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The desired property of having the same beampattern for different columns of a beamspace transformation matrix (beamforming vectors) often plays a key importance in practical applications. At most 2<sup>M - 1</sup> - 1 beamforming vectors with the same beampattern can be generated from any given beamforming vector, where M is the size of the beamforming vector. Thus, one can start with a single (mother) beamforming vector, which gives a desired beampattern, but may not satisfy some other desired properties, and generate all other beamforming vectors, which give the same beampattern, in a computationally efficient way. Then the beamforming vectors, which in addition satisfy other desired properties that the mother beamforming vector may not satisfy, can be selected. Such procedure is developed in this letter in the application to the transmit beamspace design that ensures practically important properties for multiple-input multiple-output radar. A computationally efficient sub-optimal method for selecting best beamforming vectors from a population of vectors that give the same beampattern is also developed.

Transmit Radiation Pattern Invariance in MIMO Radar With Application to DOA Estimation