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A multiple-signal-classification (MUSIC) approach of estimating the code timings of a desired user is considered for direct-sequence code-division multiple-access (DS-CDMA) multipath-fading channels when exploiting multiple receive antennas with either spatially uncorrelated or fully correlated fading. The acquisition performance of the conventional MUSIC timing estimator employing a single antenna is not good for the small size of observation windows and low signal-to-noise ratios (SNRs). Multiple antennas allow for rapid acquisition and lowers the range of detectable SNR. An efficient and improved MUSIC algorithm of estimating the multipath timings of a desired user for DS-CDMA systems is presented. In multipath-fading channels, the solution of the proposed algorithm is based on successively optimizing the cost function for increasing numbers of multipath delays, which does not require a multidimensional search for multidelay paths. Furthermore, the estimate of code timing at each path is obtained by finding the zeros of second-order polynomials, which is computationally efficient. The proposed MUSIC algorithm significantly improves the acquisition performance of conventional MUSIC algorithm in the presence of multipath time-varying Rayleigh-fading channels with arbitrary time delays. The acquisition performance of multiple antennas-based MUSIC timing estimators is much better than that of a single-antenna-based timing estimator. The Cramer-Rao bound for the code-timing estimator based on multiple antennas is presented. Index Terms--Code-division multiple access (CDMA), code-timing estimation, Cramer-Rao bound, multiantenna, multipath fading, synchronization.

This paper discusses the code-acquisition problem for preamble search in the code-division multiple-access (CDMA) uplink when multiple antennas are employed for signal reception. The multiple antennas are used either in the form of antenna array for beamforming or in the form of antenna diversity. The performance of a maximum-likelihood (ML) code-acquisition technique utilizing beamforming is analyzed by considering the detection, miss, and false-alarm probabilities. This analysis is based on the statistics of the CDMA noncoherent demodulator and beamformer output. In the case of a code-acquisition scheme utilizing antenna diversity, the probability density function of a decision variable is analytically derived for multiple antennas. The expressions for the probabilities of detection, miss, and false alarm are also presented. The acquisition performance and mean acquisition time for both code-acquisition techniques are numerically evaluated and compared. The code-acquisition approaches with multiple antennas are shown to provide much better performance than the corresponding scheme with a single antenna in a frequency-selective fading channel. Index Terms--Antenna array, code acquisition, code-division multiple access (CDMA).

We have derived a lower bound on the linear span of a binary sequence generated by a Feedback with Carry Shift Register (FCSR) under the following condition: q is a power of a prime such that q = [r.sup.e] (e [is greater than or equal to] 2) and r (= 2p + 1), where both r and p are 2-prime. This allows us to design FCSR stream ciphers similar to previously proposed Linear Feedback Shift Register (LFSR) stream ciphers. Index Terms--Feedback with carry shift register (FCSR), linear feedback shift register (LFSR), linear span, 2-adic span.