A Class of Errorless Codes for Overloaded Synchronous Wireless and Optical CDMA Systems

Pad, Pedram; Marvasti, Farokh; Alishahi, Kasra; Akbari, S.

doi:10.1109/tit.2009.2018181

Cited by 35 publications

(75 citation statements)

References 35 publications

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“…7 compares the performance of the constrained -minimax test and the asymptotically equivalent one given in , in the case of an overloaded CDMA system. Some details and examples are given in [39]- [41]. The goal of this simulation is to illustrate the performances of the proposed -minimax test, not to deal with a real practical situation.…”

Section: B Simulation Resultsmentioning

confidence: 99%

“…For this reason, the simulation is based on an arbitrary vector constellation. It must be noted that a similar constellation can be designed with realistic signature waveform vectors proposed in [39], [41]. If the resulting constellation is simpler, it is still interesting to use the -minimax test but the loss of optimality of the MGLRT may be less significant.…”

Section: B Simulation Resultsmentioning

confidence: 99%

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Constrained Epsilon-Minimax Test for Simultaneous Detection and Classification

Fillatre

2011

IEEE Trans. Inform. Theory

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Abstract-A constrained epsilon-minimax test is proposed to detect and classify nonorthogonal vectors in Gaussian noise, with a general covariance matrix, and in presence of linear interferences. This test is epsilon-minimax in the sense that it has a small loss of optimality with respect to the purely theoretical and incalculable constrained minimax test which minimizes the maximum classification error probability subject to a constraint on the false alarm probability. This loss is even more negligible as the signal-to-noise ratio is large. Furthermore, it is also an epsilon-equalizer test since its classification error probabilities are equalized up to a negligible difference. When the signal-to-noise ratio is sufficiently large, an asymptotically equivalent test with a very simple form is proposed. This equivalent test coincides with the generalized likelihood ratio test when the vectors to classify are strongly separated in term of Euclidean distance. Numerical experiments on active user identification in a multiuser system confirm the theoretical findings.Index Terms-Constrained minimax test, generalized likelihood ratio test, linear nuisance parameters, multiple hypothesis testing, statistical classification, user activity detection.

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Section: B Simulation Resultsmentioning

confidence: 99%

Section: B Simulation Resultsmentioning

confidence: 99%

Constrained Epsilon-Minimax Test for Simultaneous Detection and Classification

Fillatre

2011

IEEE Trans. Inform. Theory

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“…We can apply the previous theorems to the binary case. In the wireless case, COW and in the optical case, COO CDMA systems are studied in [22]. In overloaded CDMA systems with binary inputs, we can use COW/ COO signature matrices.…”

Section: A Generalized Codes For Overloaded Wireless Cdma Systemsmentioning

confidence: 99%

“…None of the above codes guarantee errorless transmission in the absence of channel noise for overloaded CDMA systems. There are also some codes that are not designed upon cross-correlation and are designed such that they can provide one-to-one transformation such as codes for overloaded wireless (COW) and codes for overloaded optical (COO) codes [20][21][22][23]. By using these codes, we can achieve errorless transmission in the absence of channel noise for highly overloaded systems.…”

Section: Introductionmentioning

confidence: 99%

“…In this case, the signature entries and input alphabets are completely arbitrary (real or complex) [20,21]. But in real communication systems, we deal with more practical applications, and therefore, some special cases such as the binary input and binary signature CDMA systems [22] and the codes being able to detect the active users in a CDMA system [23] are considered. We will also take a brief look at CDMA systems with WBE (Welsh Bound Equality) codes that are optimum for analog inputs [11].…”

Section: Introduction To Optimum Codes For Cdma Transmissionmentioning

confidence: 99%

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A review on synchronous CDMA systems: optimum overloaded codes, channel capacity, and power control

