Complex coefficient adaptive notch filters (ANF) have been proposed for use in applications that require detection and rejection or enhancement of narrowband signals embedded in broadband signals with in-phase and quadrature-phase components. One such applications is in the rejection of narrowband interference (NBI) in quadriphase shift keying (QPSK) spread-spectrum communication systems [1,2]. It is well known that infinite impulse response (IIR) implementation of adaptive notch filters is more advantageous as compared to finite impulse response (FIR) with much less computation complexity. A complex coefficient adaptive notch filter implemented as a constrained IIR filter with a complex Gauss-Newton adaptation algorithm was proposed in [2]. Furthermore, its application in suppression of NBI in QPSK spread-spectrum communication system showed a substantial improvement in overall system bit error ratio (BER).

A complex coefficient adaptive IIR notch filter with a simplified gradient-based algorithm that does not require any matrix inversion was proposed in [4] and its convergence and steady state behaviors were extensively analyzed in [3] and [4]. Its application in rejection of a single NBI in a QPSK DS-SS communication system over an additive white Gaussian noise (AWGN) channel was also discussed in [5]. Cascade extension of the algorithm in [4] for detection of multiple sinusoids was further proposed and analyzed in [6]. Its application in the rejection of multiple NBI in a QPSK direct sequence codedivision multiple access (DS-CDMA) system was discussed in [7] with promising improvement in BER. However, the ANF has not been attempted in rejection of multiple NBI in an orthogonal frequency division multiplexing (OFDM) system. OFDM has recently become a preferred transmission technique in emerging broadband wireless communication systems [8,9]. It has been reported that WLAN and WMAN standards based on OFDM that operate in the unlicensed frequency bands are susceptible to NBI from other systems coexisting in the same spectrum. Such systems include Bluetooth, microwave ovens, cordless telephones, etc. The observation has challenged researchers to find NBI rejection techniques that can alleviate effects of NBI in OFDM systems [10-17].

Several NBI suppression techniques for OFDM systems are found in literature. The use of pre-coding, spread spectrum OFDM, post-detection receiver techniques involving equalizers and frequency domain subtractive cancellation using singular value decomposition have been reported [11-17]. Coulson [10] proposed an NBI suppression technique based on excision filtering. It was demonstrated by computer simulation that the technique improved ensemble average BER to about 0.001 for binary phase shift keying (BPSK) modulated OFDM with signal-to-interference ratios (SIR) as low as –30 dB [10]. However, the author did not show how excision filter parameters affect the BER performance of the OFDM system.

This paper employs similar method to that proposed in [10] whereby the multiple NBI excision filter is implemented using a cascade complex coefficient adaptive IIR notch filter with simplified gradient-based algorithm presented in [8]. The OFDM system is considered to be operating in an AWGN channel. Estimating the Fast Fourier Transform (FFT) of the ANF output for each subcarrier as Gaussian distributed based on Central Limit Theorem (CLT), a closed-form BER expression is derived for small step size constant with negligible steady-state leakage NBI. It is observed that besides the received signal-to-noise ratio (SNR), BER performance depends largely on the value of notch bandwidth coefficient. Computer simulation results are included to support analytical findings.

Main contributions of this paper are as follows: 1) It presents a systematic approach to the analysis of BER performance of OFDM systems with cascaded complex coefficient filters for multiple NBI suppression. Such approach has not been presented elsewhere; 2) It presents a simple closed-form BER expression for an OFDM system with multiple NBI suppression filters. The expression relates BER with filter notch bandwidth parameter and received signal-to-noise ratio (SNR).

The organization of this paper is as follows: In Section 2, OFDM system model and the NBI suppression cascade complex coefficient adaptive IIR notch filter are presented. Section 3 presents BER analysis while simulation results and discussions on findings are presented in Section 4. Lastly, concluding remarks and future research areas are included in Section 5.

Figure 1 below shows a block diagram of the BPSKOFDM system used in this paper. Received discrete-time low pass equivalent BPSK-OFDM symbol is modeled as