990 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 3, MARCH 2007 Broadband Beamforming Using TDL-Form IIR Filters Huiping Duan, Boon Poh Ng, Chong Meng Samson See, Member, IEEE, and Jun Fang Abstract—Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse- response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss–Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based struc- ture, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Com- pared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved. Index Terms—Array, broadband beamforming, infinite impulse response (IIR), recursive Gauss–Newton (RGN), tapped delay line (TDL). I. INTRODUCTION B ROADBAND beamforming is an important research topic in array signal processing. It has found numerous applica- tions in radio communications, sonar, radar, seismology, acous- tics, and microphone arrays [1]–[3]. Two types of conventional broadband beamformers are the Frost beamformer [4] and the generalized sidelobe canceller (GSC) beamformer [5]. Both of them use the tapped delay line (TDL), i.e., finite-impulse-re- sponse (FIR) filter, in each channel to achieve good interfer- ence suppression performance over a wide bandwidth. Various Manuscript received September 2, 2005; revised April 28, 2006. The asso- ciate editor coordinating the review of this manuscript and approving it for pub- lication was Dr. Fulvio Gini. H. Duan is with the S2-B3a-06, Information System Research Laboratory, School of Electrical and Electronic Engineering, Nanyang Technological Uni- versity, Singapore, 639798 (e-mail: duan0002@ntu.edu.sg). B. P. Ng is with the School of Electrical and Electronic Engineering/NTU- Temasek Laboratories, Nanyang Technological University, Singapore 639798, Singapore (e-mail: ebpng@ntu.edu.sg). C. M. S. See is with the DSO National Laboratories/NTU-Temasek Labora- tories, Singapore 118230, Singapore (e-mail: schongme@dso.org.sg). J. Fang is with the Department of Electrical and Computer Engineering, Faculty of Engineering, National University of Singapore 117576, Singapore (e-mail: junfang@nus.edu.sg). Digital Object Identifier 10.1109/TSP.2006.887134 algorithms have been proposed based on these two FIR beam- forming structures. Investigations show that as the operating bandwidth in- creases, large numbers of taps are required to retain an acceptable signal-to-interference-plus-noise-ratio (SINR) per- formance in the FIR beamformers [6]. However, too many adaptive weights will slow down the convergence rate and in- crease the computational complexity. Some methods have been proposed to solve this problem. Broadband beamspace adaptive array is designed in [7] so that the convergence rate could be faster. The partially adaptive method with subband processing proposed in [8] and the GSC employing frequency invariant filters in [9] could also increase the convergence speed and reduce the computational complexity. Motivated by the desire to reduce the number of weights, research has been carried out to explore beamformers using infinite-impulse-response (IIR) filters. In [10], it is proven that the optimal frequency-de- pendent array weighting could be better approximated by IIR filters in broadband beamformers. Three types of pole-zero beamformers based on the GSC structure are proposed in [10]. The time-domain pole-zero beamformers proposed in [10] adopt direct-form IIR filters. Their stability is not easy to monitor. The frequency-domain beamformer in [10] applies parallel-form IIR filters. The problem of stability monitoring is overcome, but the frequency-domain implementation is not suitable for some applications due to its associated time delay. Furthermore, in [11] and [12], the beamformers are designed to cancel the poles in the ideal filter transfer functions so that the required filter length is reduced. In [13], two-pole IIR filters are used together with FIR fan filters to generate beams in the partially adaptive array. Recently, in [14], we propose a beam- former using multiple tap-to-tap IIR sections. Constrained and unconstrained least-mean-square (LMS) algorithms (named the combined LMS algorithm here) are designed to compute the weights. We would like to call the IIR filter used in [14] the TDL-form IIR filter because it is constructed by replacing all the delay ele- ments of the TDLs with the specified first-order IIR sections. In this paper, further investigations are carried out on beamforming using TDL-form IIR filters. We note that in [14] the poles are restricted on the real axis for the real input. Here, we present the second-order sections so that the complex poles are allowed for the real signals. To improve the convergence performance of the combined LMS algorithm, constrained and unconstrained recursive Gauss–Newton (RGN) algorithms are designed and combined (named the combined RGN algorithm here) to com- pute the feedforward and feedback weights in the Frost-based IIR beamformer. The GSC-based implementation with the un- constrained RGN algorithm is presented. Our analyses show 1053-587X/$25.00 © 2007 IEEE