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One approach for reducing noise from non-target locations in array beamformer applications is to use an adaptive noise cancellation algorithm referred to as the Generalized Sidelobe Canceller (GSC). An analysis is performed to derive a closed-form expression showing the relationship between stability, the number of array channels, adaptive step size ??, and forgetting factor ??. The result is verified by applying the GSC to experimental data with a range of values for ??, ??, and array channels to show when the GSC becomes unstable.