A Network Information Theory for Wireless Communication: Scaling Laws and Optimal Operation

Na/sub x/CoO/sub 2-/spl delta// (0.5/spl les/x/spl les/1) crystals were grown by a flux method. The largest Na/sub x/CoO/sub 2-/spl delta// crystal size was 10/spl times/10/spl times/0.5 mm, and the crystal phase depended on the composition of the flux. Crystals grown from a flux of NaCl mixed with Na/sub 2/CO/sub 3/ and B/sub 2/O/sub 3/ and crystals grown from a flux of Na/sub 2/CO/sub 3/ mixed with B/sub 2/O/sub 3/ were identified as Na/sub 0.6/CoO/sub 2-/spl delta// (/spl gamma/ phase) and Na/sub 0.9/CoO/sub 2-/spl gamma// (/spl alpha/ phase), respectively. The in-plane (ab-axis) thermoelectric properties of each phase were measured. The electrical resistivity (/spl rho/) of the /spl gamma/ phase and the a phase showed the almost same metallic temperature dependence except for an unusual increase of /spl rho//sub /spl alpha// at 5-20 K and the different magnitude. The value of /spl rho//sub /spl gamma// and /spl rho//sub /spl alpha// were 1.3 m/spl Omega/cm and 30 m/spl Omega/cm at 300 K, respectively. The Seebeck coefficient (S) of each phase exhibited the different S(T) behavior and the different magnitude, and the values were 100 /spl mu/V/K and 150 /spl mu/V/K at 300 K, respectively.

In this paper we first define a reduction /spl delta/ that transforms an instance /spl Gamma/ of Regular-SAT into a satisfiability equivalent instance /spl Gamma//sup /spl delta// of SAT. The reduction /spl delta/ has interesting properties: (i) the size of /spl Gamma//sup /spl delta// is linear in the size of /spl Gamma/, (ii) /spl delta/ transforms regular Horn formulas into Horn formulas, and (iii) /spl delta/ transforms regular 2-CNF formulas into 2-CNF formulas. Second, we describe a new satisfiability algorithm that determines the satisfiability of a regular 2-CNF formula /spl Gamma/ in time O(|/spl Gamma/|log|/spl Gamma/|); this algorithm is inspired by the reduction /spl delta/. Third, we introduce the concept of renamable-Horn regular CNF formula and define another reduction /spl delta/' that transforms a renamable-Horn instance /spl Gamma/ of Regular-SAT into a renamable-Horn instance /spl Gamma//sup /spl delta/'/ of SAT. We use this reduction to show that both membership and satisfiability of renamable-Horn regular CNF formulas can be decided in time O(|/spl Gamma/|log|/spl Gamma/|).

Given an integer /spl sigma/>1, a vector (/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/), of nonnegative integers, and an undirected graph G=(V, E), an L(/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/)-coloring of G is a function f from the vertex set V to a set of nonnegative integers, such that |f(u)-f(v)|/spl ges//spl delta//sub i/, if d(u,v)=i, for 1<i<(/spl sigma/-1), where d(u, v) is the distance (i.e., the minimum number of edges) between the vertices u and v. An optimal L(/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/)-coloring for G is one using the smallest range /spl lambda/ of integers over all such colorings. This problem has relevant application in channel assignment for interference avoidance in wireless networks, where channels (i.e., colors) assigned to interfering stations (i.e., vertices) at distance i must be at least /spl delta//sub i/ apart, while the same channel can be reused in vertices whose distance is at least /spl sigma/. In particular, two versions of the coloring problem - L(2, 1, 1) and L(/spl delta//sub 1/, 1,..., 1) - are considered. Since these versions of the problem are NP-hard for general graphs, efficient algorithms for finding optimal colorings are provided for specific graphs modeling realistic wireless networks, including rings, bidimensional grids, and cellular grids.

In this paper, we analyze the error probability performance of maximal ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) diversity schemes with coherent BPSK signaling on Rayleigh fading channels with Gaussian channel estimation errors. We first show that, with weighting errors, the conditional probability of error is not an explicit function of the signal-to-noise ratio (SNR) at the output of the diversity combiner. We then show that averaging the conditional probability of error with the density function of the SNR at the output of the combiner yields a lower bound on the exact probability of error, independent of the underlying diversity combining scheme. Later, we derive the exact probability of error for MRC, EGC, and SC diversity schemes and show that the exact probability of error with weighting errors is very similar to the case of perfect channel estimation, but with the average SNR per diversity branch, /spl gamma/_, for the case of perfect channel estimation, replaced by the effective SNR, /spl gamma/_/sub /spl rho//, due to weighting errors, which is a function of both /spl gamma/_ and /spl rho/, the magnitude of the normalized cross correlation between the actual and the estimated channel gains. Finally, we show that, as /spl rho/ /spl rarr/ 0, the average probability of error approaches 0.5, irrespective of the order of diversity and the diversity combining rule.

