Key reconciliation procedures are needed to correct key differences that can arise as a consequence of independent noise at the two ends of a reciprocal link. We assume a line-of-sight channel and use reconfigurable antenna elements to randomize it, such that it allows for key generation. The Linde-Buzo-Gray algorithm is employed to quantize the complex channel transfer characteristic, and adaptive guard bands, symmetric to the quantization thresholds, are further constructed. To limit the number of key errors, we ensure that only the points that fall outside the guard band interval are accepted for key generation. The steps for constructing the guard bands are presented.

When establishing secret encryption keys using estimates of the reciprocal wireless channel, the number of key bits that can be generated for a static or slowly varying propagation environment can be enhanced by randomly changing the radiation properties of a reconfigurable antenna. However, prior studies of this approach have been limited and have not considered a high degree of antenna reconfigurability. This paper uses simulations and experimental measurements to characterize the impact of reconfigurable antenna complexity on the performance of key establishment in different static propagation environments and in the presence of a multi-antenna eavesdropper. The results demonstrate that reconfigurable antennas can significantly enhance the security, even when the eavesdropper antennas are adjacent to or surround one of the legitimate nodes. The results further demonstrate that increasing the number of reconfigurable parasitic elements notably increases the achieved performance.

There is growing interest in physical-layer key generation schemes that provide very strong or even perfect security in wireless communication systems. One such scheme is reciprocal channel key generation, where two nodes quantize reciprocal channel state information to generate keys. Although the use of multiple-input multiple-output (MIMO) techniques is interesting in this case since the number of random parameters available for rapid key generation is increased, MIMO techniques may also provide more information to an eavesdropper. This work presents a new MIMO measurement campaign performed in LOS and NLOS indoor environments that studies the correlation of the channel between legitimate users with the eavesdropper channel, revealing what key generation rates can be attained in practice and what fraction of generated key bits are safe from eavesdroppers. The effect of eavesdropper separation, number of antennas, eavesdropper advantage, and covariance separability are studied.

Information theoretic limits for random key generation in multiple-input multiple-output (MIMO) wireless systems exhibiting a reciprocal channel response are investigated experimentally with a new three-node MIMO measurement campaign. As background, simple expressions are presented for the number of available key bits, as well as the number of bits that are secure from a close eavesdropper. Two methods for generating secret keys are analyzed in the context of MIMO channels and their mismatch rate and efficiency are derived. A new wideband indoor MIMO measurement campaign in the 2.51- to 2.59-GHz band is presented, whose purpose is to study the number of available key bits in both line-of-sight and nonline-of-sight environments. Application of the key generation methods to measured propagation channels indicates key generation rates that can be obtained in practice for four-element arrays.

There is growing interest in wireless security methods that provide strong or even perfect secrecy by taking advantage of features of the physical propagation channel. In advantage-based methods, high channel quality in an average or opportunistic sense is exploited between two legitimate nodes, such that nonzero secrecy capacity can be achieved. Since such methods require bounds on the quality of the eavesdropper channel, they are somewhat impractical. Secret key generation based on tracking channel evolution in time division duplex systems is a more attractive option, where two nodes generate secret key bits based on a mutually known random channel. Since the eavesdropper channel is typically independent of the legitimate channel, the key can only be broken by brute force attacks, which are difficult when new keys are continuously generated. In this paper, the information theoretic limits of key generation schemes are investigated, based on the level of estimation error, temporal correlation, and dependence of the eavesdropper and legitimate channels. Three practical candidate key generation schemes are also considered: channel quantization and channel quantization with guardband.

A method that exploits the autocorrelation of transmission signals for primary user detection in cognitive radio is proposed. A closed-form analysis of the method is presented and compared with Monte Carlo simulations. Analytical and simulation results indicate that the method provides significant improvement in the probability of detection for moderate SNR scenarios where fast sensing is required. Simulation results indicate the better performance in fading environment and collaborative sensing as well.

Previous results for correlated block-fading MIMO channels with covariance information indicate guaranteed capacity growth with additional transmit elements and that in rapidly fading channels, vanishing element spacing maximizes capacity. However, because prior analysis neglects antenna electromagnetic coupling, the observations are not necessarily valid for small inter-element spacing. This work applies radiated power considerations to the analysis to demonstrate that additional elements do not always increase capacity and that vanishing element spacing is not optimal. An effective gain metric is introduced that quantifies the performance increase with additional transmitters in the presence of transmit correlation and mutual coupling. Performance simulations using the electromagnetic properties of uniform linear arrays characterized by closed form expressions for Hertzian dipoles and detailed finite-difference time-domain (FDTD) simulations of half-wave dipoles illustrate that capacity gains arc possible when correlation stems from directional bias in the channel but not when it arises due to compact element spacing.

