In this paper, analytical expressions for the distribution of the envelope and phase of linearly modulated signals such as BPSK, M-PSK, and M-QAM in AWGN are presented. We perform numerical simulations for different orders of signal constellations. The results show that the proposed theoretical models are in excellent agreement with the estimated distributions from various numerical experiments.
Signal-to-noise ratio (SNR) information is required in many communication receivers and their proper operation is, to a large extent, related to the SNR estimation techniques they employ. Most of the available SNR estimators are based on approaches that either require large observation length or suffer from high computation complexity. In this paper, we propose a low complexity, yet accurate SNR estimation technique that is sufficient to yield meaningful estimation for short data records. It is shown that our estimator is fairly close to the (CRLB) for high SNR values. Numerical results also confirm that, in terms of convergence speed, the proposed technique outperforms the popular moment based method, M2M4.
Companding, as a variant of audio level compression, can help reduce the dynamic range of an audio signal. In analog (digital) systems, this can increase the signal-to-noise ratio (signal to quantization noise ratio) achieved during transmission. The µ-law algorithm that is primarily used in the digital telecommunication systems of North America and Japan, adapts a companding scheme that can expand small signals and compress large signals especially at the presence of high peak signals. In this paper, we present a novel multi-exponential companding function that can achieve more uniform compression on both large and small signals so that the relative signal strength over the time is preserved. That is, although larger signals may get considerably compressed, unlike µ-law algorithm, it is guaranteed that these signals after companding will definitely not be smaller than expanded signals that were originally small. Performance of the proposed algorithm is compared with µ-law using real audio signal, and results show that the proposed companding algorithm can achieve much smaller quantization errors with a modest increase in computation time.
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