Closed-Form Approximation to the Average Symbol Error Probability for Cross-QAM over κ–μ Fading Channels with Experimental Validation in the Millimeter-Wave Band

This work presents a closed-form approximation to the symbol error probability (SEP) for cross-quadrature amplitude modulation (cross-QAM) schemes over κ–μ fading channels. The proposed formulation enables accurate performance evaluation while avoiding computationally expensive numerical integration. The analysis covers millimeter-wave (mmWave) frequencies at 55, 60, and 65 GHz, under both line-of-sight (LoS) and non-line-of-sight (nLoS) conditions, and for multiple transmitter–receiver polarization configurations. A key contribution of this work is the experimental validation of the theoretical expression with real channel-measurement data, which confirms the applicability of the κ–μ model in realistic mmWave scenarios. Furthermore, we perform a detailed parametric study to quantify the influence of κ and μ on adaptive modulation performance, providing practical insights for 5G and future 6G systems. The proposed framework bridges theoretical analysis and experimental validation, offering a computationally efficient and robust tool for the design and evaluation of advanced modulation schemes in generalized fading environments.