O.V. Karavan, V.A. Timofeev

The closed-form expressions for moment-based QAM signal magnitude gain estimation using jointly the first and the second or the second and the fourth moments where derived. Additive white gaussian noise channel model was considered. Performance comparison of this estimators and algorithms based on the first, the second moments, and the sample median has been carried out via simulation for nine constellations. The results showed that when constellation has one amplitude level the least variance can be attained by using the second and the fourth moments. When constellation has more than one amplitude level the common property of considered estimators is variance error floor which appears as variance decreasing stop starting from some value while increasing SNR. For these constellations it appears that when SNR< 10 dB the least variance can be achieved by using the sample median and when SNR> 10 dB the second moment based estimator leads to the minimal variance. It was found that the second and the fourth moments based estimator always overcome the one based on first and the second moments in statistical and numerical efficiency. Thus if SNR operating point is known or can be estimated then depending on it-s value the least variance can be delivered using sample median or second moment based estimation, otherwise the best choice is the second and the fourth moments based estimation