Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. In this paper, we propose the point of view that both types of gains can be simultaneously obtained for a given multiple antenna channel, but there is a fundamental tradeo# between how much of each any coding scheme can get. For the richly scattered Rayleigh fading channel, we give a simple characterization of the optimal tradeo# curve and use it to evaluate the performance of existing multiple antenna schemes.

This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to recover f exactly from the data y? We prove that under suitable conditions on the coding matrix A, the input f is the unique solution to the ℓ1-minimization problem (‖x‖ℓ1:= i |xi|) min g∈R n ‖y − Ag‖ℓ1 provided that the support of the vector of errors is not too large, ‖e‖ℓ0: = |{i: ei ̸= 0} | ≤ ρ · m for some ρ> 0. In short, f can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted. This work is related to the problem of finding sparse solutions to vastly underdetermined systems of linear equations. There are also significant connections with the problem of recovering signals from highly incomplete measurements. In fact, the results introduced in this paper improve on our earlier work [5]. Finally, underlying the success of ℓ1 is a crucial property we call the uniform uncertainty principle that we shall describe in detail.

Abstract—We investigate the effects of fading correlations in multielement antenna (MEA) communication systems. Pioneering studies showed that if the fades connecting pairs of transmit and receive antenna elements are independently, identically distributed, MEA’s offer a large increase in capacity compared to single-antenna systems. An MEA system can be described in terms of spatial eigenmodes, which are single-input single-output subchannels. The channel capacity of an MEA is the sum of capacities of these subchannels. We will show that the fading correlation affects the MEA capacity by modifying the distributions of the gains of these subchannels. The fading correlation depends on the physical parameters of MEA and the scatterer characteristics. In this paper, to characterize the fading correlation, we employ an abstract model, which is appropriate for modeling narrow-band Rayleigh fading in fixed wireless systems. I.

In this paper, we study the capacity of multiple-antenna fading channels. We focus on the scenario where the fading coefficients vary quickly; thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver. We use a noncoherent block fading model proposed by Marzetta and Hochwald. The model does not assume any channel side information at the receiver or at the transmitter, but assumes that the coefficients remain constant for a coherence interval of length symbol periods. We compute the asymptotic capacity of this channel at high signal-to-noise ratio (SNR) in terms of the coherence time , the number of transmit antennas , and the number of receive antennas . While the capacity gain of the coherent multiple antenna channel is min bits per second per hertz for every 3-dB increase in SNR, the corresponding gain for the noncoherent channel turns out to be (1 ) bits per second per herz, where = min 2 . The capacity expression has a geometric interpretation as sphere packing in the Grassmann manifold.

Let x �1 � denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x �1 � is the largest principal component variance of the covariance matrix X ′ X, or the largest eigenvalue of a p-variate Wishart distribution on n degrees of freedom with identity covariance. Consider the limit of large p and n with n/p = γ ≥ 1. When centered by µ p = � √ n − 1 + √ p � 2 and scaled by σ p = � √ n − 1 + √ p��1 / √ n − 1 + 1 / √ p � 1/3 � the distribution of x �1 � approaches the Tracy–Widom lawof order 1, which is defined in terms of the Painlevé II differential equation and can be numerically evaluated and tabulated in software. Simulations showthe approximation to be informative for n and p as small as 5. The limit is derived via a corresponding result for complex Wishart matrices using methods from random matrix theory. The result suggests that some aspects of large p multivariate distribution theory may be easier to apply in practice than their fixed p counterparts. 1. Introduction. The

We derive performance limits for two closely related communication scenarios involving a wireless system with multiple-element transmitter antenna arrays: a point-to-point system with partial side information at the transmitter, and a broadcast system with multiple receivers. In both cases, ideal beamforming is impossible, leading to an inherently lower achievable performance as the quality of the side information degrades or as the number of receivers increases. Expected signal-tonoise ratio (SNR) and mutual information are both considered as performance measures. In the point-to-point case, we determine when the transmission strategy should use some form of beamforming and when it should not. We also show that, when properly chosen, even a small amount of side information can be quite valuable. For the broadcast scenario with an SNR criterion, we find the efficient frontier of operating points and show that even when the number of receivers is larger than the number of antenna array ...

