Method and apparatus for joint optimization of transmitted pulse shape

Abstract

In digital transmission, the combination of transmitted pulse shape and receiver sampling time that maximizes the magnitude of the channel output pulse sample is determined. The transmitted pulse shape is represented as a linear combination of orthonormal functions. The coefficients that multiply each of the functions are determined by measuring at the receiver and transmitting back to the transmitter the response of the channel to each independently transmitted function at an approximation to the optimal sampling time. A pulse shape is formed using the calculated coefficients and is transmitted to the receiver where the timing of its maximum is determined, which represents a next approximation to the optimal sampling time. By repeating a plurality of times the processes of transmitting the functions, measuring at the receiver and transmitting back to the transmitter the responses at the approximation to the optimal sampling time, calculating the coefficients, transmitting a pulse, and determining a next approximation to the optimal sampling time from the timing of the maximum in the received pulse, the coefficients and optimal sampling time will converge.