Figure shows the block diagram of a continuous-rime Mth power loop for phase recovery in an Mary PSK receiver.

(a) Show that the output of the Mth power-law device contains a tone of frequency Mf_m where f is the original carrier.

(b) The oscillator in the phase-locked loop is set to a frequency equal to Mf. Justify this choice.

(c) The Mth power loop suffers from a phase ambiguity problem in that it exhibits M phase ambiguities in the interval [0, 2π]. Explain how this problem arises in the Mth power loop. How would you overcome the problem?

Transcribed Image Text:

Phase-locked ioop M th Received M-ary PSK signal Band-pass Low-pass filter power-law device filter Voltage- controlled oscillator Frequency divider by M Phaşe-shift network M reference signals