Abstract—This paper deals with the capacity behavior of wireless Orthogonal Frequency Division Multiplexing (OFDM)-based spatial multiplexing systems in broadband fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Intro-ducing a physically motivated multiple-input multiple-output (MIMO) broadband fading channel model, we study the influence of physical parameters such as the amount of delay spread, cluster angle spread, and total angle spread, and system parameters such as the number of antennas and antenna spacing on ergodic capacity and outage capacity. We find that in the MIMO case, unlike the single-input single-output (SISO) case, delay spread channels may provide advantage over flat fading channels not only in terms of outage capacity but also in terms of ergodic capacity. Therefore, MIMO delay spread channels will in general provide both higher diversity gain and higher multiplexing gain than MIMO flat-fading channels.

End-to-end measurement is a common tool for network performance diagnosis, primarily because it can reflect user experience and typically requires minimal support from intervening network elements. Challenges in this approach are (i) to identify the locale of performance degradation; and (ii) to perform measurements in a scalable manner for large and complex networks. In this paper we show how end-to-end delay measurements of multicast traffic can be used to estimate packet delay variance on each link of a logical multicast tree. The method does not depend on cooperation from intervening network elements; multicast probing is bandwidth efficient. We establish desirable statistical properties of the estimator, namely consistency and asymptotic normality. We evaluate the approach through model based and network simulations. The approach extends to the estimation of higher order moments of the link delay distribution.

this paper. The first is the discussion of some mathematical properties relating to the eigenfunctions, while the second is the evaluation of the density in the ground state and the exact solution of (1.6) for certain initial conditions. These problems are in fact inter-related; we find that the density for each system can be written in terms of a certain eigenstate and that a summation theorem for the eigenstates gives an exact solution of (1.6). A feature of the Schrodinger operators (1.2) is that after conjugation with the ground state: \Gamma e i @ \Gamma fi @W (1.7) the resulting differential operator has a complete set of polynomial eigenfunctions. In Section 2 we consider the form of the expansion of these polynomials in terms of some different bases of symmetric functions. We note that in the N = 1 case, after a suitable change of variables, the operator (1.7) with W given by (1.3) is the eigenoperator for the classical Hermite, Laguerre and Jacobi polynomials. Previous studies of the operator for general N in the Jacobi case [1] have established an orthogonality relation. Since the polynomials in the Hermite and Laguerre cases are limiting cases of these generalized Jacobi polynomials, we can obtain the corresponding orthogonality relations via the limiting procedure. The generalized Hermite polynomials, which are the polynomial eigenfunctions of (1.4) with W = W as given by (1.3a), are studied in Section 3. Many higher-dimensional analogues of properties of the classical Hermite polynomials are obtained, including a generating function formula, differentiation and integration formulas, a summation theorem and recurrence relations. An analogous study of the generalized Laguerre polynomials is performed in Section 4. In Section 5 we relate the...

One method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter, and to decode differentially without knowing the channel coefficients at the receiver. Since channel knowledge is not required at the receiver, differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible, either because of rapid changes in the channel characteristics or because of limited system resources. Although this basic principle is well understood, it is not known how to generate good-performing constellations of unitary matrices, for any number of transmit and receive antennas and for any rate. This is especially true at high rates where the constellations must be rapidly encoded and decoded. We propose a class of Cayley codes that works with any number of antennas, and has efficient encoding and decoding at any rate. The codes are named for their use of the Cayley transform, which maps the highly nonlinear Stiefel manifold of unitary matrices to the linear space of skew-Hermitian matrices. This transformation leads to a simple linear constellation structure in the Cayley transform domain and to an information-theoretic design criterion based on emulating a Cauchy random matrix. Moreover, the resulting Cayley codes allow polynomial-time near-maximum-likelihood decoding based on either successive nulling/cancelling or sphere decoding. Simulations show that the Cayley codes allow efficient and effective high-rate data transmission in multi-antenna communication systems without knowing the channel.