Phase-comparison monopulse
Phase-comparison monopulse is a technique used in radio frequency (RF) applications such as radar and direction finding to accurately estimate the direction of arrival of a signal from the phase difference of the signal measured on two (or more) separated antennas [1] or more typically from displaced phase centers of an array antenna.
Phase-comparison monopulse differs from amplitude-comparison monopulse in that the former uses displaced phase centers with a common beam pointing direction, while the latter uses a common phase center and displaced beam pointing directions.
[2] In phase-comparison monopulse, typically an array is subdivided into sub-arrays, and then a "sum" and a "difference" or "del" channel are formed.
For a linear array, these subarrays would each be half of the elements, divided in the middle.
In a linear array, the output of each sub-array is summed to form the "sum" channel, and the same outputs are subtracted to form the "del" channel.
This ratio gives an error signal that indicates to a high degree of accuracy the actual target angle as compared to the center of the beam.
For a planar array, one sum channel is formed as the sum of the outputs of all four quadrants, but two del channels are formed, one for the elevation dimension and one for the orthogonal azimuth dimension.
Two monopulse ratios are formed just as with a linear array, each one indicating the deviation angle in one dimension from the center of the beam.
Monopulse processing is done entirely with the received signal in the array manifold and beam forming network.
Speaking in terms of only one dimension for clarity, such as with a linear array, the signal is received by the array and summed into each of two subarrays with displaced phase centers.
The del channel is formed simply by subtracting these same subarray outputs.
Second, phase-comparison monopulse doesn't technically actually do a phase comparison, but rather simply divides the del channel by the sum channel to arrive at a ratio wherein the angle information is encoded.
We can define the beam pattern (array factor) of a uniform linear array (ULA) with N elements, as:[5] It is common to perform a variable substitution to
term simply references the absolute phase to the physical center of the array.
, using phase adjustments and an amplitude taper that is often applied to reduce sidelobes.
-space, is the spatial equivalent of the discrete time Fourier transform (DTFT) of the array amplitude tapering vector times a linear phase term.
Let us now develop the monopulse "difference" or "del" pattern by dividing the array into two equal halves called subarrays.
Assuming that N is even (we could just as easily develop this using an odd N),[6] If we assume that the weight matrix is also conjugate symmetric (a good assumption), then and the sum beam pattern can be rewritten as:[7] The difference or "del" pattern can easily be inferred from the sum pattern simply by flipping the sign of the weights for the second half of the array: Again assuming that
Therefore, the monopulse ratio is only accurate to measure the deviation angle of a target within the main lobe of the system.
However, targets detected in the sidelines of a system, if not mitigated, will produce erroneous results regardless.
Before performing monopulse processing, a system must first detect a target, which it does as normal using the sum channel.
All of the typical measurements that a non-monopulse system make are done using the sum channel, e.g., range, Doppler, and angle.
Therefore, a monopulse processor functions by first detecting and measuring the target signal on the sum channel.
Then, only as necessary for detected targets, it measures the same signal on the "del" channel, dividing the imaginary part of this result by the real part of the "sum" channel, then converting this ratio to a deviation angle using the relationships: and This deviation angle, which can be positive or negative, is added to the beam pointing angle to arrive at the more accurate estimate of the actual target bearing angle.
