This paper considers the problem of estimating the signal waveforms from the noisy data obtained with an array of receiving sensors. The maximum likelihood (ML) waveform estimate, derived under the assumption that the signals are deterministic, is compared with the minimum mean-square-error linear (MMSEL) estimate, derived under the assumption of stochastic signals. When the signals are assumed to be random, the MMSEL estimate has, by construction, a smaller MSE than the ML estimate. A ridge-type extension of the MMSEL estimate is shown to still possess smaller MSE than the ML estimate, under a reasonable condition, even if the signals are assumed to be deterministic. A numerical study provides more quantitative insights into the performance of several waveform estimators, including those mentioned above.