Patent ID: 7190741

Claim:
Method of estimating signal-to-noise ratio (SNR) γ of a composite input signal e(t) on a communications link, comprising: providing a first demodulator receiving the composite input signal and a stable carrier signal, and outputting an in-phase output signal; providing a second demodulator receiving the composite input signal and a phase-shifted version of the stable carrier signal, and outputting a quadrature-phase output signal; calculating phase error θ E (t)) contained within the composite input signal e(t) from the outputs of the first and second demodulators; estimating a biased estimate γ* for the signal-to-noise ratio (SNR) γ of the composite input signal using maximum likelihood (ML) estimation techniques; and estimating an unbiased estimate {circumflex over (γ)} for the signal-to-noise ratio (SNR) γ of the composite input signal from the biased estimate γ*; taking a series of κ phase measurements θ E (t i ) of the composite signal input where κ is a number of sampled values; and calculating a biased estimate γ* for the signal-to-noise ratio (SNR) γ of the composite input signal, over all possible values of the phase error θ E (t), according to the following equation: γ * = [ 1 k ⁢ ∑ i = 1 k ⁢ ⁢ sin 2 ⁡ ( θ E ⁡ ( t i ) ) ] - 1 , γ>>1; and calculating an unbiased estimate {circumflex over (γ)} from the biased estimate γ*, according to the following equation: 〈 1 γ * 〉 = ⁢ ∫ - π 2 π 2 ⁢ sin 2 ⁡ ( θ E ) ⁢ p ⁡ ( γ ^ | θ E ) ⁢ ⁢ ⅆ θ E = ⁢ ⁢ ( 2 π ) ⁢ exp ⁡ ( - γ ^ 2 ) ⁢ ∫ 0 π 2 ⁢ sin 2 ⁢ θ E ⁢ ⁢ ⅆ θ E + ⁢ + 2 ⁢ 1 2 ⁢ ⁢ π ⁢ γ ^ ⁢ ∫ 0 π 2 ⁢ sin 2 ⁡ ( θ E ) ⁢ cos ⁡ ( θ E ) ⁢ exp ⁡ ( - γ ^ 2 ⁢ sin 2 ⁡ ( θ E ) ) ⁢ ⁢ ⅆ θ E = ⁢ ( 1 2 - 2 π ⁢ 1 γ ^ ) ⁢ exp ⁡ ( - γ ^ 2 ) + ( 1 γ ^ ) ⁢ erf ⁡ ( γ ^ 2 ) ⁢ .