of the two adjacent channels, situated at each side of it. For the antennas in a circular array, three antennas are selected according to the signal levels received, with the largest signal present at the central channel. When the signal is on the boresight of Antenna 1 (φ = 0), the signal from the other two antennas will equal and about 12 dB lower. When the signal direction is halfway between two antennas (φ = 30°), their signal levels will be equal and approximately 3 dB lower than the boresight value, with the third signal now about 24 dB lower. At other bearing angles, ø, some intermediate ratios of the signal levels will give the direction. Basic equations for three-port DF For a signal incoming at a bearing ø, taken here to be to the right of boresight of Antenna 1: Channel 1 output is Channel 2 output is Channel 3 output is where GT is the overall gain of each channel, including antenna boresight gain, and is assumed to be the same in all three channels. As before, in these equations, angles are in radians, Φ = 360/N degrees = 2 π/N radians and A = -ln(0.5). As earlier, these can be expanded and combined to give: Eliminating A/Ψ02 and rearranging where Δ1,3 = ln(P1) - ln(P3), Δ1,2 = ln(P1) - ln(P2) and Δ2,3 = ln(P2) - ln(P3), The difference values here are in nepers but could be in decibels. The bearing value, obtained using this equation, is independent of the antenna beamwidth (= 2.Ψ0), so this value does not have to be known for accurate bearing results to be obtained. Also, there is a smoothing affect, for bearing values near to the boresight of the middle antenna, so there is no discontinuity in bearing values there, as an incoming signals moves from left to right (or vice versa) through boresight, as can occur with 2-channel processing. Bearing uncertainty due to noise Many of the causes of bearing error, such as mechanical imperfections in the antenna structure, poor gain matching of receiver gains, or non-ideal antenna gain patterns may be compensated by calibration procedures and corrective look-up tables, but thermal noise will always be a degrading factor. As all systems generate thermal noise then, when the level of the incoming signal is low, the signal-to-noise ratios in the receiver channels will be poor, and the accuracy of the bearing