Studies the asymptotic characteristics of uniform scalar quantizers that are optimal with respect to mean-squared error (MSE). When a symmetric source density with infinite support is sufficiently well behaved, the optimal step size /spl Delta//sub N/ for symmetric uniform scalar quantization decreases as 2/spl sigma/N/sup -1/V~/sup -1/(1/6N/sup 2/), where N is the number of quantization levels, /spl sigma//sup 2/ is the source variance and V~/sup -1/(/spl middot/) is the inverse of V~(y)=y/sup -1/ /spl int//sub y//sup /spl infin// P(/spl sigma//sup -1/X>x) dx. Equivalently, the optimal support length N/spl Delta//sub N/ increases as 2/spl sigma/V~/sup -1/(1/6N/sup 2/). Granular distortion is asymptotically well approximated by /spl Delta//sub N//sup 2//12, and the ratio of overload to granular distortion converges to a function of the limit /spl tau//spl equiv/lim/sub y/spl rarr//spl infin//y/sup -1/E[X|X>y], provided, as usually happens, that /spl tau/ exists. When it does, its value is related to the number of finite moments of the source density, an asymptotic formula for the overall distortion D/sub N/ is obtained, and /spl tau/=1 is both necessary and sufficient for the overall distortion to be asymptotically well approximated by /spl Delta//sub N//sup 2//12. Applying these results to the class of two-sided densities of the form b|x|/sup /spl beta//e(-/spl alpha/|x|/sup /spl alpha//), which includes Gaussian, Laplacian, Gamma, and generalized Gaussian, it is found that /spl tau/=1, that /spl Delta//sub N/ decreases as (ln N)/sup 1//spl alpha///N, that D/sub N/ is asymptotically well approximated by /spl Delta//sub N//sup 2//12 and decreases as (ln N)/sup 2//spl alpha///N/sup 2/, and that more accurate approximations to /spl Delta//sub N/ are possible. The results also apply to densities with one-sided infinite support, such as Rayleigh and Weibull, and to densities whose tails are asymptotically similar to those previously mentioned.

This paper presents a 'do-it-yourself' methodology for characterizing the random component of transistor mismatch in CMOS technologies. The methodology is based on the design of a special purpose chip which allows automatic characterization of arrays of NMOS and PMOS transistors of different sizes. Up to 30 different transistor sizes were implemented in the same chip, sweeping transistors width W and length L. The standard deviation of the mismatch of these parameters is computed (/sup /spl sigma//(/spl Delta//spl beta///spl beta/), /sup /spl sigma//(/spl Delta/v/sub /spl gamma/0/), /sup /spl sigma//(/spl Delta//spl gamma/)) for each transistor type and size, as well as the statistical correlation factors between them. These standard deviations and correlations are fitted to two dimensional surfaces /spl sigma/(W, L) so that their values can be predicted as a function of transistor sizes. These functions are used in an electrical circuit simulator (Hspice) to predict transistor mismatch. Measured and simulated data are in good agreement.

A neural network that retrieves stored binary vectors, when probed by possibly corrupted versions of them, is presented. It employs sparse ternary internal coding and autocorrelation (Hebbian) storage. It is symmetrically structured and, consequently, can be folded into a feedback configuration. Bounds on the network parameters are derived from probabilistic considerations. It is shown that when the input dimension is n, the proportional activation radius is /spl rho/ and the network size is 2/sup /spl nu/n/ with /spl nu/>1-h/sub 2/(/spl rho/), the equilibrium capacity is at least 2/sup /spl alpha/n//8n/spl rho/(1-/spl rho/) for any /spl alpha/<1-h/sub 2/(/spl rho/), where h/sub 2/(/spl middot/) is the binary entropy. A similar capacity bound is derived for the correction of errors of proportional size /spl rho/ or less, when /spl rho//spl les/0.3. The performance of a finite-size symmetric network is examined by simulation and found to exceed, at the cost of higher connectivity, that of the Kanerva (1988) model, operating as a content addressable memory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The k-edge-connectivity augmentation problem for a specified set of vertices (kECA-SV) is defined as follows: Given an undirected graph G=(V, E), a subgraph G'=(V, E') of G, a specified set of verticies /spl Gamma//spl sube/V and a cost function c: rarr/Z/sup +/ (non-negative integers), find a set E/spl sube/E-E' of edges, each connecting distinct vertices of V, of minimum total cost such that /spl lambda/(/spl Gamma/; G'+E)/spl ges/k for G'+E=(V, E'/spl cup/E), where /spl lambda/(/spl Gamma/; G)/spl ges/k means that G has at least k edge disjoint paths between any pair of vertices in /spl Gamma/. The paper proposes an O(/spl Delta/+|V/spl par/E|) time 2-approximate algorithm FSA+1 for (/spl lambda/+1)ECA-SV with /spl lambda/(V; G)=/spl lambda/(/spl Gamma/; G), where /spl lambda/=/spl lambda/(/spl Gamma/; G') and /spl Delta/ is the time complexity of constructing a structural graph of a given graph G'.

