Open-loop phase estimation methods and apparatus for coherent demodulation of phase modulated carriers in mobile channels

In a ground based mobile channel, a method of coherent recovery of phase in a phase shift keyed digital signal modulated on a carrier comprising the steps of:

• (a) receiving the phase shift keyed signal modulated on a carrier and demodulating the signal using a local oscillator signal as a reference to provide inphase and quadrature components of the demodulated signal;
• (b) providing digitized samples of the inphase and quadrature components of the demodulated signal of step (a) representative of the demodulated signal at each bit time to provide digitized inphase and quadrature components of a first vector having a phase responsive to (i) an information-bearing phase component of the received signal, (ii) the phase difference between the local oscillator signal and the carrier of the received signal, and (iii) interference and noise;
• (c) squaring the first vector to provide a second vector having twice the phase angle of the first vector;
• (d) inverting every other second vector by inverting the second vector every odd bit time;
• (e) for each successive bit time n, finding an estimated error vector by taking the square root of the average of an odd number m of successive second vectors ##EQU5## through ##EQU6## using where applicable the inverted vectors of step (d);
• (f) multiplying the first vector V.sub.n of step (b) for each bit time n and the conjugate of the estimated phase error vector of step (e) for bit time n to provide a third vector;
• (g) multiplying the estimated phase error vector of step (e) for bit time n by the conjugate of the estimated phase error vector of step (e) for bit time n-1 to at least find the sign of the real part of the vector product;
• (h) decoding the third vector for each bit time to obtain a bit of data, including inverting the respective bit if the real part of the vector product of step (g) is negative.