# Adaptive filtering algorithms with quatratized cost function for linearly constrained arrays

## DOI:

https://doi.org/10.1109/ICATT.2013.6650729## Keywords:

adaptive arrays, least mean square, recursive least mean squares, linear constraints, constant modulus, blind adaptive filtering algorithms## Abstract

This article considers peculiarities of adaptive filtering algorithms for arrays based on the Linearly Constrained quadratic and multi-extreme Constant Modulus cost functions minimization. The results of using the Linearly Constrained quadratized Constant Modulus cost function in the complex-valued LMS and RLS algorithms for the adaptive arrays are presented. The algorithms efficiency is compared to that of the real-valued arithmetic versions of the considered algorithms.## References

MONZINGO, R.A.; MILLER, T.W. *Introduction to Adaptive Arrays*. SciTech Publishing, 2004.

TREICHLER, J.; LARIMORE, M. New processing techniques based on the constant modulus adaptive algorithm. *IEEE Trans. Acoustics, Speech Signal Processing*, 1985, v.33, n.2, p.420-431, doi: http://dx.doi.org/10.1109/TASSP.1985.1164567.

FROST, O.L., III. An algorithm for linearly constrained adaptive array processing. *Proc. IEEE*, 1972, v.60, n.8, p.926-935, doi: http://dx.doi.org/10.1109/PROC.1972.8817.

CHEN, Y.; LE-NGOC, T.; CHAMPAGNE, B.; XU, C. Recursive least squares constant modulus algorithm for blind adaptive array. *IEEE Trans. Signal Processing*, 2004, v.52, n.5, p.1452-1456, doi: http://dx.doi.org/10.1109/TSP.2004.826167.

DJIGAN, V.I. Multichannel RLS and fast RLS adaptive filtering algorithms. *Uspekhi Sovremennoy Radioelektroniki*, 2004, n.11, p.48-77.

DJIGAN, V.I. Joint use of constant modulus and least squares criteria in linearly-constrained communication arrays. *Radioengineering*, 2007, v.16, n.4, p.88-95.

DJIGAN, V.I.; PLETNEVA, I.D. Adaptive filtering algorithms based QR decomposition in digital arrays for communication. *Tsifrovaya Obrabotka Signalov*, 2007, n.4, p.2-7.

DJIGAN, V.I. Linearly-constrained NLMS algorithm for digital adaptive array. *Informatsionnye Tekhnologii*, 2008, n.10, p.68-74.

DJIGAN, V.I.; PLETNEVA, I.D. Adaptive filtering in antenna array based on CM affine projection algorithm with linear constraints. *Antenny*, 2008, n.10, p.14-24.

DJIGAN, V.I. Adaptive signal processing in multy-beam arrays. *Proc. of 9th IEEE East-West Design &Test Symp.*, EWDTS, 9-12 Sept. 2011, Sevastopol, Ukraine. IEEE, 2011, p.51-54, doi: http://dx.doi.org/10.1109/EWDTS.2011.6116576.

DJIGAN, V.I. Multi-beam adaptive antenna array. *Proc. of Southern Federal University*, 2012, n.2, p.23-29.

HUARNG, K.-C.; TEH, C.-C. Adaptive beamforming with conjugate symmetric weights. *IEEE Trans. Antennas Propag.*, 1991, v.39, n.7, p.926-932, doi: http://dx.doi.org/10.1109/8.86911.

DJIGAN, V.I. Multi-beam adaptive array with real-valued calculations. *Proc. of 10th IEEE East-West Design & Test Symp.*, EWDTS, Kharkov, Ukraine, 2012, p.54-59.

DJIGAN, V.I. Multi-beam adaptive arrays based LMS algorithms. *Voprosi Radioelektroniki*, 2013, n.2, p.107-121.