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52
A Random Matrix Model of Communication via Antenna Arrays
, 2001
"... A random matrix model is introduced that probabilistically describes the spatial and temporal multipath propagation between a transmitting and receiving antenna array with a limited number of scatterers for mobile radio and indoor environments. The model characterizes the channel by its richness d ..."
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Cited by 56 (7 self)
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A random matrix model is introduced that probabilistically describes the spatial and temporal multipath propagation between a transmitting and receiving antenna array with a limited number of scatterers for mobile radio and indoor environments. The model characterizes the channel by its richness delay profile which gives the number of scattering objects as a function of the path delay. Each delay is assigned the eigenvalue distribution of a random matrix that depends on the number of scatterers, receive antennas, and transmit antennas. The model allows to calculate signaltointerferenceandnoise ratios and channel capacities for large antenna arrays analytically and quantifies up to what extent rich scattering improves performance.
MIMO Channel Modelling and the Principle of Maximum Entropy
, 2004
"... In this paper , we devise theoretical grounds for constructing channel models for Multiinput Multioutput (MIMO) systems based on information theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we give her ..."
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Cited by 43 (23 self)
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In this paper , we devise theoretical grounds for constructing channel models for Multiinput Multioutput (MIMO) systems based on information theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we give here has already been fruitfully explored with success in the context of Bayesian spectrum analysis and parameter estimation. For each channel model, we conduct an asymptotic analysis (in the number of antennas) of the achievable transmission rate using tools from random matrix theory. A central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations. The results are both useful in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks .
Resource Pooling and Effective Bandwidths in CDMA Networks with Multiuser Receivers and Spatial Diversity
 IEEE Trans. Inform. Theory
, 1999
"... Much of the performance analysis on multiuser receivers for directsequence codedivision multipleaccess (CDMA) systems is focused on worst case nearfar scenarios. The user capacity of powercontrolled networks with multiuser receivers are less wellunderstood. In [1], it was shown that under som ..."
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Cited by 41 (3 self)
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Much of the performance analysis on multiuser receivers for directsequence codedivision multipleaccess (CDMA) systems is focused on worst case nearfar scenarios. The user capacity of powercontrolled networks with multiuser receivers are less wellunderstood. In [1], it was shown that under some conditions, the user capacity of an uplink powercontrolled CDMA cell for several important linear receivers can be very simply characterized via a notion of effective bandwidth. In the present paper, we show that these results extend to the case of antenna arrays. We consider a CDMA system consisting of users transmitting to an antenna array with a multiuser receiver, and obtain the limiting signaltointerference (SIR) performance in a large system using random spreading sequences. Using this result, we show that the SIR requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own requirement. Our results show that the total number of degrees of freedom of the whole system is the product of the spreading gain and the number of antennas. In the case when the fading distributions to the antennas are identical, we show that a curious phenomenon of "resource pooling" arises: the multiantenna system behaves like a system with only one antenna but with the processing gain the product of the processing gain of the original system and the number of antennas, and the received power of each user the sum of the received powers at the individual antennas.
Iterative Multiuser Joint Decoding: Optimal Power Allocation and LowComplexity Implementation
, 2002
"... We consider a canonical model for coded CDMA with random spreading, where the receiver makes use of iterative BeliefPropagation (BP) joint decoding. We provide simple DensityEvolution analysis in the largesystem limit (large number of users) of the performance of the exact BP decoder and of so ..."
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Cited by 39 (5 self)
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We consider a canonical model for coded CDMA with random spreading, where the receiver makes use of iterative BeliefPropagation (BP) joint decoding. We provide simple DensityEvolution analysis in the largesystem limit (large number of users) of the performance of the exact BP decoder and of some suboptimal approximations based on Interference Cancellation (IC). Based on this analysis, we optimize the received user SNR distribution in order to maximize the system spectral efficiency for given user channel codes, channel load (users per chip) and target user biterror rate. The optimization of the received SNR distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms. Remarkably, under the optimized SNR assignment the suboptimal Minimum MeanSquare Error (MMSE) ICbased decoder performs almost as well as the more complex exact BP decoder. Moreover, for a large class of commonly used convolutional codes we observe that the optimized SNR distribution consists of a finite number of discrete SNR levels. Based on this observation, we provide a lowcomplexity approximation of the MMSEIC decoder that suffers from very small performance degradation while attaining considerable savings in complexity. As
Capacity of MIMO systems with semicorrelated flat fading
 IEEE Trans. on Info. Theory
, 2003
"... Abstract—The primary contribution of this work lies in the derivation of the exact characteristic function (and hence, the mean and variance) of the capacity of multipleinput multipleoutput (MIMO) systems for semicorrelated flatfading channels. A Gaussian approximation to the exact capacity resu ..."
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Cited by 37 (2 self)
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Abstract—The primary contribution of this work lies in the derivation of the exact characteristic function (and hence, the mean and variance) of the capacity of multipleinput multipleoutput (MIMO) systems for semicorrelated flatfading channels. A Gaussian approximation to the exact capacity results is suggested and evaluated for its accuracy. We show that over a range of correlation levels this approximation is adequate even for moderate numbers of transmit and receive antennas. Index Terms—Multipleinput multipleoutput (MIMO) systems, Shannon capacity, spatial correlation. I.
On the Tradeoff between Two Types of Processing Gain
 IEEE Transactions on Communications
, 2002
"... One of the features characterizing almost every multiple access (MA) communication system is the processing gain. Through the use of spreading sequences, the processing gain of random direct sequence code division multiple access (RCDMA) systems, or any other CDMA systems, is devoted to both bandwid ..."
