Generation of correlated finite alphabet waveforms using gaussian random variables
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Communication Theory Lab
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AbstractCorrelated waveforms have a number of applications in different fields, such as radar and communication. It is very easy to generate correlated waveforms using infinite alphabets, but for some of the applications, it is very challenging to use them in practice. Moreover, to generate infinite alphabet constant envelope correlated waveforms, the available research uses iterative algorithms, which are computationally very expensive. In this work, we propose simple novel methods to generate correlated waveforms using finite alphabet constant and non-constant-envelope symbols. To generate finite alphabet waveforms, the proposed method map the Gaussian random variables onto the phase-shift-keying, pulse-amplitude, and quadrature-amplitude modulation schemes. For such mapping, the probability-density-function of Gaussian random variables is divided into M regions, where M is the number of alphabets in the corresponding modulation scheme. By exploiting the mapping function, the relationship between the cross-correlation of Gaussian and finite alphabet symbols is derived. To generate equiprobable symbols, the area of each region is kept same. If the requirement is to have each symbol with its own unique probability, the proposed scheme allows us that as well. Although, the proposed scheme is general, the main focus of this paper is to generate finite alphabet waveforms for multiple-input multiple-output radar, where correlated waveforms are used to achieve desired beampatterns. © 2014 IEEE.
SponsorsThe associate editor coordinating the review of this manuscript and approving it for publication was Prof. Ljubisa Stankovic. This work was funded by a CRG grant from the KAUST Office of Competitive Research Fund (OCRF). This paper is an extended version of the work presented in IEEE Asilomar Conference on Signals, Systems, and Computers (Asilomar 2012), Pacific Grove, CA, USA, November 2012.