A study on the suitability of multiple-input multiple-output (MIMO) architectures employing either single- or dual-polarization antennas is presented, with the purpose of identifying not only which architecture provides better average capacity performance, but also which is more robust for avoiding low channel rank. It is expected that systems with high robustness will be required for MIMO in demanding industrial applications. A measurement campaign employing dual-polarized 8times8 patch arrays at 2.4 and 5.2 GHz is analyzed, where measurements were performed in two very distinct indoor scenarios: an office building and an industrial environment. For both environments the performance of three 4times4 subsystems (dual-polarized, vertical- polarized and horizontal-polarized) are compared in terms of the average capacities attained by these systems and their eigenvalue distributions. Average capacities are found to be only marginally different, indicating little advantage of dual-polarized elements for average performance. However, an eigenvalue analysis indicates that the dual-polarized system is most robust for full-rank MIMO communications, by providing orthogonal channels with more equal gain.

The ability of correlation tensor and directional modeling strategies to accurately capture the spatial behavior of multiple-input multiple-output (MIMO) channels is investigated. Correlation tensor methods are based on the reduced order approximations of the full channel covariance, and do not require any a priori knowledge about the physical scattering mechanism or antenna array. Directional methods require knowledge about the array configuration and usually assume a double-directional wave-propagation mechanism. Five different tensor methods (Kronecker, separable maximum entropy, Weichselberger, principal hyperplane, and sparse core tensor) and one directional method (unstructured diffuse spectrum estimation) are compared in terms of the number of parameters required and the match to the true full covariance matrix. Simulations with a realistic cluster channel model indicate that tensor methods suffer from poor accuracy when too few values in the core tensor are retained, especially when no joint transmit/receive information is available. The directional method, on the other hand, has good accuracy with the same number of parameters as the simplest tensor model. The results stress the importance of including joint transmit/receive information in MIMO models and suggest that directional modeling is a logical choice for high accuracy modeling with few parameters.

A method for determining the maximum entropy (ME) estimate of the full joint transmit/receive MIMO channel covariance matrix is presented, where only knowledge of the separate transmit and receive covariances is assumed. The resulting ME covariance is similar to, but distinct from, the Kronecker modelling strategy, warranting a direct comparison of the two techniques. Application of the method to wideband indoor multiple-input multiple-output (MIMO) measurements taken at 2.4 GHz indicates a slight improvement in the modelling accuracy of the dominant covariance eigenvalues compared to the Kronecker model. On the other hand, the double-directional joint transmit/receive Bartlett spectra are nearly identical, indicating that the ME technique does not significantly improve modelling of the channel multipath structure. This fact suggests that accurate multipath modelling for MIMO systems may not be possible without detailed joint transmit/receive channel knowledge.

A recent study on correlated block-fading MIMO channels with transmit covariance information indicates guaranteed capacity growth with additional transmit elements, in contrast to previous results for uncorrelated channels. Also, for very rapidly fading channels, the results indicate the optimality of placing antenna elements as close together as possible. In this work, application of radiated power considerations indicates that transmit beamforming only increases capacity when this gain results from correlation inherent in the channel, not correlation that is simply offset by increased antenna coupling. The new analysis reveals that when multipath is directionally biased, antenna spacings of 0.3 to 0.6 wavelengths are optimal, and that when no such bias is present, antennas should be placed as far apart as possible. As expected, the electromagnetic analysis shows that at zero element separation, the array yields no capacity gain over a single antenna.

A cost-effective, experimental MIMO channel sounder is presented, capable of performing measurements with up to eight transmit and eight receive elements over 80 MHz of system bandwidth. The system provides the wideband channel transfer matrix for both indoor and outdoor wireless communication scenarios, allowing direct measurement of key MIMO system parameters. The system is described, fundamental hardware building blocks are outlined, and post-processing data algorithms are presented. Initial investigations on the effect of frequency scaling and array configuration at 5.2 GHz and 2.4 GHz are also presented.

In antenna diversity systems, mutual coupling of closely-spaced antennas alters the element radiation and impedance properties, thereby impacting the system diversity performance. Past studies have emphasized the effect of the distorted pattern and largely neglected the effect of altered impedance (and therefore receive signal-to-noise ratio) on the diversity behavior. Here, we present a new network analysis which facilitates a complete characterization of the system and comparison of diversity performance for various impedance terminations. Representative results reveal that for closely-spaced antennas, the termination can play a noticeable role in determining the diversity gain offered by coupled antennas.

A diffuse spectrum estimation method is presented that is suitable for direction finding for channels with diffuse electromagnetic scattering. The diffuse channel may be the result of physical phenomena (e.g., rough-surface scattering) or limited angular and temporal discrimination of the channel probing equipment. The method decomposes the ideal noncoherent spectrum into a sum of power-weighted basis functions. The basis function coefficients are obtained through a linear programming solution. The method is applied to recent radio channel data collected on the Vienna University of Technology campus. Parameters for a path-based model are extracted using the technique. Site-specific spectra and global capacity comparisons indicate the utility of this new method.