Hosseini

Javidbakht

Pad

et al. 2011

J Wireless Com Network

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This paper is a tutorial review on important issues related to code-division multiple-access (CDMA) systems such as channel capacity, power control, and optimum codes; specifically, we consider optimum overloaded codes that achieve errorless transmission in the absence of noise for the binary and nonbinary cases. A survey of lower and upper bounds for the sum channel capacity of such systems is given in the presence and absence of channel noise. The asymptotic results for the channel capacity are also investigated. The channel capacity, errorless transmission codes, and power estimation for near-far effects are also explored. The emphasis of this tutorial review is on the overloaded CDMA systems.Keywords: Code Division Multiple Access (CDMA), Optimum codes, channel capacity bounds, near-far effects, power control I Introductioncode-division multiple access (CDMA) has been the most important multiple access technology for the 3rd generation GSM and American Cellular systems [1]. Optical CDMA systems have become an alternative multiple access for fiber optics and optical wireless systems [2][3][4].In CDMA systems, each user is assigned a unique code signature that consists of a number of chips. The signature length (also called chip rate) is defined as the number of chips in each signature code. Each user signature is multiplied by the respective data, and the transmitted vectors are added up in the common channel. The resultant vector is then observed at the received user end. In order to decode the received signal, the detector of the received user should know its own unique signature. These codes should be designed such that the cross-correlations between the code of the desired user and the codes of the other users are minimal.For the wireless case, the most well-known binary (Endnote a) code for the synchronous case is Hadamard orthogonal code that is appropriate for fully and underloaded CDMA systems. (Endnote b) But because of bandwidth limitation in the communication systems, we are interested in finding codes that can support more users than the chip rate (overloaded case). In the overloaded case, we cannot use Hadamard codes; Even random codes create interference that cannot be eliminated completely [5][6][7]. Optical orthogonal codes (OOC) [3,8] are not really orthogonal; however, using interference cancelation, we can remove interference completely. Most of the research in the overloaded case is related to code design and multi-access interference (MAI) cancelation in order to decrease the probability of error. Examples of these types of codes are pseudo random spreading [9,10], Welsh Bound Equality (WBE) codes with minimal total square correlation (TSC) [11][12][13][14], OCDMA [15][16][17], Multiple-OCDMA [18], and PN/ OCDMA [19] signature sets. None of the above codes guarantee errorless transmission in the absence of channel noise for overloaded CDMA systems. There are also some codes that are not designed upon cross-correlation and are designed such that they can provide one-to-one transfor...

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Twin tree hierarchy: a regularized approach to construction of signature matrices for overloaded CDMA

Singh

Amini

et al. 2016

Wirel. Commun. Mob. Comput.

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Overloaded code division multiple access being the only means of the capacity extension for conventional code division multiple access accommodates more number of signatures than the spreading gain. Recently, ternary Signature Matrices with Orthogonal Subsets (SMOS) has been proposed, where the capacity maximization is 200%. The proposed multi-user detector using matched filter exploits the twin tree hierarchy of correlation among the subsets to guarantee the errorless recovery. In this paper, we feature the non-ternary version of SMOS (i.e., 2k-ary SMOS) of same capacity, where the binary alphabets in all the k constituent (orthogonal) subsets are unique. Unlike ternary, the tree hierarchy for 2k-ary SMOS is non-uniform. However, the errorless detection of the multi-user detector remains undeviated. For noisy transmission, simulation results show the error performance of the right child for each subset of 2k-ary to be significantly improved over the left. The optimality of the right child of the largest (Hadamard) subset is also discovered. At higher loading, for larger and smaller subsets the superiority is reported for the 2k-ary and ternary, respectively, and the counter-intuitive deviations observed for the lower loading scenarios are logically explained. For the overall capacity maximization being 150%, superiority is featured by the 2k-ary, but beyond, it becomes a conditional entity.where y and r D CAx are the noisy and noiseless received vector for C D OEc 1 , c 2 , c 3 , , c M being a N M matrix representing M signatures of length N, x D OEx 1 , x 2 , x 3 , , x M T represents the input data vector corresponding to all M users or signatures, A D I M M = Identity matrix with diagonal elements representing the amplitudes assuming the system to be perfectly power controlled, and n denotes zero mean Additive white Gaussian noise vector. While for conventional (underloaded) CDMA the maximum achievable value of M is N (i.e., M Ä N), this capacity limit can be maximized beyond N (i.e., M > N) using the feature of overloaded CDMA, which subsequently leads to the significant rise in the loading (overloading) factorˇD . M =N/.Over a decade, the popularity of CDMA besides the military applications can be well-speculated from its growing commercialization of the wireless communication systems like Third Generation cellular architecture using wideband CDMA (WCDMA). Although for the Fourth Generation architecture, the scope of participation of CDMA has been fully obliterated, its further advancement in terms of sparse coded multiple access [1] using low density signature [2] has regained its priority and been prospectively provisioned for the Fifth Generation [3] cellular architecture.

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A Class of Errorless Codes for Overloaded Synchronous Wireless and Optical CDMA Systems

Cited by 35 publications

References 35 publications

Constrained Epsilon-Minimax Test for Simultaneous Detection and Classification

Constrained Epsilon-Minimax Test for Simultaneous Detection and Classification

A review on synchronous CDMA systems: optimum overloaded codes, channel capacity, and power control

Twin tree hierarchy: a regularized approach to construction of signature matrices for overloaded CDMA

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