An adaptive array code acquisition for direct-sequence/code-division multiple access (DS/CDMA) systems was recently proposed to enhance the performance of the conventional correlator-based method. The scheme consists of an adaptive spatial and an adaptive temporal filter, and can simultaneously perform beamforming and code-delay estimation. Unfortunately, the scheme uses a least-mean-square (LMS) adaptive algorithm, and its convergence is slow. Although the recursive-least-squares (RLS) algorithm can be applied, the computational complexity will greatly increase. In this paper, we solve the dilemma with a low-complexity conjugate gradient (LCG) algorithm, which can be considered as a special case of a modified conjugate gradient (MCG) algorithm. Unlike the original conjugate gradient (CG) algorithm developed for adaptive applications, the proposed method, exploiting the special structure inherent in the input correlation matrix, requires a low computational-complexity. It can be shown that the computational complexity of the proposed method is on the same order of the LMS algorithm. However, the convergence rate is improved significantly. Simulation results show that the performance of adaptive array code acquisition with the proposed CG algorithm is comparable to that with the original CG algorithm.

The maximum likelihood sequence estimator (MLSE) is usually implemented by the Viterbi algorithm (VA). The computational complexity of the VA grows exponentially with the length of the channel response. With some performance reduction, a decision-feedback equalizer (DFE) can be used to shorten the channel response. This greatly reduces the computational requirement for the VA. However, for many real-world applications, the complexity of the DFE/MLSE approach may be still too high. In this paper, we propose a constrained DFE that offers much lower VA computational complexity. The basic idea is to pose some constraints on the DFE such that the postcursors of the shortened channel response have only discrete values. As a result, the multiplication operations can be replaced by shift operations making the VA almost multiplication free. This will greatly facilitate the real world applications of the MLSE algorithm. Simulation results show that while the proposed algorithm basically offers the same performance as the original MLSE performance, the VA is much more efficient than the conventional approach.

Similar to orthogonal frequency-division multiplexing (OFDM) systems, orthogonal frequency-division multiple access (OFDMA) is vulnerable to carrier frequency offset (CFO). Since the CFO of each user is different, CFO compensation in OFDMA uplink is much more involved than that in OFDM systems. It has been shown that the zero-forcing (ZF) compensation method is a simple yet effective remedy; however, it requires the inversion of a large matrix and the computational complexity can be very high. Recently, we have developed a low-complexity iterative method to alleviate this problem. In this paper, we consider the theoretical aspect of the algorithm. We specifically analyze the output signal-to-interference-plus-noise-ratio (SINR) of the algorithm. Two approaches are used for the analysis; one is simple but approximated, and the other is complicated but exact. The convergence problem is also discussed. In addition to the analysis, we propose a pre-compensation (PC) method enhancing the performance of the algorithm. Simulations show that our analysis is accurate and the PC method is effective.

An adaptive interpolated FIR (IFIR) echo canceller was recently proposed for xDSL applications. This canceller consists of an FIR filter, an IFIR filter, and a tap-weight overlapping and nulling scheme. The FIR filter is used to cancel the short and rapidly changing head echo while the IFIR filter is used to cancel the long and slowly decaying tail echo. This echo canceller, which inherits the stable characteristics of the conventional FIR filter, requires low computational complexity. It is well known that the interpolation filter for an IFIR filter has great influence on the interpolated result. In this paper, a least-squares method is proposed to obtain optimal interpolation filters such that the performance of the IFIR echo canceller can be further improved. Simulations with a wide variety of loop topologies show that the optimal IFIR echo canceller can effectively cancel the echo up to 73.0 dB (for an SHDSL system). About 57% complexity reduction can be achieved compared to a conventional FIR filter.

Non-stationary glint noise is often observed in a radar tracking system. The distribution of glint noise is non-Gaussian and heavy-tailed. Conventional recursive identification algorithms use the stochastic approximation (SA) method. However, the SA method converges slowly and is invalid for non-stationary noise. This paper proposes an adaptive algorithm, which uses the stochastic gradient descent (SGD) method, to overcome these problems. The SGD method retains the simple structure of the SA method and is suitable for real-world implementation. Convergence behavior of the SGD method is analyzed and closed-form expressions for sufficient step size bounds are derived. Since noise data are usually not available in practice, we then propose a noise extraction scheme. Combining the SGD method, we can perform on-line adaptive noise identification directly from radar measurements. Simulation results show that the performance of the SGD method is comparable to that of the maximum-likelihood (ML) method. Also, the noise extraction scheme is effective that the identification results from the radar measurements are close to those from pure glint noise data.