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A maximum likelihood optimum detector with an asymptotic
complexity per user of 0(1.5<sup>K</sup>) has been derived for the
synchronous DS/CDMA channels. The detector employs a local descent
algorithm through the Voronoi regions for the equivalent hypothesis
detector

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... Much research has been done to reduce the computational complexity of this receiver. Agrell and Ottosson [8] proposed a new ML receiver that uses the neighbor descent (ND) algorithm. They implemented an iterative approach using the ND algorithm to locate the region where the actual observations belong. ...

... The original computational complexity of the ML optimal receiver is (2) K [5]. Another research paper [8] has reduced the complexity from (2) K to (3/2) K . This paper [8], also known as the ND algorithm, has reduced the computational complexity after considering a synchronous DS-CDMA system. ...

... Another research paper [8] has reduced the complexity from (2) K to (3/2) K . This paper [8], also known as the ND algorithm, has reduced the computational complexity after considering a synchronous DS-CDMA system. ...

Next generation wireless receivers demand low computational complexity algorithms with high computing power in order to perform fast signal detections and error estimations. Several signal detection and estimation algorithms have been proposed for next generation wireless receivers which are primarily designed to provide reasonable performance in terms of signal to noise ratio (SNR) and bit error rate (BER). However, none of them have been chosen for direct implementation as they offer high computational complexity with relatively lower computing power. This paper presents a low-complexity power-efficient algorithm that improves the computing power and provides relatively faster signal detection for next generation wireless multiuser receivers. Measurement results of the proposed algorithm are provided and the overall system performance is indicated by BER and the computational complexity. Finally, in order to verify the low-complexity of the proposed algorithm we also present a formal mathematical proof.

... Much research has been done to reduce this receiver's computational complexity. Recently, Ottosson and Agrell [5] proposed a new ML receiver that uses the neighbor descent (ND) algorithm. They implemented an iterative approach using the ND algorithm to locate the region where the actual observations belong. ...

... The original asymptotic computational complexity of the ML optimal receiver is (2) k [1]. Another research paper [5] has reduced the complexity from (2) k to (3/2) k . This paper [5], also known as ND algorithm, has reduced the computational complexity after considering a synchronous DS-CDMA system. ...

... Another research paper [5] has reduced the complexity from (2) k to (3/2) k . This paper [5], also known as ND algorithm, has reduced the computational complexity after considering a synchronous DS-CDMA system. According to our numerical results, we successfully reduced the computational complexity at an acceptable BER after considering the DS-CDMA synchronous LTI system. ...

A new transformation matrix (TM) algorithm for reducing the computational complexity of multiuser receivers for DS-CDMA wireless system is presented. Next generation multiuser wireless receivers will need to use low computational complexity algorithm in order to perform both fast signal detection and error estimation. Several multiuser signal detection algorithms have proposed for next generation wireless receivers, which are designed to give good performance in terms of signal to noise ratio (SNR) and bit error rate (BER), are discarded for a direct implementation as they have high computational complexity. In this paper, we propose a new low-complexity TM algorithm that can be used to perform fast signal detection for multiuser wireless receives. This reduction in computational complexity would likely to give us a considerable improvement in the performance of multiuser wireless receivers such as high computing power and low error rate. In addition, we also present a formal mathematical proof for computational complexities that verifies the low-complexity of the proposed algorithm

... The significant performance gap between suboptimal multiuser detectors, such as the decorrelator [1], [2], the multistage [3], [4], the decision-feedback multiuser detector [5], [6], and the optimum detector [7] has motivated much research in the design of optimum or near-optimum detectors of low complexity. Examples include Sankaran and Ephremides [8] who identified a class of optimum multiuser detection problems that can be solved in polynomial time complexity, and Agrell and Ottosson [9], [10] who showed that the optimum detector, in general, has an average time complexity of O(1:5 K ). They also state a version of Theorem 1 in this paper without proof, and suggest a proof may be obtained using Verdú's notion of indecomposable error sequences. ...

