**Local Maximum Likelihood Multiuser Detection for CDMA Communications**
A Proposal to NSF CISE/CCR: Communications Research
Yi Sun
Department of Electrical Engineering
The City College of City University of New York
E-mail: sun@ccny.cuny.edu
Third-generation mobile radio networks have been under intense research. Code division multiple access (CDMA) has emerged as the mainstream air interface solution for the third-generation networks. As the demand of usable bandwidth is ever increasing, multiuser detection is a necessary means for CDMA systems to reduce effect of multiple access interference and hence increase system capacity. The global maximum likelihood (GML) multiuser detector achieves the minimum error probability of joint user detection as well as optimum near-far resistance. However, the complexity of the GML detector grows exponentially with the number of users and is infeasible for practical systems. There have been many suboptimum multiuser detectors each achieving some performance-complexity tradeoff. However, none of them achieves a *local maximum likelihood* (LML) solution with an arbitrary neighborhood size. Moreover, most of the existing suboptimum multiuser detectors are ad hoc developed. They have low ratio of performance to computational complexity.
In this project, we will develop local maximum likelihood detectors with *an arbitrary neighborhood size*. These LML multiuser detectors can provide a broad spectrum of performance-complexity tradeoff. Their error performance spans from that comparable to the conventional detector, MMSE receiver, MMSE-DF receiver, superior to MMSE-DF receiver, etc., up to that of the GML detector and their computational complexity spans from linear, quadratic, etc., up to exponential in the number of users. Furthermore, these LML multiuser detectors achieve high ratio of performance to computational complexity as demonstrated in preliminary simulations. Specifically, we will develop a family of linear-complexity likelihood ascent search (LAS) multiuser detectors in some combinations of the following conditions: wireless multipath fading channels, on-the-move (Doppler), known and unknown interference users (group blind), broadband and multirate data, power control, adaptive modulation, turbo coded data, space-time coding, and large systems in CDMA networks with direct sequence, frequency hopping, and multicarrier modulation. Another family of local maximum likelihood LAS (LMLAS) multiuser detectors achieving LML detection with an arbitrary neighborhood size will also be developed in the above various cases. The both families of LAS and LMLAS detectors with soft intermediate decision will be investigated. We will study strategies to determine the optimum order of bit update. Performance analysis will include the characterization of local maximum likelihood points with an arbitrary neighborhood size, the dynamical stability, monotonic likelihood ascent characterization, expected computational complexity, error probability, asymptotic multiuser efficiency, near-far resistance, optimum power control, and spectral efficiency.
The proposed investigation on LML detection will impact basic research in nonlinear signal processing for multiuser communications, and is expected to benefit directly applications to third and fourth-generation wireless mobile communications systems. This project will also contribute new knowledge to theories of the fields of multiuser detection, hypothesis testing, wireless communications, image processing, and neural networks. This project will help set up a strong program in communications in this department and provide new research opportunities for both graduate and undergraduate students, and in particular the minority students. The increased minority students’ research activities in modern communications will strengthen the traditional diversity environment of this collage.
## Project Description
## C. 1 Objectives
Wideband code division multiple access (CDMA) has emerged as the mainstream air interface solution for the third-generation networks [1]. As the demand on usable bandwidth is ever increasing, multiuser detection is a necessary means for CDMA systems to reduce the effect of multiple access interference and hence increase the system capacity and alleviate the near-far problem.
Consider a *K*-user bit-synchronous CDMA system with spreading gain *M*. The received baseband CDMA signal sampled at the rate higher than or equal to the chip rate can be written in matrix form as
**y** = **SAb** + **n**
where **y** ^{M} is a sufficient statistic of **b**, **S** ^{M}^{}^{K} is the matrix of signature waveforms which may include multipath fading effect, **A** = diag(*A*_{1}, …, *A*_{K}) where *A*_{k} is the signal amplitude of the *k*th user, **b** {1, 1}^{K} is the transmitted bit vector, and **n** ~ *N*(**0**, **^{2}**I**) is a noise vector. When the signature waveforms are known, the received baseband CDMA signal sampled at the output of a bank of matched filters can be equivalently written in matrix form as
**r** = **S**^{T}**y** = **RAb** + **z**
where **r** ^{K} is also a sufficient statistic of **b**, **R** = **S**^{T}**S** ^{K}^{}^{K} is the crosscorrelation matrix of signature waveforms, and **z** ~ *N*(**0**, **^{2}**R**). The task of multiuser detection is to demodulate **b** from **y** or **r** with or without knowing **S** and **A**. Bit-asynchronous CDMA signal with transmission of a burst data can also be modeled as and .
