On Discrete-Time Modeling of Time-Varying WSSUS Fading Channels

In this paper, we consider the serial concatenation of linear time-varying (LTV) systems and its impact on the discrete-time modeling of wide-sense stationary uncorrelated scattering (WSSUS) fading channels. By deriving an expression for the composite impulse response of the overall concatenated system, we find that unlike the time-invariant case, the concatenation of LTV systems is not commutative, i. e., the order of arrangement affects the overall impulse response. This has significant impact when a digital transmission over a time-varying fading channel, which is an LTV channel, is represented by an equivalent discrete-time model that incorporates both transmitter and receiver filters. We further show that if the maximum Doppler frequency is much smaller than the system bandwidth, the concatenation of LTV systems is approximately commutative, then a convenient and efficient representation in the discrete-time domain for WSSUS fading channels is obtainable

Noncoherent Capacity of Underspread Fading Channels

We derive bounds on the noncoherent capacity of wide-sense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel's delay spread and Doppler spread is small. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channel's scattering function, are accurate for a large range of bandwidth and allow to coarsely identify the capacity-optimal bandwidth as a function of the peak power and the channel's scattering function. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of large bandwidth, and show that our bounds are tight in the wideband regime. For input signals that are peak constrained in time only (and, hence, allowed to be peaky in frequency), we provide upper and lower bounds on the infinite-bandwidth capacity and find cases when the bounds coincide and the infinite-bandwidth capacity is characterized exactly. Our lower bound is closely related to a result by Viterbi (1967). The analysis in this paper is based on a discrete-time discrete-frequency approximation of WSSUS time- and frequency-selective channels. This discretization explicitly takes into account the underspread property, which is satisfied by virtually all wireless communication channels.Comment: Submitted to the IEEE Transactions on Information Theor

Stationarity analysis of V2I radio channel in a suburban environment

Due to rapid changes in the environment, vehicular communication channels no longer satisfy the assumption of wide-sense stationary uncorrelated scattering. The non-stationary fading process can be characterized by assuming local stationarity regionswith finite extent in time and frequency. The local scattering function (LSF) and channel correlation function (CCF) provide a framework to characterize the mean power and correlation of the non-stationary channel scatterers, respectively. In this paper, we estimate the LSF and CCF from measurements collected in a vehicle-to-infrastructure radio channel sounding campaign in a suburban environment in Lille, France. Based on the CCF, the stationarity region is evaluated in time as 567 ms and used to capture the non-stationary fading parameters. We obtain the time-varying delay and Doppler power profiles fromthe LSF, and we analyze the corresponding root-mean-square delay and Doppler spreads. We show that the distribution of these parameters follows a lognormal model. Finally, application relevance in terms of channel capacity and diversity techniques is discussed. Results show that the assumption of ergodic capacity and the performance of various diversity techniques depend on the stationarity and coherence parameters of the channel. The evaluation and statistical modeling of such parameters can provide away of tracking channel variation, hence, increasing the performance of adaptive schemes

Karhunen-Loève expansion of the WSSUS channel output and its application to efficient simulation

This paper derives a Karhunen-Loève (K-L) expansion of the time-varying output of a multipath Rayleigh fading wide-sense-stationary uncorrelated-scattering (WSSUS) channel. It is shown that under the same mean-squared error condition, the number of terms required by the truncated K-L expansion is less than that of the series expansion obtained by using the discrete-path approximation of the channel so that simulation using the K-L expansion is more efficient This computational advantage becomes more significant as higher simulation accuracy is required. The derived K-L expansion is applied to develop an efficient simulation technique for digital transmission over a multipath Rayleigh fading WSSUS channel using an optimum receiver. We show that the proposed technique requires shorter computation time than two other known simulation techniques.published_or_final_versio

Analysis of the Local Quasi-Stationarity of Measured Dual-Polarized MIMO Channels

