S. Verd and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 622--640, Mar. 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....analysis of the particular allocation of fading gains and spreading sequences. In order to gain more general insight into the performance of the multiple access system, random fading gains and random spreading sequence models should be used. Pursu ing this basic motivation two important results [38], 39] published in March 1999 in the Transactions on Information Theory, analyzed random sequence and fading gain allocation. These results stirred considerable interest in the analysis of the perfor mances of various receivers for large multiple access DS CDMA systems. Both results deal with ....

....and [43] the asymptotic approach for the performance analysis of large system mul tiuser receivers is capable of producing analytically tractable and easily comparable results. A short review of some of these results on eigenvalue distribution of random matrices is given in Appendix A. In [38], asymptotic spectral efficiencies of linear and optimum receivers for syn chronous CDMA systems with equal user powers have been derived. The spectral efficiencies of linear multiuser receivers have been previously analyzed through sim ulations for finite systems in [44] Extending the results ....

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S. Verdfi and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. on Inform. Theory, pp. 622 640, March 1999.

....depend on the distribution of the entries . The asymptotic behavior of the mutual information follows directly from this proposition where the convergence is almost surely. This observation was previously made by Foschini [3] The integral can actually be computed in closed form, as was done in [16] in the context of a related capacity analysis problem for randomly spread codedivision multiple access (CDMA) systems. 9) We now turn to the water filling capacity. By relabeling the parameter as we can rewrite (5) and (6) as where satisfies (10) As , the empirical distribution of converges ....

S. Verd and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

....as both the number of users and processing gain grow. The QoS measure for each user is taken as the signal to interference ratio (SIR) achieved at the output of the multiuser receiver. Related results for the case when all users have the same SIR requirement are obtained independently in [6]. A concept of effective bandwidth has emerged from this work as a succinct measure of network capacity: given a set of SIR requirements for the users in an uplink power controlled cell, they can all be met if and only if the sum of the effective bandwidths of the users is less than a certain ....

S. Verd and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

....are controlled or when they are relatively weak (such as from out of cell) The performance of the decorrelator, on the other hand, does not depend on the interferers powers. The SIR performance of the MMSE receiver under power control will be studied. In recent independent studies [22] [25], it was shown that in a random environment, the SIR of a user under both the MMSE receiver and the decorrelator converges to a deterministic limit in a large system. The scaling is by letting the processing gain and the number of interferers go to infinity, keeping the number of interferers per ....

....of the decorrelator, before proceeding to the MMSE receiver, which requires a more sophisticated analysis. The following result shows that in a system with large processing gain and many users, the random SIR of a user converges to a deterministic limit. It is proved independently in [22] and [25]. Theorem 3.1: Let be the (random) SIR of the decorrelating receiver for user 1 when the spreading length is and the number of users , where is a fixed constant. Then converges to in probability as , where is given by . In the scaling considered, the number of users per degree of freedom (or, ....

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S. Verd and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

....have witnessed an explosion in the development of code division multiple access (CDMA) systems. It is well known that CDMA systems have the desirable features of dynamic channel sharing, wide range of operating environments, graceful degradation, and ease of cellular planning (see, e.g. 11] [31]) CDMA systems also offer the potential to support a heterogeneous mix of transmitting sources with a broad range of bursty traffic characteristics and quality of service (QoS) requirements. In this paper, we consider a model for Manuscript received March 22, 1999; revised May 15, 2000. The work ....

....from symbol to symbol, but they are randomly and independently selected initially when the users are admitted to the system. In this case, the more interesting quantity is the conditional distribution of the filter output given the signatures. In an information theoretical setting, Verd and Shamai [31] assumed that all the users had equal received powers and obtained that for almost every choice of signatures, the output MAI of the matched filter receiver converges (in the sense of divergence) to a Gaussian random variable. In this paper, we study the distributions of the MAI at the output of ....

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S. Verd and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

....in fading, IEEE Trans. Commun. vol. 47, pp. 352 355, Mar. 1999. 11] T. G. Donnelly, Bivariate normal distribution, Commun. ACM, vol. 16, p. 636, 1973. Algorithm 462. 12] J. Galambos and I. Simonelli, Bonferroni Type Inequalities with Applications. New York: Springer Verlag, 1996. [13] J. Hagenauer, Joint source and channel coding for broadcast applications, in Audio and Video Digital Radio Broadcasting Systems and Techniques. Amsterdam, The Netherlands: Elsevier, 1994. 14] D. Hunter, An upper bound for the probability of a union, J. Appl. Probab. vol. 13, pp. 597 603, ....

.... performance of direct sequence spread spectrum with random antipodal spreading in the large system limit, when the number of users K grows without bound and the ratio of the number of users to the spreading gain N is kept fixed to = fi: 5) More specifically, under that asymptotic regime, [13] has found the Shannon capacity achievable by the maximum likelihood decoder, the single user matched filter, the decorrelating detector, and the minimum mean square error (MMSE) multiuser detector, for systems with perfect power control; and [14] has investigated the signal to interference ratio ....

