[Paper Review] Explore and Eliminate: Optimized Two-Stage Search for Millimeter-Wave Beam Alignment

Min Li, Chunshan Liu+3 more|arXiv (Cornell University)|Dec 3, 2018

Millimeter-Wave Propagation and Modeling34 references4 citations

TL;DR

This paper proposes an Optimized Two-Stage Search (OTSS) algorithm for millimeter-wave beam alignment that splits training energy into two phases: an exploration stage to eliminate weak beam pairs and a refinement stage to select the best beam pair. OTSS asymptotically outperforms existing methods by maximizing the misalignment probability decay rate under a single-path channel model with ideal beams.

ABSTRACT

Swift and accurate alignment of transmitter (Tx) and receiver (Rx) beams is a fundamental design challenge to enable reliable outdoor millimeter-wave communications. In this paper, we propose a new Optimized Two-Stage Search (OTSS) algorithm for Tx-Rx beam alignment via spatial scanning. In contrast to one-shot exhaustive search, OTSS judiciously divides the training energy budget into two stages. In the first stage, OTSS explores and trains all candidate beam pairs and then eliminates a set of less favorable pairs learned from the received signal profile. In the second stage, OTSS takes an extra measurement for each of the survived pairs and combines with the previous measurement to determine the best one. For OTSS, we derive an upper bound on its misalignment probability, under a single-path channel model with training codebooks having an ideal beam pattern. We also characterize the decay rate function of the upper bound with respect to the training budget and further derive the optimal design parameters of OTSS that maximize the decay rate. OTSS is proved to asymptotically outperform state-of-the-art beam alignment algorithms, and is numerically shown to achieve better performance with limited training budget and practically synthesized beams.

Motivation & Objective

• To address the challenge of swift and accurate beam alignment in outdoor mmWave communications, where high path loss and blockage degrade performance.
• To overcome the limitations of exhaustive and hierarchical search methods, which either require excessive training or suffer from misalignment error propagation.
• To design a two-stage beam training strategy that optimally allocates training energy to minimize misalignment probability.
• To derive the optimal design parameters of the two-stage search that maximize the decay rate of misalignment probability under a single-path channel model.

Proposed method

• OTSS divides the total training energy budget into two stages: exploration and refinement.
• In the first stage, all candidate beam pairs are trained, and less favorable pairs are eliminated based on received signal strength profiles.
• In the second stage, each surviving beam pair undergoes an additional measurement, and the best pair is selected using combined measurements from both stages.
• The method uses large deviations techniques to derive an upper bound on the misalignment probability and characterizes its decay rate with respect to training energy.
• The decay rate is maximized by optimizing the energy split between stages and the number of beams retained after elimination.
• Theoretical analysis assumes a single-path channel and ideal beam codebooks with known beam patterns.

Experimental results

Research questions

• RQ1 How can training energy be optimally allocated between exploration and refinement stages to minimize beam alignment misalignment?
• RQ2 What is the asymptotic decay rate of the misalignment probability for a two-stage beam training scheme under ideal beam codebooks?
• RQ3 Does the proposed two-stage search outperform exhaustive and hierarchical search in terms of misalignment probability decay rate?
• RQ4 What is the optimal number of beams to retain after the first stage for maximum performance?
• RQ5 How do the design parameters (energy split and beam count) affect the decay rate of misalignment probability?

Key findings

• OTSS asymptotically outperforms both exhaustive and hierarchical beam alignment algorithms in terms of misalignment probability decay rate.
• The optimal energy split between the two stages is derived such that the decay rate is maximized, with the optimal split depending on the number of beams and system parameters.
• The optimal number of beams retained after the first stage is approximately N - round(√N), where N is the total number of beams.
• The decay rate of the misalignment probability is given by I_p̄_miss = |γ|²FRWT / (2σ²(N - K*(N-K*-1)/(2(N-K*)))) with optimal K* = N - round(√N).
• The decay rate of the second-stage misalignment probability is ξ₁⁽²⁾ / 4, which is higher than that of hierarchical search, indicating superior performance.
• Numerical results confirm that OTSS achieves better performance than state-of-the-art methods even with practical, non-ideal beam patterns.