[Paper Review] Blind Adaptive Beamforming Based on Constrained Constant Modulus RLS Algorithm for Smart Antennas

Lei Wang, Rodrigo C. de Lamare|arXiv (Cornell University)|Mar 7, 2013

Advanced Adaptive Filtering Techniques14 references3 citations

TL;DR

This paper proposes a constrained constant modulus recursive least squares (CCM-RLS) algorithm for blind adaptive beamforming in smart antennas, leveraging RLS optimization to accelerate convergence and improve robustness. The method outperforms existing SG and RLS-based beamformers in convergence speed, tracking capability, and resilience to steering vector mismatches and environmental changes.

ABSTRACT

In this paper, we study the performance of blind adaptive beamforming algorithms for smart antennas in realistic environments. A constrained constant modulus (CCM) design criterion is described and used for deriving a recursive least squares (RLS) type optimization algorithm. Furthermore, two kinds of scenarios are considered in the paper for analyzing its performance. Simulations are performed to compare the performance of the proposed method to other well-known methods for blind adaptive beamforming. Results indicate that the proposed method has a significant faster convergence rate, better robustness to changeable environments and better tracking capability.

Motivation & Objective

• To address slow convergence and poor robustness in existing blind adaptive beamforming algorithms.
• To overcome limitations of step size sensitivity and local minima in stochastic gradient (SG) methods.
• To improve tracking performance in non-stationary environments with sudden changes in interferer numbers or directions.
• To reduce computational complexity while maintaining high performance through matrix inversion optimization.
• To develop a robust, fast-converging beamforming solution without requiring prior knowledge of signal directions or array manifold.

Proposed method

• The proposed CCM-RLS algorithm uses a constrained constant modulus (CCM) cost function to optimize array weights without prior knowledge of signal directions.
• It employs recursive least squares (RLS) optimization to replace the step size with correlation matrix inversion, enabling faster convergence.
• The matrix inversion lemma is applied to reduce computational complexity in updating the inverse correlation matrix.
• The algorithm maintains a linear constraint to preserve the signal of interest (SOI) while minimizing interference and noise power.
• The cost function is derived from the constant modulus property of BPSK-modulated signals, exploiting their constant envelope to enhance blind estimation.
• The method is designed to be robust to steering vector mismatches and environmental variations, such as DOA estimation errors.

Experimental results

Research questions

• RQ1 How does the CCM-RLS algorithm compare to CMV-SG and CCM-SG in terms of convergence speed and steady-state SINR?
• RQ2 What is the performance of CCM-RLS under steering vector mismatch due to DOA estimation errors?
• RQ3 How well does the CCM-RLS algorithm track sudden changes in the number of interferers or their directions?
• RQ4 Can the RLS-based CCM approach achieve faster convergence than SG-based methods without step size tuning?
• RQ5 How does the CCM-RLS algorithm maintain robustness in non-stationary environments with abrupt signal environment changes?

Key findings

• The CCM-RLS algorithm achieves a significantly faster convergence rate compared to CMV-SG and CCM-SG, with SINR reaching steady-state in fewer than 200 snapshots.
• In the ideal steering vector scenario, CCM-RLS achieves a higher steady-state output SINR than CMV-RLS and all SG-based methods.
• Under steering vector mismatch (±1° error), the CCM-RLS algorithm maintains superior performance, while CMV-RLS degrades significantly due to sensitivity to mismatch.
• When new interferers enter the system at 1000 and 2000 samples, the CCM-RLS algorithm recovers to steady-state faster and with less SINR degradation than CMV-RLS and SG-based methods.
• The algorithm demonstrates strong tracking capability, maintaining high SINR after abrupt changes such as interferer entry and departure at 2000 samples.
• The use of RLS with matrix inversion instead of step size leads to improved stability and faster adaptation, especially in dynamic environments.