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The third-generation (3G) mobile communication system uses a technique called code division multiple access (CDMA), in which multiple users use the same frequency and time domain. The data signals of the users are distinguished using codes. When there are many users, interference deteriorates the quality of the system. For more efficient use of res...
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Over the last two decades, wireless communication services and applications worldwide have witnessed exponential growth with corresponding progression in subscribers' population but without resultant increase in bandwidth required for their effective functionality. Solution to this challenge has led to the adoption of multiple-input-multiple-output...
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Citations
... @BULLET For k too small the estimate in (9) in Theorem 4.1 is certainly wrong. For example, it was shown by van der Hofstad and Klok [20] that for k = 2 the speed of convergence is O(e −cn ) for some constant c > 0 rather than O(e −cn 2 ). This could also be expected, since for k = 2, Ξ n is close to a U-statistics and we are in a large deviations regime. ...
We study two systems that are based on sums of weakly dependent Bernoulli random variables that take values 1 with equal probabilities. We show that already one step of the so-called soft decision parallel interference cancellation, used in the third generation of mobile telecommunication CDMA, is able to considerably increase the number of users such a system can host. We also consider a variant of the well-known Hopfield model of neural networks. We show that this variant proposed by Amari and Yanai [CITE] has a larger storage capacity than the original model. Both situations lead to the question of the moderate deviations behavior of a sum of weakly dependent Bernoulli random variables. We prove a moderate deviations principle for such a sum on the appropriate scale. Nous étudions deux systèmes basés sur des sommes de variables aléatoires de Bernoulli valant 1 avec égale probabilité et faiblement dépendantes. Nous montrons qu'une seule étape de la méthode de suppression d'interférences SD-PIC, utilisée dans la troisième génération de télécommunication mobile CDMA, permet déjà d'augmenter considérablement le nombre d'utilisateurs supporté par le système. Nous considérons également une variante du modèle neuronal de Hopfield. Nous montrons que cette variante, proposée par Amari et Yanai [CITE], admet une capacité de stockage supérieure au modèle original. Les deux situations conduisent à l'étude des déviations modérées d'une somme de variables aléatoires de Bernoulli faiblement corrélées. Nous montrons un principe de déviations modérées pour une telle somme convenablement normalisée.
... In these systems, each user is identified by a specific pseudo-noise (PN) code56789 . So, the average performance of these systems can degrade significantly when the number of active users increases, due to the increase in the level of multiple-access interference (MAI) in the channel [7,91011121314. This depends on the (out-of-phase auto and cross) correlation properties of the PN spreading sequences [13, 14]. ...
Based on two methods recently proposed—the ‘Ranging Criterion’ (RC) and the ‘Generators Ranging Criterion’ (GRC)—new (quasi-orthogonal) even BCH-derived sequences are generated which are very attractive for synchronous or quasi-synchronous Code Division Multiple-Access (CDMA) systems. Numerical results show that the new family of BCH-derived sequences can contain a higher number of quasi-orthogonal sequences with lower correlation values and higher processing gains (PGs) than the spreading sequences typically used in the third generation of mobile communications system, UMTS or in the recent large area synchronised CDMA (LAS-CDMA) technology. It is shown that the even BCH-derived sequences are easily generated by a linear shift register generator, allowing the construction of systems with receiver structures of low complexity as compared with those of quasi-synchronous systems using low correlation zone sequences, as for instance the LAS-CDMA system. Copyright © 2007 John Wiley & Sons, Ltd.
... holds without the 1 + o(1) as an upper bound. As explained in [13,Sec. 1.2], without loss of generality, we may assume that bm = 1 for all m = 1; . . . ...
... The second case is when we allow s to grow slowly with n, namely, proportionally with log n, and we allow the number of users to grow proportionally to n. All the results stated in this section are consequences of results in [12], [13] for HD-PIC and [7] for SD-PIC. For fixed s, our main result is the following: In words, applying s 0 1 stages of HD-PIC allows for a maximal number of users that is at least s times as large as for the MF system. ...
... The proof of Theorem III.2 is to a large extent contained in [13] for HD-PIC. The latter results are given in this paper to contrast the result on the existence of bit-errors in (III.2). ...
In this correspondence, we study a lightly loaded code-division multiple-access (CDMA) system with and without multistage hard- and soft-decision parallel interference cancelation (HD-PIC and SD-PIC). Throughout this paper we will only consider the situation of a noiseless channel, equal powers and random spreading codes. For the system with no or a fixed number of steps of interference cancelation, we give a lower bound on the maximum number of users such that the probability for the system to have no bit-errors converges to one. Moreover, we investigate when the matched filter system, where parallel interference cancelation is absent, has bit errors with probability converging to one. This implies that the use of HD-PIC and SD-PIC significantly enhances the number of users the system can serve
... In that paper, large deviation techniques are used to prove properties of the exponential rate and the BEP. In [7] and [11] , various results have been proven for the HD-PIC sys- tem. ...
... In this paper, we start by repeating results of one-stage and multi-stage HD-PIC of [7] and [11]. We extend these results to values of the processing gain and the number of users that are comparable using Chernoff bounds. ...
... In [7], we have obtained an analytic formula for the rate after one stage of HD-PIC. Theorem II.1: ...