The multiuser detection problem exists in broad areas of communication systems including wireless communication, high-speed data transmission, wireless internet, and magnetic recording. Many practical problems in other areas also can be formulated as to solve , including symbol detection for multiple-in/multiple-out (MIMO) channels such as OFDM [2], global positioning system [4], and image restoration [5].
To solve problem , it is well-known [6] that when **R**, **A** and ** are known, the (joint) optimum demodulation selects the hypothesis maximizing the likelihood function of **b** or minimizing the metric
** **, **r** ^{K}
where the metric is defined as *f*(**r**|**b**) = ½ **b**^{T}**Wb** **q**^{T}**b** with **W** = **ARA** and **q** = **Ar**. The optimum detector in terms of the global maximum likelihood (GML) achieves the minimum error probability [7]. However, the GML detector^{1} needs the comparison of 2^{K} metric values for arbitrary signature waveforms. Its complexity grows exponentially with the number of users and prevents implementation for a reasonable number of users in practical systems.
There have been many suboptimum multiuser receivers each achieving some performance-complexity tradeoff. However, none of them achieves a *local maximum likelihood* (LML) solution with an arbitrary neighborhood size. Moreover, most of the existing suboptimum multiuser receivers are ad hoc developed. They have low ratio of performance to computational complexity and are difficult to analyze. This is particularly true for nonlinear iterative detectors. The objective of this project is to develop multiuser detectors that provide a broad spectrum of performance-complexity tradeoff with high ratios of performance to computational complexity. The approach is the local likelihood ascent search (LAS) [10] and local maximum likelihood (LML) multiuser detectors [11]. As demonstrated in our preliminary study, the error performance of these LML detectors spans from that comparable to the conventional detector, MMSE receiver, MMSE-DF receiver, superior to MMSE-DF receiver, etc., up to that of the GML detector and their computational complexity ranges from linear, quadratic, etc., up to exponential in the number of users. Moreover, these LML multiuser detectors achieve high ratio of performance to computational complexity as demonstrated in some preliminary simulations.
Specifically, we will develop a family of linear-complexity likelihood ascent search (LAS) multiuser detectors [10] in some combinations of the following conditions: wireless multipath fading channels, on-the-move (Doppler), known and unknown interference users (group blind), broadband and multirate data, power control, adaptive modulation, turbo coded data, space-time coding, and large systems in CDMA networks with direct sequence, frequency hopping, and multicarrier modulation. Another family of local maximum likelihood LAS (LMLAS) multiuser detectors [11] achieving LML detection with an arbitrary neighborhood size will also be developed in the above various cases. The both families of LAS and LMLAS detectors with soft intermediate decision will be investigated. We will study strategies to determine the optimum order of bit update. Performance analysis will include the characterization of local maximum likelihood points with an arbitrary neighborhood size, the dynamical stability, monotonic likelihood ascent characterization, expected computational complexity, error probability, asymptotic multiuser efficiency, near-far resistance, optimum power control, and spectral efficiency.
The proposed investigation on LML detection will impact basic research in nonlinear signal processing for multiuser communications, and is expected to benefit directly applications to third and fourth-generation wireless mobile communications systems. This project will also contribute new knowledge to theories of the fields of multiuser detection, hypothesis testing, wireless communications, image processing, and neural networks. This project will help set up a strong research program in communications in this department and provide new research opportunities for both graduate and undergraduate students, and in particular the minority students. The increased minority students’ research activities in modern communications will strengthen the traditional diversity environment of this collage.
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