. This greedy approach replaces exhaustive search over K! assignments with O(K log K) sorting, while extending to multiple cells through iterative coordination.
- The exhaustive-search formulation considers all K! pilot assignments, creating high computational complexity.
- The SPA scheme quantifies each pilot sequence’s inter-cell interference caused by same-pilot users in adjacent cells.
- The assignment avoids pairing high-interference pilots with users having poor channel quality, which otherwise produces relatively low uplink SINR.
- SPA sorts pilot sequences by descending interference severity and users by descending channel quality before assigning corresponding sequence-user pairs.
- The proposed sorting procedure has complexity O(K log K), compared with O(K!) for exhaustive search.
- For L cells, cells solve their optimization problems sequentially and repeat the procedure iteratively until convergence.
C. Performance Analysis
The analysis proves that the greedy SPA assignment solves the large-scale-fading optimization problem and examines its relationship to the original problem. Simulations then evaluate the minimum-user SINR, capacity, and convergence behavior.
- The paper proves that the assignment generated greedily by SPA is one solution to optimization problem P′.
- When users have equal channel quality, exchanging their assigned pilot sequences does not change the minimum uplink SINR.
- As M →∞, the solution to P′ is also the solution to P; with finite M, it can approach the solution to P.
IV. NUMERICAL RESULTS
Simulations evaluate SPA in a typical multi-cell massive MIMO network, showing gains over conventional assignment and convergence toward optimal performance as the antenna count increases.
- With M = 32, SPA outperforms conventional schemes by about 2 dB in the CDF of minimum uplink SINR, while exhaustive search gains another 0.5 dB.
- With M = 512, SPA performance is almost the same as the exhaustive-search optimal solution.
- As M grows large, SPA performance approaches the optimal solution for the average capacity of the minimum-SINR user.
- For the sequential iterative scheme across all L cells, convergence takes about 5 iterations at M = 32 and fewer iterations as M increases.
V. CONCLUSIONS
The letter proposes SPA to improve the minimum uplink SINR of users in a target cell. SPA assigns the least-interfered pilots sequentially to users with the worst channel quality, approaching the original optimization as M grows.
- SPA improves the minimum uplink SINR of all users in the target cell by assigning the least-interfered pilot to the worst-channel user sequentially.
- The SPA assignment solves the simplified optimization problem P′ and can approach the original problem P as M grows to infinity.
- For 128 BS antennas, simulations show that SPA improves the minimum uplink SINR by about 2 dB.