... We present two example detectors that approximate the ML by approximating its Voronoi diagram. The two multiuser detectors are descent search algorithms similar to that in [9], [10], with some differences to lower complexity: 1) we truncate the search list; 2) we bound the time complexity by bounding the number of searches for each point to a fixed number K0 after which the search stops; 3) we save the elements in the search list in some order, based on the Voronoi diagram; and, 4) a predetector is added to obtain an initial estimate. Other work related to descent algorithms in multiuser detection are reported in [19] and [20], where a trellis search scheme is proposed and a likelihood threshold is used to reduce the number of search paths at each stage. ...

... The popular Godard [6] algorithm and the earlier Shalvi-Weinstein algorithm [7] are well-known examples of this class of method. As a matter of fact, these two algorithms are closer than they initially appear as they both amount to seeking a maximum of a same cost function (see, e.g., [8]), belonging to the family of Donoho's deconvolution objective functions [9]. ...

We consider a geometric view of multiuser detection and present
results on the problem of efficient computation of the optimal decision
regions (Voronoi diagram) for synchronous direct-sequence code division
multiple access (DS/CDMA). Among other results, it is shown that Verdu's
(1986) algebraic notion of “indecomposable error sequences”
relates directly to the geometric construction of the Voronoi diagram
for multiuser detection. Based on the presented geometric results we
introduce two multiuser detectors whose performance compares favorably
to some popular existing detectors

... The interference from the other users, in all subsystems is (2)(3)(4)(5) where . 1. The sufficient statistics are a bank of filters matched to each of the spreading sequences [73]. ...

... Hence, the optimal receiver is a one shot receiver. Collect the outputs from all filters in the vector 1 . In this way, the matched filter outputs can be expressed in matrix notation as ...

... Usually this is done with a suboptimal receiver. However, in this section we derive a ML optimal receiver with reduced complexity (first presented in [1]). ...

ii iii Abstract i Contents iii Acknowledgements vii 1 INTRODUCTION 1 1-1 Background 1 1-2 Outline 3 1-3 Contributions 3 1-4 Notation 4 2 MULTIRATE SCHEMES FOR MULTIMEDIA APPLICATIONS 5 2-1 Introduction 5 2-2 System Models 6 Amplitude Modulated DS/CDMA Systems Quadrature Amplitude Modulated DS/CDMA Systems 2-3 Performance in AWGN Channels 9 Multi-Modulation Systems Multi Processing-Gain Systems Multi-Channel Systems Multi Chip-Rate Systems Miscellaneous Multirate Schemes CONTENTS iv 2-4 Performance in Multipath Rayleigh Fading Channels 15 Channel Model Performance Without Diversity Reception Performance of Diversity Receivers using Maximum Ratio Combining Performance of Diversity Receivers using Selection Combining 2-5 Numerical Results 19 2-6 Conclusions 25 2-7 Future Work 26 APPENDIX 2A: The Gaussian Approximations 26 APPENDIX 2B: Linearity Measure for the Multi-Channel Scheme 31 APPENDIX 2C: The Accuracy of the Gaussian Approximation 33 3 MULTIUSER DETECTION 39 3...

... Much research has been done to reduce this receiver's computational complexity. Ottosson and Agrell [16] proposed a ML receiver that uses the neighboring decent (ND) algorithm. They implemented an iterative approach using the ND algorithm to locate the region where the actual observations belong. ...

... In this section, we use the results in [16, 24] to compare the computational complexity, SNR, and the BER performance of the proposed TM algorithm with the ND and the ML multiuser detection algorithms. The system is modeled in MATLAB and the results are presented in the subsequent sections. ...

