FSK、PSK基带信号高阶累积量理论值

本文介绍了FSK和PSK基带信号的高阶累积量理论值计算,包括MFSK和MPSK信号的详细分析。针对2FSK和BPSK信号,给出了具体的高阶累积量公式,并讨论了循环累积量的概念,为数字调制信号的自动识别提供理论基础。

高阶累积量计算公式

Mpq=E{ Xp−q(t)[X∗(t)]q}{M_{pq}} = E\left\{ { {X^{p - q}}(t){ {\left[ { {X^*}(t)} \right]}^q}} \right\}M<

MATLAB高阶累积量工具箱,包含内容有: Higher-Order Spectrum Estimation: conventional methods % cum2x - Estimates cross-covariance % cum3x - Estimates third-order cross-cumulants % cum4x - Estimates fourth-order cross-cumulants % cumest - Estimates auto-cumulants, orders two, three, or four % (cum2est, cum3est, cum4est are sub-ordinate routines) % bicoher - Estimates bicoherence, direct method % bicoherx - Estimates cross-bicoherence, direct method % bispecd - Bispectrum estimation (direct method) % bispecdx - Cross-Bispectrum estimation (direct method) % bispeci - Bispectrum estimation (indirect method) % glstat - Gaussianity-Linearity detection statistics (Hinich test) % % Higher-Order Spectrum Estimation: parametric methods % armaqs - Estimates ARMA parameters via q-slice algorithm % armarts - Estimates ARMA parameters via residual time-series algorithm % armasyn - Generates ARMA synthetics % arorder - Estimates AR order % arrcest - Estimates AR parameters using correlation &/or cumulants % bispect - Theoretical bispectrum of an ARMA process % cumtrue - Computes theoretical (true) cumulants of ARMA processes % maest - Estimates MA parameters (GM algorithm) % maorder - Estimates MA order % rpiid - Generates a sequence of i.i.d. random variables, various p.d.f.'s % trispect - Computes 2-D slice of true trispectrum of ARMA process % % Quadratic Phase Coupling (QPC) % qpcgen - Generates quadratically-phase coupled harmonics in noise % qpctor - Detection of quadratic phase coupling via the TOR method % % Second-Order Volterra Systems % nlgen - Computes the output of a second-order Volterra system % nlpow - Power's method for parameters of 2nd-order Volterra system % nltick - Tick 's method for parameters of 2nd-order Volterra system % % Harmonic Retrieval % harmest - Estimates frequencies of h
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