Likelihood-Based Modulation Classification for Multiple-Antenna Receiver

Likelihood-based algorithms for the classification of linear digital modulations are systematically investigated for a multiple receive antennas configuration. Existing modulation classification (MC) algorithms are first extended to the case of multiple receive antennas and then a critical problem is identified that the overall performance of the multiple antenna systems is dominated by the worst channel estimate of a particular antenna. To address the performance degradation issue, we propose a new MC algorithm by optimally combining the log likelihood functions (LLFs). Furthermore, to analyze the upper-bound performance of the existing and the proposed MC algorithms, the exact Cramer-Rao Lower Bound (CRLB) expressions of non-data-aided joint estimates of amplitude, phase, and noise variance are derived for general rectangular quadrature amplitude modulation (QAM). Numerical results demonstrate the accuracy of the CRLB expressions and verify that the results reported in the literature for quadrature phase-shift keying (QPSK) and 16-QAM are special cases of our derived expressions. Also, it is demonstrated that the probability of correct classification of the new algorithm approaches the theoretical bounds and a substantial performance improvement is achieved compared to the existing MC algorithm.