Multiuser detection is an important technology in wireless CDMA systems for improving both data rate as well as user capacity. However, the computational complexity of multiuser detection prevents the widespread use of this technique. Most of the CDMA systems today and in the near future will continue to use the conventional matched filter with its comparatively low user capacity and a slow data rate. However, if we could lower the computational complexity of multiuser detectors, CDMA systems would offer an increased system capacity with a better data rate. In this paper, a new scheme for reducing the computational complexity of multiuser receivers is proposed. It utilizes the transformation matrix algorithm to improve the performance of multiuser receivers by effectively reducing the bit error rate (BER). In addition to the transformation matrix algorithm, a quantitative analysis of the processing gain for a multiuser DS-CDMA system is presented. The quantitative analysis of the processing gain demonstrates that how the reduced BER could be used to achieve reasonable values of processing gain by which unwanted signals or interference can be suppressed relative to the desired signal at the receiving end. We present that the proposed scheme can reduce the asymptotic computational complexity of multiuser receivers while at the same time effectively eliminates the unwanted signals. The proposed algorithms not only are shown to substantially improve the performance of the multiuser detectors by means of reduced BER but also have a much lower multi-access interference. The performance measure adopted in this paper is the achievable bit rate for a fixed probability of error (10-7) and consistent values of SNR.

... On the other hand, linear multiuser receivers apply a linear transformation to an observation vector, which serves as soft decision for the transmitted data. Recently, Ottosson and Agrell [2] proposed a new ML receiver that uses the neighbor descent (ND) algorithm. They implemented a linear iterative approach using the ND algorithm to locate the region where the actual observations belong. ...

... The complexity of multiuser receiver grows exponentially in an order of O (2) K , where K is the number of active users. Recently, [2] proposed a ML receiver that uses the neighboring decent (ND) algorithm with an iterative approach to locate the regions. The linearity of the iterative approach increases noise components at the receiving end. ...

Wireless Multiuser receivers suffer from their relatively higher computational complexity that prevents widespread use of this technique. In addition, one of the main characteristics of multi-channel communications that can severely degrade the performance is the inconsistent and low values of SNR that result in high BER and poor channel capacity. It has been shown that the computational complexity of a multiuser receiver can be reduced by using the transformation matrix (TM) algorithm [4]. In this paper, we provide quantification of SNR based on the computational complexity of TM algorithm. We show that the reduction of complexity results high and consistent values of SNR that can consequently be used to achieve a desirable BER performance. In addition, our simulation results suggest that the high and consistent values of SNR can be achieved for a desirable BER performance. The performance measure adopted in this paper is the consistent values of SNR. Comment: 9 pages IEEE format, International Journal of Computer Science and Information Security, IJCSIS July 2009, ISSN 1947 5500, Impact Factor 0.423

... Several new algorithms have been proposed in the literature [1,4], in order to reduce the complexity of the original ML detection scheme proposed by Verdu. Recently, [4] proposed a ML receiver that uses the neighboring decent (ND) algorithm. ...

... Several new algorithms have been proposed in the literature [1,4], in order to reduce the complexity of the original ML detection scheme proposed by Verdu. Recently, [4] proposed a ML receiver that uses the neighboring decent (ND) algorithm. They implemented an iterative approach using the ND algorithm to locate the region where the actual observations belong. ...

A closed-form expression to determine an average error rate for synchronous DS-CDMA multi-user detector is derived based on the transformation matrix (TM) algorithm proposed in [1]. The derived expression for average bit error rate (BER) can be used to produce higher and consistent values of signal-to-noise ratio (SNR) that consequently results good quality signal. In addition, the closed-form expression can be used to quantify the multiple access interference (MAI) for a desirable BER performance by which unwanted signals or interference can be suppressed relative to the desired signal at the receiving end. The derived closed-form expression for BER is not only shown to substantially improve the performance of the multiuser detectors by means of higher values of SNR but also has much lower MAI. The performance measure adopted in this paper is the achievable bit rate for a fixed probability of bit error (10<sup>-7</sup>) and the consistent values of SNR.

