MIMO Beampattern Synthesis using Adaptive Frequency Modulated Waveforms

TL;DR

This paper introduces a method to synthesize narrowband MIMO beampatterns using adaptive frequency modulated waveforms, leveraging their Fourier series representation and correlation properties for optimized pattern design.

Contribution

It presents a novel approach to design MIMO waveforms with desired beampatterns by exploiting the analytical correlation matrix of MTSFM waveforms.

Findings

Successful synthesis of MIMO beampatterns using the proposed method

Analytical expression for the correlation matrix of MTSFM waveforms

Demonstrated optimization routine effectively approximates desired patterns

Abstract

This paper demonstrates a method that synthesizes narrowband Multiple-Input Multiple-Output (MIMO) beampatterns using the Multi-Tone Sinusoidal Frequency Modulated (MTSFM) waveform model. MIMO arrays transmit unique waveforms on each of their elements which increases the degrees of freedom available to synthesize novel transmit beampatterns. The MIMO beampattern shape is determined by the structure of the MIMO correlation matrix whose entries are the inner products between the waveforms transmitted on each element. The MTSFM waveform possesses an instantaneous phase that is represented as a finite Fourier series. The Fourier coefficients are modified to synthesize sets of waveforms whose correlation matrix realizes a desired MIMO transmit beampattern. The MIMO correlation matrix for a MTSFM waveform set has an analytical form expressed in terms of Generalized Bessel Functions. These mathematical properties are utilized to develop an optimization routine that synthesizes MTSFM waveform sets to approximate a desired MIMO transmit beampattern. The performance of this optimization routine is then demonstrated via an illustrative design example.