A Givens Rotation-Based QRD-RLS-CMA Blind Equalizer for 4 × 4 Real-Valued MIMO Coherent Optical Receivers

Multiple-input multiple-output (MIMO) equalization is essential for robust coherent optical transmission. However, conventional 2×2 complex-valued equalizers provide limited compensation for in-phase and quadrature (IQ) imbalance, degrading signal recovery. Conventional recursive least-squares constant-modulus algorithms (RLS-CMAs) may suffer numerical divergence when long adaptive filters are used. We propose a Givens rotation-based QR decomposition RLS-CMA (QRD-RLS-CMA) for a 4×4 real-valued MIMO equalizer. We compensate for IQ imbalance through real-valued processing and introduce QR decomposition to improve numerical stability without explicitly updating the inverse sample covariance matrix. The algorithm is experimentally evaluated in a 25-GBaud polarization division-multiplexed 16-quadrature amplitude modulation (QAM) coherent optical link over 20 km of standard single-mode fiber. In simulation experiments, separate 3-dB gain-imbalance and 15∘ phase-imbalance tests yield an error vector magnitude (EVM) of approximately 13.8% for the 4×4 equalizer, compared with approximately 25.3% and 22.1%, respectively, for the 2×2 complex-valued baseline. The conventional RLS-CMA exhibits numerical degradation with an increasing tap count and diverges beyond 25 taps, whereas the QRD-RLS-CMA maintains stable convergence through 31 taps. In finite-precision evaluations across fractional word lengths of 8–18 bits, the QRD-RLS-CMA consistently outperforms the conventional RLS-CMA in bit error rate (BER) performance, providing a 2-bit margin in fractional word length at the hard-decision forward error correction (HD-FEC) threshold. The numerical robustness provided by QRD supports the use of longer adaptive filters and offers a basis for reduced-precision hardware implementations in coherent optical receivers.