Signal Acquisition in Coherent Receiving Systems

In this paper, the synchronizing of a coherent receiver with a transmitter is investigated. It is assumed that the receiver knows the exact nature of the arriving signal, except its carrier frequency and arrival time. These, however, are known to be within some bounds. The receiver must then search through this frequency and arrival time space and find the signal in the shortest average time. The receiver is only required to find the carrier frequency within some
\Delta f
and the arrival time within some
\Delta \tau
. Thus, the frequency-time space is quantized into a number of cells. It is assumed that the receiver has a detector that tests each cell for some time and then decides that the signal is or is not in that cell. It is first assumed that the receiver knows the exact value of the SNR, and that the signal is equally likely to be in any part of the frequency-time space. For this case, it is found that the receiver should test each cell in the space and if, at the end of the complete scan, the signal is not found, the same test should be repeated over and over again until the signal is found. It is then assumed that the SNR is not known. If an a priori probability density of the SNR is given, an optimum synchronizing procedure may in principle be obtained, but in general it is difficult to obtain. If however, no a priori probability density of the SNR is given, then a synchronizing method is found that is approximately two times as long as the synchronizing method for the SNR known exactly. Thus, the penalty for no information about the SNR is approximately a factor of two in time.