We consider the relative stability of time invariant and time varying unnormalized lattice filters. First, we consider a set of lattice filters whose reflection parameters /spl alpha//sub i/, obey |/spl alpha//sub i/|/spl les//spl delta//sub i/, and provide necessary and sufficient conditions on the /spl delta//sub i/ that guarantee that each time invariant Lattice in the set has poles inside a circle of prescribed radius 1//spl rho/ 1//spl rho/.

Let /spl delta//sub /spl Sigma// be a measure of the relative stability of a stable dynamical system /spl Sigma/. Let /spl tau//sub A(/spl Sigma//) be a measure of the computational efficiency of a particular algorithm A which verifies the stability property of /spl Sigma/. For two representative cases of /spl Sigma/, we demonstrate the existence of a particular measure /spl delta//sub /spl Sigma// and an algorithm A such that, /spl delta//sub /spl Sigma///spl tau//sub A(/spl Sigma//)=c where c depends possibly on the dimension of the system /spl Sigma/ and parameters which are specific to the algorithm A, but independent of any other system characteristics. In particular, given /spl Sigma/ and A, one can estimate /spl delta//spl Sigma/ by measuring /spl tau//sub A(/spl Sigma//).

Total magnetic field measurements were obtained at ocean floor depths averaging about 100 m over a period of several days. Ambient or background fluctuations are deduced from the data by three schemes: high pass filtering in the frequency domain, detrending in the time domain, and synchronous reference subtraction. For frequencies larger than 2(32) mHz, the fluctuations have a vanishing mean, and a standard deviation of 3.3(0.1) nT. Our analysis shows that the magnitude of the background fluctuations, which set the threshold in classical target detection, varies with the high pass frequency and the detrending interval. We discuss the corresponding threshold limitations. We find that the fluctuations, when scaled by their respective standard deviations, have a common probability distribution function. This distribution is neither Gaussian nor exponential but is closely approximated by a stretched exponential (i.e. /spl sim/ e/sup -|/spl eta/|/spl gamma//) with /spl gamma/ < 1 for rms deviations 0.3 < /spl eta/ < 3. The frequency power spectra of the magnetic field measurements have f/sup /spl delta// power-law scaling with /spl delta/ /spl sim/ -2 for frequency 0.06 /spl les/ f /spl les/ 0.6 mHz and /spl delta/ /spl sim/ -11/3 for 1 < f < 10 mHz.

Bandpass modulators sampling at high IFs (/spl sim/200 MHz) allows direct sampling of the RF signal, reducing analog hardware, and makes it easier to realize completely software programmable receivers. This paper presents the circuit design of and test results from a continuous time tunable IF sampling 4/sup th/ order bandpass delta-sigma modulator implemented in InP HBT IC technology for use in a multi-mode digital receiver application. The bandpass /spl Delta//spl Sigma/ modulator is fabricated in AlInAs/GaInAs heterojunction bipolar technology with a peak unity current gain cutoff frequency (f/sub T/) of 130 GHz and a maximum frequency of oscillation (f/sub MAX/) of 130 GHz. The 4/sup th/ order bandpass /spl Delta//spl Sigma/ modulator consists of two bandpass resonators that can be tuned to optimize both wideband and narrowband operation. The IF is tunable from 140 MHz to 210 MHz in this /spl Delta//spl Sigma/ modulator for use in multiple platform applications. Operating from /spl plusmn/5 V power supplies, the fabricated 4/sup th/ order /spl Delta//spl Sigma/ modulator sampling at 4 GSPS demonstrates stable behavior and achieves a signal to (noise+distortion) ratio (SNDR) of 78 dB @ 1 MHz BW and 50 dB @ 60 MHz BW. The average SNDR performance measured on over 250 parts is 72.5 dB @ 1 MHz BW and 47.7 dB @ 60 MHz BW.