This paper provides an analytical framework useful for assessing the use of all six electric and magnetic electromagnetic field polarizations for multiantenna communications systems. The approach uses a mapping between the induced signal currents and the received electromagnetic field in order to formulate a diversity interpretation of the six-polarization problem. Application of the framework to a simple, yet representative, channel model demonstrates that for full multipath elevation and azimuthal angle spread, six communication modes are theoretically possible. However, to implement the system requires more antenna design work since a straightforward implementation is found to reduce the potential number of modes to three.

A new framework for the analysis of multiple-input multiple-output (MIMO) wireless systems is introduced to account for mutual coupling effects in the antenna arrays. The multiport interactions at transmit and receive are characterized by representing the channel using a scattering parameter matrix. A new power constraint that limits the average radiated power is also introduced. The capacity of the MIMO system with mutual coupling is defined as the maximum mutual information of the transmit and receive vectors over all possible transmit signaling and receive loading. Full-wave electromagnetic antenna simulations combined with a simple path-based channel model are used to demonstrate the utility of the method.

Measurements taken at the campus of Brigham Young University (BYU) are used to investigate the statistical properties of the indoor MIMO channel. Two statistical tests, Royston's and Henze-Zirkler's, are applied to the MIMO data to assess whether the data belongs to a multivariate normal distribution or not. The possibility of modeling the covariance matrix as a Kronecker product of the correlations at the transmitter and receiver are also investigated by deriving a likelihood ratio test. It is found that small MIMO systems such as 2 /spl times/ 2 can be considered normally distributed and can also be approximated with a Kronecker structure. Larger systems, on the other hand, show evidence of strong non-normality and are not well modeled using a Kronecker product. However, for short measurement segments, these distributions can be used for approximate channel capacity calculations.

A common practice when analyzing systems using multiple antennas at both ends is to focus on the multipath properties and normalize the SNR out of the channel matrix. This paper studies the relationship between the signal strength and multipath richness using indoor measurements taken at the Brigham Young University campus. It is found that the SNR and multipath richness can be strongly corrected. Hence, some caution is needed when normalizing out the SNR in system performance studies. Furthermore, for unnormalized channel, the channel capacity usually rises when moving from NLOS into LOS since the loss in multipath is more than compensated for by an increase in SNR. A theoretical study also reveals that for moderate sized systems, the required SNR increase for a LOS channel to yield the same channel capacity as a NLOS channel is not very large.

Detailed performance assessment of space-time coding algorithms in realistic channels is critically dependent upon accurate knowledge of the wireless channel spatial characteristics. This paper presents an experimental measurement platform capable of providing the narrowband channel transfer matrix for wireless communications scenarios. The system is used to directly measure key multiple-input-multiple-output parameters in an indoor environment at 2.45 GHz. Linear antenna arrays of different sizes and construction with up to ten elements at transmit and receive are utilized in the measurement campaign. This data is analyzed to reveal channel properties such as transfer matrix element statistical distributions and temporal and spatial correlation. Additionally, the impact of parameters such as antenna element polarization, directivity, and array size on channel capacity are highlighted. The paper concludes with a discussion of the relationship between multipath richness and path loss, as well as their joint role in determining channel capacity.

In MIMO wireless communication using space-time coding techniques, it is important to understand channel characteristics so that optimum coding schemes, array configurations, and performance analysis can be developed. Increasingly, understanding of MIMO channels is being aided by direct channel probing experiments to measure transfer matrix, H. An alternate channel representation based on propagating ray parameters has many advantages. We propose an algorithm to compute high precision estimates of channel ray parameters directly from H measurements. Examples are presented where rays are identified, and departure angles, arrival angles, and complex path gains are estimated.

Detailed performance assessment of space-time coding algorithms in realistic channels is critically dependent upon accurate knowledge of the wireless channel spatial characteristics. This paper presents an experimental measurement platform capable of providing the channel transfer matrix for indoor and outdoor wireless communications scenarios. The system allows direct measurement of key multiple input multiple output parameters for 16 transmit and 16 receive antennas. The basic hardware blocks are outlined, and the data post-processing algorithms are presented. Representative data showing, channel capacity and spatial correlation for several indoor sites are provided.

This paper presents measured data from a narrowband multiple-input multiple-output (MIMO) channel probe in an indoor office/laboratory environment. The system employs ten transmit and ten receive antennas and computes the 10 /spl times/ 10 narrowband channel matrix at 2.45 GHz every 80 milliseconds. We use the data to study the statistical behavior of the channel coefficients and the resulting channel capacity. We also demonstrate the ability of a simple statistically based physical model to accurately represent the channel behavior. The results of this model are compared to more conventional models that assume complex normal distributions of the channel matrix elements.

This paper presents results from an experimental platform designed to measure the transfer matrix for indoor and outdoor multiple-input multiple-output (MIMO) channels with up to 16 transmit and receive antenna elements. Key aspects of the hardware system and data post-processing techniques are provided. A variety of measurements have been taken with the platform at 2.45 GHz in a typical indoor environment. The collected data have been processed to highlight a variety of channel features, including the statistical distributions of the channel matrix elements and the inherent capacity of the wireless MIMO channel for different numbers of antenna elements, polarizations, and element directivities.