... The key innovation in the proposed receiver is a low-complexity soft channel estimator, which divides a processing block into overlapped cells and performs The significant performance gap between suboptimal multiuser detectors, such as the decorrelator [2], [3], the multistage [9], [21], and the decision-feedback multiuser detector [12], [22], and the optimum detector [23] has motivated much research in the design of optimum or near-optimum detectors of low complexity. Examples include Sankaran and Ephremides [24] who identified a class of optimum multiuser detection problems that can be solved in polynomial time complexity, and Agrell and Ottosson [25] [26] who showed that the optimum detector, in general, has an average time complexity of O(1.5 K ). ...

... We present two example detectors that approximate the ML by approximating its Voronoi diagram. The two multiuser detectors are descent search algorithms similar to that in [25,26], with some differences to lower complexity: 1) we truncate the search list; 2) we bound the time complexity by bounding the number of searches for each point to a fixed number K 0 after which the search stops; 3) we save the elements in the search list in some order, based on the Voronoi diagram; and, 4) a pre-detector is added to obtain an initial estimate. Other work related to descent algorithms in multiuser detection are reported in [16] [17], where a trellis search scheme is proposed and a likelihood threshold is used to reduce the number of search paths at each stage. ...

An iterative receiver structure is proposed for decoding multiuser
information data in a turbo-coded DS-CDMA system. The receiver performs
two successive soft-output decisions, achieved by a soft-input
soft-output (SISO) multiuser detector and a bank of single-user SISO
channel decoders, through an iterative process. At each iteration,
extrinsic information is extracted from detection and decoding stages
and is then used as a priori information in the next iteration, just as
in turbo decoding. A low-complexity SISO multiuser detector is developed
based on a novel nonlinear interference suppression technique, which
makes use of both soft-interference cancellation and instantaneous
linear MMSE filtering. Turbo multiuser detectors for both the simple
synchronous CDMA channels and the more complex asynchronous multipath
CDMA channels are developed

... Since the CLOSESTPOINT algorithm does not require an initial value for , the desired complexity measure is . 4 In this context, a "uniform distribution" is assumed to be uniform over a region large enough to make boundary effects negligible. This is equivalent to a uniform distribution over just one Voronoi region. ...

... [60]. Similar properties have been established for the Voronoi regions of binary linear codes [2] and of parallelepipeds [4]. ...

In this semitutorial paper, a comprehensive survey of closest point search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closest point search algorithm, based on the Schnorr-Euchner (1995) variation of the Pohst (1981) method, is implemented. Given an arbitrary point x ∈ R<sup>m</sup> and a generator matrix for a lattice Λ, the algorithm computes the point of Λ that is closest to x. The algorithm is shown to be substantially faster than other known methods, by means of a theoretical comparison with the Kannan (1983, 1987) algorithm and an experimental comparison with the Pohst (1981) algorithm and its variants, such as the Viterbo-Boutros (see ibid. vol.45, p.1639-42, 1999) decoder. Modifications of the algorithm are developed to solve a number of related search problems for lattices, such as finding a shortest vector, determining the kissing number, computing the Voronoi (1908)-relevant vectors, and finding a Korkine-Zolotareff (1873) reduced basis.

... The popular Godard [6] algorithm and the earlier Shalvi–Weinstein algorithm [7] are well-known examples of this class of method. As a matter of fact, these two algorithms are closer than they initially appear as they both amount to seeking a maximum of a same cost function (see, e.g., [8]), belonging to the family of Donoho's deconvolution objective functions [9]. ...

... This family of functions traces back to Donoho [9] and is very relevant in blind deconvolution. For example, the popular Godard algorithm [6] as well as the earlier Shalvi-Weinstein algorithm [7] ...