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S. Verd and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

.... baseband representations of bandpass communication systems (see, e.g. 3, 10] In particular, for communications in fading environments it is sometimes more reasonable to assume for the baseband model that the signals are complex [16, Chapter 2] We focus on systems with random spreading, as in [14, 17, 19, 20]. The random signature model is applicable to many practical systems. For example, this model is applicable to CDMA systems with very long pseudo random spreading sequences, and also applicable to CDMA systems with random short signatures (i.e. the period of the signature equals the information ....

....up the system (as N 1) the ratio of 1 Proper complex random processes are also known as circularly symmetric random processes [3] We elaborate further on proper complex random processes in Section 3. 2 K to N is denoted by ff 4 = K N and taken to be fixed, as is standard (see, e.g. [14, 17, 19]) In this paper, we first study the distribution of the multiple access interference (MAI) at the output of the MMSE receiver. The output MAI distribution is a physical layer performance metric and plays a crucial role in determining bit error probability. We focus on systems where repetition of ....

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S. Verd'u and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Transactions on Information Theory, vol. 45, pp. 622--640, Mar. 1999.

....as for frequency selective channels with a large number of propagation paths. I. INTRODUCTION Recently, the search for information theoretical bounds regarding the transmission of K users with code division multiple access (CDMA) to a single receiver has attracted considerable attention. So, in [1, 2] the system s capacity resulting for several linear multiuser receivers with and without decision feedback was derived for synchronous transmission over additive white Gaussian noise (AWGN) channels. Further, for transmission over attenuated single path channels with constant path gains which are ....

.... the Dirac impulse) is solved 1 Z 0 1=SNR lim ( f a 2 L ( d = SNR lim ( 1 SNR lim ( 15) Thus, for L 1 the required SNR can be obtained explicitly only relying on the load and the signal as well as noise power 2 x and 2 n , respectively (see also [5] [1]) SNR lim ( 1 2 (1 ) 2 x 2 2 n (16) s (1 ) 2 4 x 4 4 n (1 ) 2 x 2 2 n 1 4 : Then, the corresponding capacities C( are derived as C( L=1 = 1 ln(2) exp 1=SNR lim ( Ei 1=SNR lim ( 17) C( L 1 = log 2 1 2 (1 ....

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S. Verdu and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Transactions on Information Theory, vol. 45, pp. 622--640, Mar. 1999.

.... the resulting limit is shown to have a very nice form from which the concepts of effective interference and effective bandwidth emerge (see [30] for details) The same modelling paradigm of random spreading and large systems was extended to asynchronous systems in [31] Also see [32] 33] [34], 35] for some parallel work based on random spreading sequences. In this paper we extend the philosophy and the techniques of [30] to the situation where the channel is time varying. We drop the assumption that the channels of all users are perfectly known and assess receiver performance as a ....

S. Verd'u and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

.... 1 streams that overlap in both time and frequency [1] Linear and non linear receivers that take into account the presence of multiaccess interference can achieve substantial gains in spectral efficiency, as evidenced by the information theoretic analysis of the capacity of randomly spread CDMA [2, 3]. The analysis in [2, 3] obtains the maximum throughput (total rate) in a multiaccess channel where all active users are reliably decoded regardless of their received powers assuming that the transmit ters can adjust their rates (and possibly also their powers) as a function of the channel fade ....

.... in both time and frequency [1] Linear and non linear receivers that take into account the presence of multiaccess interference can achieve substantial gains in spectral efficiency, as evidenced by the information theoretic analysis of the capacity of randomly spread CDMA [2, 3] The analysis in [2, 3] obtains the maximum throughput (total rate) in a multiaccess channel where all active users are reliably decoded regardless of their received powers assuming that the transmit ters can adjust their rates (and possibly also their powers) as a function of the channel fade levels they experience. ....

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S. Verdfi and S. Shamai (Shitz), "Spectral Efficiency of CDMA with Random Spreading," IEEE Trans. Inform. Theory, Vol. 45, No. 2, pp. 622-640, March 1999.

....multiuser information theory, power control, spread spectrum . I. INTRODUCTION R ECENT results on the asymptotic distribution of the singular values of certain random matrices have enabled the study of the asymptotic limits of randomly spread code division multiple access (CDMA) channels [1] [3] In those multiple access channels, signature waveforms are assigned randomly and independently to the users. The analysis applies to both pseudonoise sequences spanning many symbol periods as well as randomly selected signature waveforms that remain fixed from symbol to symbol as in the ....

....fixed from symbol to symbol as in the basic CDMA model [4] Since it depends on the correlations between the signature waveforms, the capacity of the randomly spread basic CDMA channel model is random. However, as the number of users grows, the capacity converges to a deterministic limit. In [1] we analyzed the total capacity (rate sum) per chip, or spectral efficiency in bits per second per hertz (b s Hz) of the randomly spread synchronous CDMA channel when all the users are received with identical powers in the presence of additive white Gaussian noise. In that simple model, the ....

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S. Verd and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Information Theory, vol. 45, pp. 622--640, Mar. 1999.

