This paper introduces an algorithm for beamforming systems by the aid of multidimensional harmonic retrieval(MHR).This algorithm resolves problems,removes limitations of samp-ling and provides a more robust beamformer.A new sample space is created that can be used for estimating weights of a new beamforming called spatial-harmonics retrieval beam-former(SHRB).Simulation results show that SHRB has a better performance,accuracy,and applicability and more powerful eigenvalues than conventional beamformers.A simple mathema-tical proof is provided.By changing the number of harmonics,as a degree of freedom that is missing in conventional beam-formers,SHRB can achieve more optimal outputs without in-creasing the number of spatial or temporal samples.We will demonstrate that SHRB offers an improvement of 4 dB in signal to noise ratio(SNR)in bit error rate(BER)of 10-4 over conven-tional beamformers.In the case of direction of arrival(DOA)esti-mation,SHRB can estimate the DOA of the desired signal with an SNR of-25 dB,when conventional methods cannot have ac-ceptable response.