This article reviews the super-exponential algorithm proposed by
Shalvi and Weinstein (1993) for blind channel equalization. The
principle of this algorithm-Hadamard exponentiation, projection over the
set of attainable combined channel-equalizer impulse responses followed
by a normalization-is shown to coincide with a gradient search of an
extremum of a cost function. The cost function belongs to the family of
functions given as the ratio of the standard l<sub>2p</sub> and l<sub>2
</sub> sequence norms, where p>1. This family is very relevant in
blind channel equalization, tracing back to Donoho's (1981) work on
minimum entropy deconvolution and also underlying the Godard (1980) (or
constant modulus) and the earlier Shalvi-Weinstein algorithms. Using
this gradient search interpretation, which is more tractable for
analytical study, we give a simple proof of convergence for the
super-exponential algorithm. Finally, we show that the gradient
step-size choice giving rise to the super-exponential algorithm is
optimal

... The complexity of multiuser receiver grows exponentially in an order of O (2) K , where K is the number of active users. Recently, [2] proposed a ML receiver that uses the neighboring decent (ND) algorithm with an iterative approach to locate the regions. The linearity of the iterative approach increases noise components at the receiving end. ...

Wireless Multiuser receivers suffer from their relatively higher computational complexity that prevents widespread use of this technique. In addition, one of the main characteristics of multi-channel communications that can severely degrade the performance is the inconsistent and low values of SNR that result in high BER and poor channel capacity. It has been shown that the computational complexity of a multiuser receiver can be reduced by using the transformation matrix (TM) algorithm [4]. In this paper, we provide quantification of SNR based on the computational complexity of TM algorithm. We show that the reduction of complexity results high and consistent values of SNR that can consequently be used to achieve a desirable BER performance. In addition, our simulation results also suggest that the high and consistent values of SNR can be achieved for a desirable BER performance. The performance measure adopted in this paper is the consistent values of SNR.

... On the other hand, linear multiusers receivers apply a linear transformation to an observation vector, which serves as soft decision for the transmitted data. Recently, Ottosson and Agrell [6] proposed a new ML receiver that uses the neighbor descent (ND) algorithm. They implemented a linear iterative approach using the ND algorithm to locate the region where the actual observations belong. ...

A new transformation matrix technique for reducing the complexity of a multiuser receiver for DS-CDMA system is presented. The reduction in complexity of multiuser receiver would result in better bit error rate (BER) performance. The reduction in error rate would allow us to maximize the data throughput of a communication network by minimizing the packet loss. Our simulation results demonstrate that the proposed technique successfully reduces the computational complexity of an optimal multiuser receiver for the DS-CDMA systems. The complexity of the proposed technique is not polynomial in the number of users, but it still gives comparatively reduced complexity that can be used to achieve optimum performance in terms of a reduced BER and increased network data throughput.

... On the other hand, linear multiusers receivers apply a linear transformation to an observation vector, which serves as soft decision for the transmitted data. Recently, Ottosson and Agrell [5] proposed a new ML receiver that uses the neighbor descent (ND) algorithm. They implemented a linear iterative approach using the ND algorithm to locate the region (s). ...

This paper presents a new transformation matrix system for reducing the computational complexity of multiuser receiver. The proposed system observes the coordinates of the constellation diagram to determine the location of the transformation points. Since most of the decisions are correct, we can reduce the number of required computations by using the transformation matrixes only on those coordinates which are most likely to lead to an incorrect decision. Our results show that the proposed system successfully reduces the computational complexity of an optimal multiuser receiver. The complexity of the proposed system is not polynomial in the number of users, but it still gives comparatively reduced complexity.

... Much research has been done to reduce this receiver's computational complexity. Recently, Ottosson and Agrell [4] proposed a ML receiver that uses the neighboring decent (ND) algorithm. They implemented an iterative approach using the ND algorithm to locate the region where the actual observations belong. ...