We study a multiuser detection system for code-division multiple access (CDMA). We show that applying multistage hard-decision parallel interference cancellation (HD-PIC) significantly improves performance compared to the matched filter system. In (multistage) HD-PIC, estimates of the interfering signals are used iteratively to improve knowledge of the desired signal. We use large deviation theory to show that the bit-error probability (BEP) is exponentially small when the number of users is fixed and the processing gain increases. We investigate the exponential rate of the BEP after several stages of HD-PIC. We propose to use the exponential rate of the BEP as a measure of performance, rather than the signal-to-noise ratio (SNR), which is often not reliable in multiuser detection models when the system is lightly loaded. We show that the exponential rate of the BEP remains fixed after a finite number of stages, resulting in an optimal hard-decision system. When the number of users becomes large, the exponential rate of the BEP converges to (log 2)/2 $1/4. We provide guidelines for the number of stages necessary to obtain this asymptotic exponential rate. We also give Chernoff bounds on the BEPs. These estimates show that the BEPs are quite small as long as k = o(n/log n) when the number of stages of HD-PIC is fixed, and even exponentially small when k = O(n) for the optimal HD-PIC system, and where k is the number of users in the system and n is the processing gain. Finally, we extend the results to the case where the number of stages depends on k in a certain manner. The above results are proved for a noiseless channel, and we argue that we expect similar results in a noisy channel as long as the two-sided spectrum of the noise decreases proportionally to n.
... Parallel Interference Canceller (PIC), Successive Interference Canceller (SIC), and Zero-Forcing Decision- Feedback (ZF-DF) receivers are classified to be suboptimum non-linear receivers [1]. There have been several works focused on multiuser receivers with MAI cancellers under Gaussian approximation of other user's interference [7] [8] [9], i.e., the total MAI from other users is considered as a summation of infinite number of random variables. However, the validity of Gaussian approximation depends on the number of users, wherein, for small number of users, the reliability of such approximation is decreased [10]. ...
... In DS-CDMA systems, the average performance it is strongly limited by the number of active users, i.e. the level of multiple-access interference (MAI) in the channel [7], [8]. This is a function of correlation properties of the pseudo-noise (PN) spreading sequences [9]. ...
Based on two recently proposed methods in the literature − the "Ranging Criterion" and the "Generators Ranging Criterion" − new (quasi-orthogonal) even BCH-derived sequences are generated, which are very attractive for (synchronous or quasi-synchronous) CDMA applications. These sequences can be easily generated by a linear shift register generator, adding one extra zero or by a cyclically read memory table. Simulation results showed that the new family of even BCH-derived sequences can contain a higher number of sequences with lower correlation values and higher processing gains than the spreading sequences typically used in the third generation of mobile communications system, UMTS.
We study sample covariance matrices of the form W = (1 / n ) C C T , where C is a k x n matrix with independent and identically distributed (i.i.d.) mean 0 entries. This is a generalization of the so-called Wishart matrices, where the entries of C are i.i.d. standard normal random variables. Such matrices arise in statistics as sample covariance matrices, and the high-dimensional case, when k is large, arises in the analysis of DNA experiments. We investigate the large deviation properties of the largest and smallest eigenvalues of W when either k is fixed and n → ∞ or k n → ∞ with k n = o ( n / log log n ), in the case where the squares of the i.i.d. entries have finite exponential moments. Previous results, proving almost sure limits of the eigenvalues, require only finite fourth moments. Our most explicit results for large k are for the case where the entries of C are ∓ 1 with equal probability. We relate the large deviation rate functions of the smallest and largest eigenvalues to the rate functions for i.i.d. standard normal entries of C . This case is of particular interest since it is related to the problem of decoding of a signal in a code-division multiple-access (CDMA) system arising in mobile communication systems. In this example, k is the number of users in the system and n is the length of the coding sequence of each of the users. Each user transmits at the same time and uses the same frequency; the codes are used to distinguish the signals of the separate users. The results imply large deviation bounds for the probability of a bit error due to the interference of the various users.
We study sample covariance matrices of the form W = 1 n CC T , where C is a k × n matrix with i.i.d. mean zero entries. This is a generalization of so-called Wishart matrices, where the entries of C are independent and identically distributed standard normal random variables. Such matrices arise in statistics as sample covariance matrices, and the high-dimensional case, when k is large, arises in the analysis of DNA experiments. We investigate the large deviation properties of the largest and smallest eigenvalues of W when either k is fixed and n → ∞, or kn → ∞ with kn = o(n/ log log n), in the case where the squares of the i.i.d. entries have finite exponential moments. Previous results, proving a.s. limits of the eigenvalues, only require finite fourth moments. Our most explicit results for k large are for the case where the entries of C are ±1 with equal probability. We relate the large deviation rate functions of the smallest and largest eigenvalue to the rate functions for independent and identically distributed standard normal entries of C. This case is of particular interest, since it is related to the problem of the decoding of a signal in a code division multiple access system arising in mobile communication systems. In this example, k plays the role of the number of users in the system, and n is the length of the coding sequence of each of the users. Each user transmits at the same time and uses the same frequency, and the codes are used to distinguish the signals of the separate users. The results imply large deviation bounds for the probability of a bit error due to the interference of the various users.
The introduction of the so-called third-generation wireless communication system, also known as UMTS or IMT-2000, is a large-scale revolution in telecommunications. It uses a technique called code division multiple access (CDMA). An advanced algorithm to improve the performance of such a CDMA system is called hard-decision parallel interference cancellation and was studied by van der Hofstad and Klok for a rather basic model. We extend many of their results to a more realistic model, where different users transmit at different powers and where additive noise is present.
