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IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 7, JULY 2002

1849

Performance of Blind and Group-Blind Multiuser Detectors
Anders Høst-Madsen, Member, IEEE, and Xiaodong Wang, Member, IEEE Abstract—In blind (or group-blind) linear multiuser detection, the detector is estimated from the received signals, with the prior knowledge of only the signature waveform of the desired user (or the signature waveforms of some but not all users). The performance of a number of such estimated linear detectors, including the direct-matrix-inversion (DMI) blind linear minimum mean square error (MMSE) detector, the subspace blind linear MMSE detector, and the form-I and form-II group-blind linear hybrid detectors, are analyzed. Asymptotic limit theorems for each of the estimates of these detectors (when the signal sample size is large) are established, based on which approximate expressions for the average output signal-to-interderence-plus-noise ratios (SINRs) and bit-error rates (BERs) are given. To gain insights on these analytical results, the performance of these detectors in an equicorrelated code-division multiple-acces (CDMA) system is compared. Examples are provided to demonstrate the excellent match between the theory developed here and the simulation results. Index Terms—Asymptotic analysis, blind multiuser detection, group-blind multiuser detection, signal subspace.

, , and . In a direct-sequence spread-spectrum system with spreading gain , the signature sequence of the th user is of the form

form as

I. INTRODUCTION HIS paper is concerned with the analysis of the performance of blind and group-blind linear multiuser detection techniques for the basic discrete-time synchronous code-division multiple-access (CDMA) multiple-access -user channel

T

(1) , , and are the received where amplitude, data bit, and unit-energy signature sequence of is the the th user, respectively; and additive white Gaussian noise. (In this paper, we denote as an identity matrix.) These are collected in vector Manuscript received October 1, 2000; revised September 15, 2001. This work was supported in part by the U.S. National Science Foundation (NSF) under Grants CCR-9875314 and CCR-9980599. The material in this paper was presented in part at the 38th Annual Allerton Conference on Communications, Control, and Computing, Monticello, IL, October 4–6, 2000; at the 2000 International Symposium on Information Theory and its Applications (ISITA’00), Honolulu, HI, November 5–8, 2000; and at the 2001 IEEE International Symposium on Information Theory (ISIT’01), Washington, DC, June 24–29, 2001. A. Høst-Madsen is with the Department of Electrical Engineering, University of Hawaii, Honolulu, HI 96822 USA (e-mail: madsen@spectra.eng. hawaii.edu). X. Wang is with the Department of Electrical Engineering, Columbia University, New York, NY 10027 USA (e-mail: wangx@ee.columbia.edu). Communicated by U. Madhow, Associate Editor for Detection and Estimation. Publisher Item Identifier S 0018-9448(02)05163-5.

A number of recent works [2], [5], [6], [11]–[13], [15], [20]–[22] have analyzed the asymptotic performance of various CDMA receivers for systems with random antipodal long grows spreading sequences, when the number of users to the without bound and the ratio of the number of users spreading gain is kept fixed. This work is motivated by the recent development of blind and group-blind multiuser detection techniques [4], [16]–[18]. So far, the research in this area has been focused on the development of signal processing algorithms to achieve improved receiver performance. And the performance assessment is largely done via computer simulations. The main difficulty in obtaining the analytical performance stems from the fact that in these blind methods, the detectors are estimated from the received signals; and those estimates coincide with the true detectors only when becomes infinitely large. In the number of received signals this paper, we...
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