In this paper, a new scheme for reducing the computational complexity of multiuser receivers is presented. It utilizes the transformation matrix (TM) algorithm to improve the performance of multiuser receivers by effectively reducing the bit error rate (BER). In addition, a deterministic formalization of the processing gain (PG) for a multiuser DS CDMA system is presented. The proposed formalization of the PG demonstrates that how the reduced BER could be used to achieve reasonable values of PG by which unwanted signals or interference can be suppressed relative to the desired signal at the receiving end. The proposed algorithms not only are shown to substantially improve the performance of the multiuser detectors by means of reduced BER but also have a much lower multi-access interference. The performance measure adopted in this paper is the achievable bit rate for a fixed probability of error (10-7) and consistent values of the PG

... Much research has been done to reduce this receiver's computational complexity. Recently, Ottosson and Agrell [8] proposed a ML receiver that uses the neighboring decent (ND) algorithm. They implemented an iterative approach using the ND algorithm to locate the region where the actual observations belong. ...

Multiuser detection is an important technology in wireless CDMA systems for improving both data rate as well as user capacity. However, the computational complexity of multiuser detection prevents the widespread use of this technique. Most of the CDMA systems today and in the near future will continue to use the conventional matched filter with its comparatively low user capacity and a slow data rate. However, if we could lower the computational complexity of multiuser detectors, most of the CDMA systems would be likely to take advantage of this technique in order to gain increased system capacity and a better data rate. In this paper, a novel approach for reducing the computational complexity of multiuser receivers is proposed. It utilizes the transformation matrix technique to improve the performance of multiuser detectors. We show that the mathematical computations of the implementation complexity can turn in overall less complex system that has strong impact on the system's signal to noise ratio (SNR) and the bit error rate (BER). The performance measure adopted in this paper is the achievable bit rate for a fixed probability of error (10<sup>-7</sup>) and consistent values of SNR.

Multiuser detectors suffer from their relatively higher computational complexity that prevents widespread use of this technique. In addition, one of the main characteristics of multichannel communications that can severely degrade the performance is the inconsistent values of processing gain (PG) that result in high multiple access interference (MAI). However, if we could lower the complexity of multiuser detectors and produce better values of PG, most of the CDMA systems would likely take advantage of this technique in terms of increased system capacity and a better data rate .This paper presents a deterministic formalization of the PG for a wireless multi-channel DS-CDMA system The proposed deterministic formalization demonstrates that how the reduced BER could be used to achieve reasonable values of PG by which unwanted signals can be suppressed relative to the desired signal at the receiving end. The performance measure adopted in this paper is the achievable bit rate for a fixed probability of error (10<sup>-7</sup>).

Communication networks using code division multiple access (CDMA)
include applications where several packets of information are
transmitted synchronously and simultaneously over a common channel.
Consideration is given to the problem of simultaneously demodulating
every packet from such a transmission. A nonlinear detection scheme
based on a linear complexity multistage multiple-access interference
rejection algorithm is studied. A class of linear detectors is
considered as constituting the first stage for the multistage detector.
A bit-error probability comparison of the linear and multistage
detectors is undertaken. It is shown that the multistage detectors are
capable of achieving considerable improvements over the linear
detectors, particularly in near-far situations, i.e., in the
demodulation of weak signals in the presence of strong interfering
signals. This problem has been of primary concern for currently
operational CDMA systems

Spread spectrum-based code division multiple access (CDMA), has
taken on a significant role in cellular and personal communications. We
concentrate on direct sequence CDMA (DS/CDMA). We show that there is a
natural modification of the present systems that is potentially capable
of significant capacity increases. By “natural modification”
we mean a modification that can be made conceptually clear, not that it
is easy to implement. Indeed, the optimal multiuser detector is much too
complex and most of the present research addresses the problem of
simplifying multiuser detection for implementation. The objective of the
article is to make the basic idea intuitive and then show how
investigators are trying to reduce the idea to practice. We also
indicate multiuser receiver structures with potentially acceptable
levels of complexity and address potential obstacles for achieving
theoretically predicted performance in practice. As a result of these
investigations, an answer to the following question is expected. Is
there a suboptimal multiuser detector that is cost effective to build
with significant enough performance advantage over present day systems?
A definitive answer is not yet available