....analyzes of direct sequence code division multiple access (DS CDMA) systems have gained much attention in recent years, as a result of the rapid development of commercial cellular systems employing this multi access strategy. Results for a single cell DS CDMA system were recently presented in [1] [4] see also references therein) These works explicitly relate to CDMA systems with random spreading sequences, and the limiting scenario is examined, where both the number of users and the processing gain go to infinity, while their ratio goes to some finite constant. This ratio is commonly ....

....size, demonstrating the practical importance of these limits. The reader is referred to [3] 6] and [7] for some numerical examples and an analysis of the rate of convergence. Assuming equal received powers and nonfading channels, four multiuser detection strategies are compared and analyzed in [1], in terms of spectral efficiency. The authors examine optimum decoding, the matched filter detector, the decorrelating detector, and the linear minimum mean squared error (MMSE) detector. In addition to explicit analytical expressions for the spectral efficiencies of the four detection ....

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S. Verd and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

....no AWGN is present. However, the asymptotic SINR grows exponentially with the order of the approximation for . A. Linear Receivers The previous results on the SINR with random spreading can be plugged into the definitions of power and bandwidth efficiency reading (58) 59) respectively [18] [19], with denoting the channel capacity of an individual user s channel. A parametric description of the functional relationship between power and bandwidth efficiency is given by (58) and (59) While, for the MMSE detector with random spreading, an explicit expression can be found [18] this is not ....

....(56) Fig. 1. Spectral efficiency versus load for approximations of zeroth to 26th order as E =N 1. Fig. 2. Spectral efficiency versus system load for several linear multiuser receivers and fixed 10 log (E =N ) 10dB in comparison to limits for orthogonal systems and joint decoding reported in [19]. approximate its exact counterpart rather fast, while the approximate decorrelator specified in (5) does not show promising performance for . Additionally, spectral efficiency is hardly affected by fluctuations of the load. All these properties result from proper weighting of the powers of the ....

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S. Verd and S. S. Shitz, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

....that although is common for all users, the individual rates need not be equal. The resulting system energy per bit can be seen to be equal to the harmonic mean of the individual energies per bit. Because of the different definition of , instead of (16) it is easy to see that we now have (cf. [27], 15] 127) where the ratio of users to dimensions is denoted by (128) Accordingly, in this case (129) Despite those differences, turns out to be the same as before. Theorem 8: Consider the user multiple access channel (130) where the dimensional complex Gaussian vector has independent and ....

S. Verd and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

....MMSE receivers and multiple antenna receivers. 1 Introduction In order to gain insight into the performance of receivers in a DS CDMA system with large processing gain and many users, much work has been devoted to the asymptotic analysis for synchronous DS CDMA with random spreading [17, 7, 15]. In [15] the asymptotic output signal to interference plus noise ratio (SINR) of the MMSE receiver is shown to satisfy a fixed point equation by using recent results on the asymptotic eigenvalue distribution of certain infinite random matrices. The reduced rank MMSE receiver is proposed and ....

S. Verd u and S. Shamai, "Spectral efficiency of CDMA with random spreading", IEEE Transactions on Information Theory, 45(2), pp.622-640, March 1999.

....decorrelator and MMSE receivers. Since these linear transformations operate on both the received observable vector and its conjugate, we refer to them as linear conjugate receivers. Our new performance results of the linear conjugate receivers use the tools developed in recent years [13] 5] [14] for the analysis of multiuser detectors in the wideband limit when the number of users goes to infinity while keeping the ratio of users to spreading gain constant. The performance gain afforded over the classical linear multiuser receivers by the linear conjugate receivers can be quite dramatic. ....

....random variables with zero mean and variance for all . The normalization ensures that ; additionally we need also the assumption . Let us focus now on near far resistance and on the (finite SNR) multiuser efficiency of the proposed receivers evaluated in limiting regime. It is well known [13] [14] that the near far resistance of detectors (8) and (10) converges almost surely as to (29) Additionally, define a nonnegative random variable whose distribution is the limit distribution of . For the conventional MMSE structure (10) the multiuser efficiency converges almost surely to the ....

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S. Verd and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

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S. Verd and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 622--640, Mar. 1999.

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S. Verd and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

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S. Verd and S. Shamai (Shitz), "Spectral Efficiency of CDMA with Random Spreading," IEEE Trans. Info. Theory, vol. 45, no. 2, Mar. 1999, pp. 622--40.

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S. Verd and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, no. 2, pp. 622--640, Mar. 1999.

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S. Shamai (Shitz) and S. Verd u, "Spectral efficiency of CDMA with random spreading" IEEE Trans. on Information Theory, Vol. 45, no. 2, March 1999.

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S. Verd and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

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S. VERD U AND S. SHAMAI (SCHITZ), Spectral efficiency of cdma with random spreading, IEEE Transactions on Information Theory, 45 (1999), pp. 622--640.

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S. Verd and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

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S. Verd and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inform. Theory, vol. 45, pp. 622--640, Mar. 1999.

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