The problem of joint estimation of time delay and Doppler shift is considered through the point of view of the Wigner distribution of the signal. A very efficient method of obtaining the optimum signal with minimum estimation error based on the convexity of the design region is developed. Practical applications, however, demand the signal to satisfy other constraints which present complications in acquiring the optimum signal. A design approach based on the method of simulated annealing is suggested to solve for the optimum signal under constraints. The performance of the signals so obtained is evaluated and compared with those obtained by synthesis.