Consider a Gaussian multiple-access channel shared by K users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms. The uncoded probability of error achievable by optimum multiuser detectors is investigated. It is shown that the K -user maximum-likelihood sequence detector consists of a bank of single-user matched filters followed by a Viterbi algorithm whose complexity per binary decision is O(2^{K}) . The upper bound analysis of this detector follows an approach based on the decomposition of error sequences. The issues of convergence and tightness of the bounds are examined, and it is shown that the minimum multiuser error probability is equivalent in the Iow-noise region to that of a single-user system with reduced power. These results show that the proposed multiuser detectors afford important performance gains over conventional single-user systems, in which the signal constellation carries the entire burden of complexity required to achieve a given performance level.

Under the assumptions of symbol-synchronous transmissions and
white Gaussian noise, the authors analyze the detection mechanism at the
receiver, comparing different detectors by their bit error rates in the
low-background-noise region and by their worst-case behavior in a
near-far environment where the received energies of the users are not
necessarily similar. Optimum multiuser detection achieves important
performance gains over conventional single-user detection at the expense
of computational complexity that grows exponentially with the number of
users. It is shown that in the synchronous case the performance achieved
by linear multiuser detectors is similar to that of optimum multiuser
detection. Attention is focused on detectors whose linear memoryless
transformation is a generalized inverse of the matrix of signature
waveform crosscorrelations, and on the optimum linear detector. It is
shown that the generalized inverse detectors exhibit the same degree of
near-far resistance as the optimum multiuser detectors. The optimum
linear detector is obtained

ÔMultiuser detection for CDMA systemsÕ ÔLinear multiuser detectors for synchronous codedivision multiple-access channelsÕ ÔNear-optimum detection is synchronous code-division multiple-access systemsÕ

- A Holtzman
- R Verdò

1
DUEL -HALLEN, A., HOLTZMAN, J., and ZVONAR, Z.: ÔMultiuser detection for
CDMA systemsÕ, IEEE Personal Comm., 1995, 2, (2), pp. 46Ð58
2
LUPAS, R., and VERDò, S.: ÔLinear multiuser detectors for synchronous codedivision multiple-access channelsÕ, IEEE Trans. Inform. Theory, 1989, 35, (1), pp.
123Ð136
3
VARANASI, M.K., and AAZHANG, B.: ÔNear-optimum detection is synchronous
code-division multiple-access systemsÕ, IEEE Trans. Comm., 1991, 39, (5), pp. 725Ð
736

ÔMultiuser detection for CDMA systemsÕ

- A Duel -Hallen
- J Holtzman

DUEL -HALLEN, A., HOLTZMAN, J., and ZVONAR, Z.: ÔMultiuser detection for
CDMA systemsÕ, IEEE Personal Comm., 1995, 2, (2), pp. 46Ð58

ÔLinear multiuser detectors for synchronous codedivision multiple-access channelsÕ

- R Lupas
- S Verdò

LUPAS, R., and VERDò, S.: ÔLinear multiuser detectors for synchronous codedivision multiple-access channelsÕ, IEEE Trans. Inform. Theory, 1989, 35, (1), pp.
123Ð136

ÔMinimum probability of error for asynchronous Gaussian multipleaccess channelsÕ

- S Verdò

VERDò, S.: ÔMinimum probability of error for asynchronous Gaussian multipleaccess channelsÕ, IEEE Trans. Inform. Theory, 1986, IT-32, (1), pp. 85Ð96

ÔOptimal multiuser receivers in a synchronous CDMA systemÕ

- E Agrell

AGRELL, E., and OTTOSSON, T.: ÔOptimal multiuser receivers in a synchronous
CDMA systemÕ. Tech. Rep., Dept. of Information Theory, Chalmers Univ. of
Technology, Gšteborg, Sweden, in preparation