Signal-to-noise ratio estimation using higher-order moments

We consider the problem of estimation of the signal-to-noise ratio (SNR) of an unknown deterministic complex phase signal in additive complex white Gaussian noise. The phase of the signal is arbitrary and is not assumed to be known a priori unlike many SNR estimation methods that assume phase synchronization. We show that the moments of the complex sequences exhibit useful mean-ergodicity properties enabling a "method-of-moments" (MoM)-SNR estimator. The Cramer-Rao bounds (CRBs) on the signal power, noise variance and logarithmic-SNR are derived. We conduct experiments to study the efficiency of the SNR estimator. We show that the estimator exhibits finite sample super-efficiency/inefficiency and asymptotic efficiency, depending on the choice of the parameters. At 0 dB SNR, the mean square error in log-SNR estimation is approximately 2 dB2. The main feature of theMoM estimator is that it does not require the instantaneous phase/frequency of the signal, a priori. Infact, the SNR estimator can be used to track the instantaneous frequency (IF) of the phase signal. Using the adaptive pseudo-Wigner-Ville distribution technique, the IF estimation accuracy is the same as that obtained with perfect SNR knowledge and 8-10 dB better compared to the median-based SNR estimator.

[1]  Björn E. Ottersten,et al.  The evil of superefficiency , 1996, Signal Process..

[2]  Sailes K. Sengijpta.  Fundamentals of Statistical Signal Processing: Estimation Theory , 1995 .

[3]  Nader Sheikholeslami Alagha,et al.  Cramer-Rao bounds of SNR estimates for BPSK and QPSK modulated signals , 2001, IEEE Communications Letters.

[4]  Norman C. Beaulieu,et al.  A comparison of SNR estimation techniques for the AWGN channel , 2000, IEEE Trans. Commun..

[5]  Rafik A. Goubran,et al.  SNR estimation of speech signals using subbands and fourth-order statistics , 1999, IEEE Signal Processing Letters.

[6]  Khaled H. Hamed,et al.  Time-frequency analysis , 2003 .

[7]  LJubisa Stankovic,et al.  Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length , 1998, IEEE Trans. Signal Process..

[8]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. II. A/lgorithms and applications , 1992, Proc. IEEE.

[9]  Srdjan Stankovic,et al.  An analysis of instantaneous frequency representation using time-frequency distributions-generalized Wigner distribution , 1995, IEEE Trans. Signal Process..

[10]  Braham Barkat,et al.  Instantaneous frequency estimation of polynomial FM signals using the peak of the PWVD: statistical performance in the presence of additive gaussian noise , 1999, IEEE Trans. Signal Process..

[11]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[12]  Georgios B. Giannakis,et al.  Hybrid FM-polynomial phase signal modeling: parameter estimation and Cramer-Rao bounds , 1999, IEEE Trans. Signal Process..

[13]  Douglas A. Gray,et al.  Performance bounds for polynomial phase parameter estimation with nonuniform and random sampling schemes , 2000, IEEE Trans. Signal Process..

[14]  Patrick J. Loughlin,et al.  Multiwindow time-varying spectrum with instantaneous bandwidth and frequency constraints , 2001, IEEE Trans. Signal Process..

[15]  Bin Li,et al.  New results on SNR estimation of MPSK modulated signals , 2003, 14th IEEE Proceedings on Personal, Indoor and Mobile Radio Communications, 2003. PIMRC 2003..

[16]  Bernard C. Picinbono,et al.  On instantaneous amplitude and phase of signals , 1997, IEEE Trans. Signal Process..

[17]  D. C. Reid,et al.  Aircraft flight parameter estimation based on passive acoustic techniques using the polynomial Wigner–Ville distribution , 1997 .

[18]  Thippur V. Sreenivas,et al.  Adaptive spectrogram vs. adaptive pseudo-Wigner-Ville distribution for instantaneous frequency estimation , 2003, Signal Process..

[19]  Benjamin Friedlander,et al.  Asymptotic statistical analysis of the high-order ambiguity function for parameter estimation of polynomial-phase signals , 1996, IEEE Trans. Inf. Theory.

[20]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[21]  R. Matzner,et al.  An SNR estimation algorithm using fourth-order moments , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[22]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[23]  Thippur V. Sreenivas,et al.  Adaptive Window Zero-Crossing-Based Instantaneous Frequency Estimation , 2004, EURASIP J. Adv. Signal Process..