Spatial Fading Correlation Research Articles

On the Performance of Space–Time Codes Over Spatially Correlated Rayleigh Fading Channels

We derive the exact pairwise error probability (PEP) for space-time coding over quasi-static Rayleigh fading channels in the presence of spatial fading correlation. We show that receive correlation always degrades the PEP for all signal-to-noise ratios (SNRs). We quantify the effect of receive correlation by employing the notion of "majorization". We show that the stronger the receive correlation, the worse the PEP for all SNRs. We show that at low SNR, depending on the codes, transmit correlation can either improve or degrade the PEP performance. We show that to guarantee robust performance for arbitrary transmit correlation, the minimum eigenvalue of the codeword pair difference matrix should be maximized among all codeword pairs.

Comments on “Spatial Fading Correlation Function of Circular Antenna Arrays With Laplacian Energy Distribution”

For original paper see Tsai et al. (IEEE Commun. Lett., vol.6, p.178-80, 2002 May). This comment points out three inaccurate formulae and the problems in results of the numerical simulations. The correct formulae and results of the voltage correlation coefficients are provided. Our simulations have shown the simulation results exhibit good agreement with the analytical results as long as the items of the series expansion long enough.

BER Performance of a Uniform Circular Array Versus a Uniform Linear Array in a Mobile Radio Environment

In this letter, we present a comparison between the bit error rate (BER) performance of a uniform circular array (UCA) and a uniform linear array (ULA) assuming quadrature phase-shift keying (QPSK) and maximal-ratio-combining (MRC) in a mobile radio communication environment. The results are based on analysis, assuming a flat Rayleigh fading channel with omni-directional antennnas and considering the azimuthal plane only. The analytical BER is derived as a function of the spatial fading correlation for both types of antenna arrays. Results show that for similar aperture sizes the UCA outperforms the ULA when considering all angles-of-arrival. However, there is considerable variability over central angle-of-arrival (AOA) for low-to-moderate angle spreads. For angles-of-arrival concentrated near the broadside of the linear array, the ULA typically performs as well as or better than the UCA. A truncated Gaussian AOA (AOA) distribution is assumed to model spatial correlation and the numerical results focus on four element arrays.

Spatial and temporal fading correlations of a uniform circular array smart antenna in urban vehicular propagation

AbstractFor smart antenna systems, the space‐time correlation of received signals at an antenna array is a crucial parameter in most adaptive beamforming techniques. In this paper, we experimentally investigate the variation of spatial and temporal fading correlations and the eigenspread of a space–time correlation matrix for a seven‐element uniform circular array (UCA) under the line‐of‐sight (LOS) and the non‐line‐of‐sight (NLOS) urban propagation conditions. A space‐time fading correlation model for the UCA, which depends on angular distribution of multipaths, array geometry, Doppler shift, and time offset, is also proposed. The results show that spatial correlations between any pair of antenna elements in the NLOS propagation are less than those in the LOS propagation, and temporal correlations are approximately the same for both propagation conditions. The NLOS propagation causes larger eigenspread for the space‐time correlation matrix, as compared to the NLOS propagation. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 61–65, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11285

Characterizing the statistical properties of mutual information in mimo channels

We consider Gaussian multiple-input multiple-output (MIMO) frequency-selective spatially correlated fading channels, assuming that the channel is unknown at the transmitter and perfectly known at the receiver. For Gaussian codebooks, using results from multivariate statistics, we derive an analytical expression for a tight lower bound on the ergodic capacity of such channels at any signal-to-noise ratio (SNR). We show that our bound is tighter than previously reported analytical lower bounds, and we proceed to analytically quantify the impact of spatial fading correlation on ergodic capacity. Based on a closed-form approximation of the variance of mutual information in correlated flat-fading MIMO channels, we provide insights into the multiplexing-diversity tradeoff for Gaussian code books. Furthermore, for a given total number of antennas, we consider the problem of finding the optimal (ergodic capacity maximizing) number of transmit and receive antennas, and we reveal the SNR-dependent nature of the maximization strategy. Finally, we present numerical results and comparisons between our capacity bounds and previously reported bounds.

Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole

The capacity of multiple-input multiple-output (MIMO) wireless channels is limited by both the spatial fading correlation and rank deficiency of the channel. While spatial fading correlation reduces the diversity gains, rank deficiency due to double scattering or keyhole effects decreases the spatial multiplexing gains of multiple-antenna channels. In this paper, taking into account realistic propagation environments in the presence of spatial fading correlation, double scattering, and keyhole effects, we analyze the ergodic (or mean) MIMO capacity for an arbitrary finite number of transmit and receive antennas. We assume that the channel is unknown at the transmitter and perfectly known at the receiver so that equal power is allocated to each of the transmit antennas. Using some statistical properties of complex random matrices such as Gaussian matrices, Wishart (1928) matrices, and quadratic forms in the Gaussian matrix, we present a closed-form expression for the ergodic capacity of independent Rayleigh-fading MIMO channels and a tight upper bound for spatially correlated/double scattering MIMO channels. We also derive a closed-form capacity formula for keyhole MIMO channels. This analytic formula explicitly shows that the use of multiple antennas in keyhole channels only offers the diversity advantage, but provides no spatial multiplexing gains. Numerical results demonstrate the accuracy of our analytical expressions and the tightness of upper bounds.

