A sparse array is formed from a linear equi-spaced array by omitting elements and substituting self- and crosspower terms from remaining elements to preserve the pattern and gain characteristics of the full array. However, the output noise is generally increased for any given averaging time. Analytical techniques permit evaluating the output noise for any sparse array under general conditions of substitution scheme, signal-to-noise ratio, and interelement noise correlations. An optimum substitution scheme is selected from a linear combination constrained to give identical patterns for the sparse and full arrays. For example, omitting an inner element of a four-element array increases the output noise by 3.2 dB when the signal and correlations are zero (the worst case); for an SNR of −3 dB, the noise increase is 1.1 dB. When the interelement correlation is 0.10, the noise increase is 2.2 dB for zero signal. In a five-element array with zero signal and uncorrelated noise, omitting the center element increases the noise by 2.7 dB but omitting either of the other two inner elements increases the noise by just 2.2 dB.