Using oversampled sigma-delta (/spl Sigma/-/spl Delta/) techniques a signal can be represented as a single bit binary data stream ({-1, 1}), with the quantization noise high pass filtered out of baseband. In this paper adaptive LMS digital filters are presented that directly use binary /spl Sigma/-/spl Delta/ input streams and update the PCM adaptive filter weights at the oversampled rate to realize architectures that are very suitable for mixed analog/digital VLSI implementation. Using the /spl Sigma/-/spl Delta/ adaptive architecture PCM values are multiplied by single bits, and can therefore be easily performed by a simple multiplexor. Also using the /spl Sigma/-/spl Delta/ approach, the decimation and interpolation stages required for converting from /spl Sigma/-/spl Delta/ to PCM (and vice-versa) suitable for Nyquist DSP algorithms are circumvented. The paper describes the sigma delta adaptive LMS filter architecture and presents preliminary results for adaptive echo cancellation using adaptive sigma delta and standard PCM architectures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The perovskite La/sub 0.67/Ba/sub 0.33/Mn/sub 0.99//sup 57/Fe/sub 0.01/O/sub 3/ compound was prepared by wet chemical solution process at 1200/spl deg/C for 3 h. Magnetic properties of La/sub 0.67/Ba/sub 0.33/Mn/sub 0.99//sup 57/Fe/sub 0.01/O/sub 3/ were studied using X-ray diffraction, Rutherford backscattering spectroscopy (RBS), neutron diffraction, Mossbauer spectroscopy, vibrating sample magnetometry, and magnetoresistance measurements. The polycrystalline La/sub 0.67/Ba/sub 0.33/Mn/sub 0.99//sup 57/Fe/sub 0.01/O/sub 3/ had a space group Pnma of orthorhombic perovskite structure with lattice constants a/sub 0/=5.526 /spl Aring/, b/sub 0/=7.830 /spl Aring/, and c/sub 0/=5.540 /spl Aring/, respectively. A chemical composition was confirmed to be stoichiometric by RBS. The maximum magnetoresistance ratio (/spl Delta//spl rho///spl rho/(0)) was observed at 281 K, with a magnitude of 9.5% in 1 Tesla. The Curie temperature (T/sub C/) was determined to be 345 K. Mossbauer spectra of La/sub 0.67/Ba/sub 0.33/Mn/sub 0.99//sup 57/Fe/sub 0.01/O/sub 3/ were taken at various temperatures ranging from 15 to 400 K. Below 77 K, two magnetic phases were increased and showed two sharp sextets of spectra. The magnetic hyperfine fields of outer (51%) and inner (49%) subspectrum were H/sub hf/=530 and 480 kOe, respectively. These unusual phenomena provide direct evidence of the two-magnetic phase character of the metallic state in the mixed valence of La/sub 0.67/Ba/sub 0.33/Mn/sub 0.99//sup 57/Fe/sub 0.01/O/sub 3/ powder. The outer sextet of Mossbauer spectra rapidly collapsed to paramagnetic phase with increasing temperature.

The magnitude and time variations of the SAW propagation velocity /spl Delta/v/v, of the mass and elastic loading, and of the fractional changes in the density /spl Delta//spl rho///spl rho/ and in the elastic modulii /spl Delta/c/sub ij//c/sub ij/ of Pd films are experimentally evaluated at room temperature and atmospheric pressure for 0.1, 0.5, 1% H/sub 2/, 1% CO, 1% N/sub 2/O and 1% NO gas mixtures in pure nitrogen. Two different thermally evaporated Pd films have been tested: one as evaporated, the other one after annealing at 423/spl deg/K and 10/sup -5/ Pa for 15 hours. The annealing is shown to change all set of the parameters. For not annealed films, hydrogen gives rise to large variations in the elastic constants (/spl sime/5-40%) and to an increase in the phase velocity; while for annealed films, it produces small variations in the elastic constants (/spl sime/1-2%) and a decrease in the phase velocity. The difference is attributed to weakly and strongly coupled oxygen preadsorbed in the film. The results obtained can allow an improvement of Pd-based sensors.