Acquisition for DS/CDMA systems with multiple antennas in frequency-selective fading channels

A generalized code acquisition scheme for direct-sequence code-division multiple-access systems with multiple antennas is proposed over frequency-selective fading channels. The proposed scheme is developed on the framework of a generalized configuration of multiple antennas and correlators. The nonconsecutive search method is generalized and extended to multiple antenna systems to exploit multipath signals in improving acquisition performance over frequency-selective fading channels. The proposed scheme also adopts a hybrid decision strategy to make effective decisions on acquisition. The mean acquisition time performance of the proposed acquisition scheme is analyzed and evaluated in frequency-selective Rayleigh-fading channels with general multipath delay profiles and spatial-fading correlations. The effects of nonconsecutive search on mean acquisition time are investigated for various channel environments, and the optimal choice of decision strategy is discussed. Furthermore, effects of various configurations of multiple antennas and correlators, decision thresholds, and correlation interval on the performance are also investigated.

Impact of the propagation environment on the performance of space-frequency coded MIMO-OFDM

Previous work on space-frequency coded multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) has been restricted to idealistic propagation conditions. In this paper, using a broadband MIMO channel model taking into account Ricean K-factor, transmit and receive angle spread, and antenna spacing, we study the impact of the propagation environment on the performance of space-frequency coded MIMO-OFDM. For a given space-frequency code, we quantify the achievable diversity order and coding gain as a function of the propagation parameters. We find that while the presence of spatial receive correlation affects all space-frequency codes equally, spatial fading correlation at the transmit array can result in widely varying performance losses. High-rate space-frequency codes such as spatial multiplexing are typically significantly more affected by transmit correlation than low-rate codes such as space-frequency block codes. We show that in the MIMO Ricean case the presence of frequency-selectivity typically results in improved performance compared to the frequency-flat case.

A three-dimensional spatial fading correlation model for uniform rectangular arrays

A closed-form expression for the spatial fading correlation function of a uniform rectangular array (URA) in a three-dimensional (3D) multipath channel is derived. The fading correlation function is expressed in terms of both the azimuth and elevation angle of arrival as well as the antenna spacing and geometry of the URA. Verification is achieved by means of computer simulation where the theoretical and simulation results are shown to be in good agreement. Our results demonstrate that azimuth spread (AS) is the primary determinant of the antenna correlation and the impact of the elevation spread is mainly noticeable at low AS values. The results obtained are vital for capacity analysis in multiple-input multiple-output systems, as well as for sensitivity analysis of the antenna array under study.

Outdoor MIMO wireless channels: models and performance prediction

We present a new model for multiple-input-multiple-output (MIMO) outdoor wireless fading channels and their capacity performance. The proposed model is more general and realistic than the usual independent and identically distributed (i.i.d.) model, and allows us to investigate the behavior of channel capacity as a function of the scattering radii at transmitter and receiver, distance between the transmit and receive arrays, and antenna beamwidths and spacing. We show how the MIMO capacity is governed by spatial fading correlation and the condition number of the channel matrix through specific sets of propagation parameters. The proposed model explains the existence of channels which exhibit low spatial fading correlation at both ends of the link but still have poor rank properties, and hence, low ergodic capacity. In fact, the model suggests the existence of a more general family of channels spanning continuously from full rank i.i.d. to low-rank pinhole cases. We suggest guidelines for predicting high rank (and hence, high ergodic capacity) in MIMO channels, and show that even at long ranges, high channel rank can easily be sustained under mild scattering conditions. Finally, we validate our results by simulations using ray tracing techniques. Connections with basic antenna theory are made.

Code acquisition schemes using antenna arrays for DS-SS systems and their performance in spatially correlated fading channels

We propose parallel and serial code-acquisition schemes using antenna arrays for initial acquisition of direct-sequence spread-spectrum signals, which can lower substantially the range of detectable signal-to-noise ratio (SNR) as compared to the corresponding conventional schemes with a single antenna. The proposed schemes use the sum of all the single-antenna decision samples from antenna arrays, corresponding to an identical subsequence of a given pseudonoise code as a decision variable in order to enhance SNR of the resulting signal. We analyze the mean acquisition time performance under an additive white Gaussian noise channel and spatially correlated time-varying flat Rayleigh fading channels by deriving the expressions for the probabilities of detection, missing, and false alarm. We consider two extreme cases of spatial fading correlation among antenna arrays, the case of uncorrelated diversity antennas and the case of perfectly correlated antennas. From numerical results, we see that the acquisition performance of the proposed schemes using antenna arrays becomes improved continually as the number of antennas increases and the performance improvement depends on the degree of spatial fading correlation.

Spatial fading correlation function of circular antenna arrays with Laplacian energy distribution

We derive an analytical formula for the fading correlation function of a uniform circular array (UCA) when the angular energy follows a Laplacian distribution. The fading correlation for a UCA is a function of antenna spacing, array geometry, as well as the distribution of the received energy in terms of the angle-of-arrival (AOA). Computer simulations are carried out to verify the analytical results.

Effect of spatial fading correlation on performance of space-time codes

The performance of space-time codes is investigated over Rayleigh fading channels with spatially correlated fading between transmit antennas. An exact pairwise error probability is derived based on which an analytical estimate for bit error probability is computed. The analytical results are verified through computer simulation.

On the performance of single frequency networks in correlated shadow fading

All transmitters in a single frequency network (SFN) simultaneously transmit the same information within the same frequency block. Simulcasting provides a diversity gain which has been shown to yield good coverage. In traditional analysis uncorrelated shadow fading is used. In some cases this assumption does not capture the behaviour of the shadow fading, e.g., when several transmitters are shadowed by a large obstacle. We investigate the changes in coverage due to correlation among the received signals field strength from different transmitters. A spatial shadow fading correlation model is proposed and validated using the Blomquist-Ladell (1974) prediction method on a digital terrain data base. Results for both wide area and local SFN show that the coverage properties depends on the correlation in the shadow fading. This will affect the planning process since strong correlation, due to the structure of the terrain, yields better coverage for high transmitter powers (interference limited systems) and worse coverage for low transmitter powers (noise limited systems).