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In array antenna systems, array gain is the measure of the improvement in signal-to-noise ratio (SNR) achieved by the array. It is calculated as the SNR of the array output signal divided by the SNR of the array input signal. Intuitively, the array gain is realized by the fact that the signal is coherently added from N array elements, while the noise is incoherently added from those same elements. If the noise is presumed to be uncorrelated the array gain is ≤ N, the number of array elements, and the array gain reduces to the inverse of the square of the 2-norm of the array weight vector, under the assumption that the weight vector is normalized such that its sum is unity, so that
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