A novel robust spectrum sensing method is proposed based on the higher-order statistics of signals received over a large antenna array. The proposed method formulates the test statistics by estimating multiple cumulants of the spatial samples, and in turn differentiates the primary signals from the Gaussian noise within a short sensing period. This work is an extension of [1] and enhances significantly its detection performance by utilizing the statistical information of more than one cumulant. In addition, it remains robust in the presence of unknown noise correlation that often exists in large antenna array.