easily derived the sum pattern by first determining the pattern of each subarray individually and adding these two results together. In monopulse practice, this is what is actually done. The reader is left to show that is conjugate symmetric, so it can be re-written in terms of only its first half, using an exchange matrix, , that "flips" this vector. Note that . Assuming that N is even (we could just as easily develop this using an odd N), If we assume that the weight matrix is also conjugate symmetric (a good assumption), then and the sum beam pattern can be rewritten as: 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 , the del pattern can be shown to reduce to: Monopulse Ratio The monopulse ratio is formed as: One can see that, within the 3dB beam width of the system, the monopulse ratio is almost linear. In fact, for many systems a linear approximation is good enough. One can also note that the monopulse ratio is continuous within the null-to-null beam width, but has asymptotes that occur at the beam nulls. 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. Concept of Operations 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. However, the angle measurement is limited in that the target could be anywhere within the beam width of the sum beam, and therefore the system can only assume that the beam pointing direction is the same as the actual target angle. In reality, of course, the actual target angle and the beam steered angle will differ. 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