Demonstrate the equivalence of the two complex representations given in (7.276) and (7.277), which pertain to the likelihood function.

a. In the recursive algorithm of (7.295) for symbol timing recovery, the control signals cn and cn + 1 are both dimensionless. Discuss the units in which the error signal en and step-size parameter are measured.

b. In the recursive algorithm of (7.300) for phase recovery, the old estimate and the updated estimate of the carrier phase q are both measured in radians. Discuss the units in which the error signal en and step-size parameter are measured.