# GPS range and signal to noise ratio

GPS receiver can measure pseudoranges to a satellite with a precision of 0.5 meters or better. In the last chapter, we attributed this ranging prowess to the auto-correlation functions of the C/A-codes and more specifically to the slope of the main peak of that function. In this chapter, we will substantiate that claim with a quantitative analysis of ranging precision in the presence of white noise. We will discover that the ranging precision does indeed depend on the slope of the correlation function, which in turn depends on the bandwidth of the signal.

As we shall see, the ranging performance also depends on the signal-to-noise ratio, C/N0, and the averaging time used by the receiver. C/N0 is the ratio of the power in the received signal to the power spectral density of the competing noise. Signal power, C, has units of watts or joules/sec. Power spectral density, N0, has units of watts/hertz. Hence, C/N0 has units of hertz.

The power available for the C/A-code on the satellite is approximately 27 watts, but the power collected by a typical receiver on the earth’s surface is only 10–16 watts or so. When received, the GPS signal is swamped by the noise in the front end of the receiver. In this chapter, we develop estimates of the received signal power and the received noise power spectral density. The ratio of these two powers is key to ranging precision.