How Many Beamforming Vectors Generate the Same Beampattern?

In this letter, we address the fundamental question of how many beamforming vectors exist which generate the same beampattern? The question is relevant to many fields such as, for example, array processing, radar, wireless communications, data compression, dimensionality reduction, and biomedical engineering. 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. The result is that at most 2^{M-1}-1 beamforming vectors with the same beampattern can be generated from any given beamforming vector. Here M is the dimension of the beamforming vector. At the constructive side, the answer to this question allows for computationally efficient techniques for the beamspace transformation design. Indeed, one can start with a single beamforming vector, which gives a desired beampattern, and generate a number of other beamforming vectors, which give absolutely the same beampattern, in a computationally efficient way. We call the initial beamforming vector as the mother beamforming vector. One possible procedure for generating all possible new beamforming vectors with the same beampattern from the mother beamforming vector is proposed. The application of the proposed analysis to the transmit beamspace design in multiple-input multiple-output radar is also given.Comment: 12 pages, 3 figures, 2 tables, Submitted to the IEEE Signal Processing Letters in February 201

Broadbeam for Massive MIMO Systems

Massive MIMO has been identified as one of the promising disruptive air interface techniques to address the huge capacity requirement demanded by 5G wireless communications. For practical deployment of such systems, the control message need to be broadcast to all users reliably in the cell using broadbeam. A broadbeam is expected to have the same radiated power in all directions to cover users in any place in a cell. In this paper, we will show that there is no perfect broadbeam. Therefore, we develop a method for generating broadbeam that can allow tiny fluctuations in radiated power. Overall, this can serve as an ingredient for practical deployment of the massive MIMO systems