Communications and Radar Receiver Gains for Minimum Average Cost of Excluding Randomly Fluctuating Signals in Random Noise

Since the ability of both communications and radar receivers to perform satisfactorily can be seriously degraded when the signal amplitude does not lie within the dynamic range of the receiver, the setting of receiver gain to minimize or prevent saturation at the upper and lower dynamic range bounds is an important problem. The problem arises in various forms. In simple receivers, the gain might be fixed 1753 175G T H E BELL SYSTEM TECHNICAL J O U R N A L , OCTOBER 10f>7 to optimize performance for nominal signal and noise parameters. More complicated receivers can adjust the gain automatically by any of several methods. The most common AGC circuits, for example, use a time averaged baseband signal as an indication of signal strength. Another possibility is to have the gain adjusted on command from a digital computer. This latter configuration has important implications for communications terminals which can use sophisticated techniques for estimation of signal and noise parameters as well as for certain radars which must observe from look-to-look radar targets of different cross-section which have been illuminated by various transmitted waveforms. The analysis presented here does not depend on the particular configuration and is applicable to both linear and nonlinear receivers including those of the logarithmic and lin-log type. The application to a nonlinear receiver can be accomplished by referring the overall dynamic range of the signal processing chain to a point before the nonlinearity.