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Cited by 36 (26 self)
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One of the features characterizing almost every multiple access (MA) communication system is the processing gain. Through the use of spreading sequences, the processing gain of random direct sequence code division multiple access (RCDMA) systems, or any other CDMA systems, is devoted to both bandwidth expansion and orthogonalization of the signals transmitted by different users. Another type of multiple access systems is Impulse Radio (IR). In many aspects, IR systems are similar to time division multiple access (TDMA) systems, and the processing gain of IR systems represents the ratio between the actual transmission time and the total time between two consecutive transmissions (onplusoff to on ratio). While CDMA systems, which constantly excite the channel, rely on spreading sequences to orthogonalize the signals transmitted by different users, IR systems transmit a series of short pulses and the orthogonalization between the signals transmitted by different users is achieved by the fact that at the receiver most of the pulses do not collide with each other.
MMSE Analysis of Certain Large Isometric Random Precoded Systems
 IEEE Transactions on Information Theory, Volume: 49 Issue: 5, Page(s): 1293 1311
, 2001
"... Linear Precoding consists in multiplying by a N K matrix a Kdimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted. In this paper, we analyse the performance of MMSE receivers for certain large random isometric precoded systems on fading channels. Using ..."
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Cited by 21 (11 self)
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Linear Precoding consists in multiplying by a N K matrix a Kdimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted. In this paper, we analyse the performance of MMSE receivers for certain large random isometric precoded systems on fading channels. Using new tools, borrowed from the socalled Free Probability Theory, it can be shown that the Signal to Interference plus Noise Ratio at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when N 1. These asymptotic results are used to optimally balance the redundancy introduced between Linear Precoding and classical Convolutional Coding, while preserving a simple MMSE equalization scheme at the receiver.
Asymptotical Analysis of Optimum and SubOptimum CDMA Downlink MMSE Receivers
 IEEE Trans. on Inf. Th
, 2004
"... In this paper, we investigate the performance of two linear receivers for CDMA downlink transmissions over frequency selective channels, the users having possibly different powers. The optimum Minimum Mean Square Error (MMSE) receiver is first considered. Because this receiver requires the knowledge ..."
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Cited by 18 (2 self)
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In this paper, we investigate the performance of two linear receivers for CDMA downlink transmissions over frequency selective channels, the users having possibly different powers. The optimum Minimum Mean Square Error (MMSE) receiver is first considered. Because this receiver requires the knowledge of the code vectors attributed to all the users within the cell when these vectors are time varying, its use may be unrealistic in the forward link. A classical suboptimum receiver, consisting in a chip rate equalizer followed by a despreading with the code of the user of interest, is therefore studied and compared to the optimum MMSE receiver. Performance of both receivers is assessed through the Signal to Interference plus Noise Ratio (SINR) at their outputs. The analytical expressions of these SINRs depend in a rather non explicit way on the codes allocated to the users of the cell, and are therefore not informative. This difficulty is dealt with by modeling the users code matrix by a random matrix. Because the code matrices used in the forward link are usually isometric, the code matrix is assumed to be extracted from a Haar distributed random unitary matrix. The behavior of the SINRs is studied when the spreading factor and the number of users converge to ∞ at the same rate. Using certain results of the free probability theory, we establish the fact that the SINRs converge almost surely toward quantities that depend only on the (1)
NonAtomic Games for MultiUser Systems
"... In this contribution, the performance of a multiuser system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel ..."
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Cited by 11 (5 self)
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In this contribution, the performance of a multiuser system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). This scenario illustrates the case of decentralized schemes, where limited information on the network is available at the terminal. Various receivers are considered, namely the matched filter, the MMSE filter and the optimum filter. The goal of this paper is to extend previous work, and to derive simple expressions for the noncooperative Nash equilibrium as the number of mobiles becomes large and the spreading length increases. To that end two asymptotic methodologies are combined. The first is asymptotic random matrix theory which allows us to obtain explicit expressions of the impact of all other mobiles on any given tagged mobile. The second is the theory of nonatomic games which computes good approximations of the Nash equilibrium as the number of mobiles grows.
How fading affects CDMA: an asymptotic analysis with linear receivers
 IEEE Journal on Selected Areas in Communications, Volume 19, Issue 2, Pages:191  201
, 2001
"... Abstract—Using asymptotic analysis, we study the effect of frequencyflat fading on code division multiple access (CDMA) systems with linear receivers and random spreading sequences. Specifically, we let the number of users grow without bound, while the ratio of number of users to spreading sequence ..."
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Cited by 9 (0 self)
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Abstract—Using asymptotic analysis, we study the effect of frequencyflat fading on code division multiple access (CDMA) systems with linear receivers and random spreading sequences. Specifically, we let the number of users grow without bound, while the ratio of number of users to spreading sequence length is kept fixed to a value. We treat separately the cases of slow fading (nonergodic channel) and of fast fading (ergodic channel). For the former channel, we derive the outage probability, while for the latter, we compute the channel capacity. In both cases, multiple classes of users with different qualities of service are dealt with. As, the system throughput tends to the same limit of 1.44 bit/symbol as for the nonfading channel with both singleuser matched filter (SUMF) and linear minimum meansquareerror (MMSE) receivers. The outage probability exhibits a floor for all with the SUMF receiver, while with MMSE receiver the floor is present only for 1. We also address the tradeoffs involved in the allocation of available bandwidth between spreading and coding. Index Terms—CDMA, channel capacity, fading channels, outage probability. I.