It is common practice in wireless communications to assume strict or wide-sense stationarity of the wireless channel in time and frequency. While this approximation has some physical justification, it is only valid inside certain time-frequency regions. This paper presents an elaborate characterization of the non-stationarity of wireless dual-polarized channels in time. The evaluation is based on urban macrocell measurements performed at 2.53 GHz. In order to define local quasi-stationarity (LQS) regions, i.e., regions in which the change of certain channel statistics is deemed insignificant, we resort to the performance degradation of selected algorithms specific to channel estimation and beamforming. Additionally, we compare our results to commonly used measures in the literature. We find that the polarization, the antenna spacing, and the opening angle of the antennas into the propagation channel can strongly influence the non-stationarity of the observed channel. The obtained LQS regions can be of significant size, i.e., several meters, and thus the reuse of channel statistics over large distances is meaningful (in an average sense) for certain algorithms. Furthermore, we conclude that, from a system perspective, a proper non-stationarity analysis should be based on the considered algorithm

Efficient Channel Modeling Methods for Mobile Communication Systems

Siirretty Doriast

Information Theory of underspread WSSUS channels

The chapter focuses on the ultimate limit on the rate of reliable communication through Rayleigh-fading channels that satisfy the wide-sense stationary (WSS) and uncorrelated scattering (US) assumptions and are underspread. Therefore, the natural setting is an information-theoretic one, and the performance metric is channel capacity. The family of Rayleigh-fading underspread WSSUS channels constitutes a good model for real-world wireless channels: their stochastic properties, like amplitude and phase distributions match channel measurement results. The Rayleigh-fading and the WSSUS assumptions imply that the stochastic properties of the channel are fully described by a two-dimensional power spectral density (PSD) function, often referred to as scattering function. The underspread assumption implies that the scattering function is highly concentrated in the delay-Doppler plane. Two important aspects need to be accounted for by a model that aims at being realistic: neither the transmitter nor the receiver knows the realization of the channel; and the peak power of the transmit signal is limited. Based on these two aspects the chapter provides an information-theoretic analysis of Rayleigh-fading underspread WSSUS channels in the noncoherent setting, under the additional assumption that the transmit signal is peak-constrained

Time- and Frequency-Varying KK-Factor of Non-Stationary Vehicular Channels for Safety Relevant Scenarios

Vehicular communication channels are characterized by a non-stationary time- and frequency-selective fading process due to fast changes in the environment. We characterize the distribution of the envelope of the first delay bin in vehicle-to-vehicle channels by means of its Rician $K$-factor. We analyze the time-frequency variability of this channel parameter using vehicular channel measurements at 5.6 GHz with a bandwidth of 240 MHz for safety-relevant scenarios in intelligent transportation systems (ITS). This data enables a frequency-variability analysis from an IEEE 802.11p system point of view, which uses 10 MHz channels. We show that the small-scale fading of the envelope of the first delay bin is Ricean distributed with a varying $K$-factor. The later delay bins are Rayleigh distributed. We demonstrate that the $K$-factor cannot be assumed to be constant in time and frequency. The causes of these variations are the frequency-varying antenna radiation patterns as well as the time-varying number of active scatterers, and the effects of vegetation. We also present a simple but accurate bi-modal Gaussian mixture model, that allows to capture the $K$-factor variability in time for safety-relevant ITS scenarios.Comment: 26 pages, 12 figures, submitted to IEEE Transactions on Intelligent Transportation Systems for possible publicatio

A geometry-based stochastic MIMO model for vehicle-to-vehicle communications

Vehicle-to-vehicle (VTV) wireless communications have many envisioned applications in traffic safety and congestion avoidance, but the development of suitable communications systems and standards requires accurate models for the VTV propagation channel. In this paper, we present a new wideband multiple-input-multiple-output (MIMO) model for VTV channels based on extensive MIMO channel measurements performed at 5.2 GHz in highway and rural environments in Lund, Sweden. The measured channel characteristics, in particular the non-stationarity of the channel statistics, motivate the use of a geometry-based stochastic channel model (GSCM) instead of the classical tapped-delay line model. We introduce generalizations of the generic GSCM approach and techniques for parameterizing it from measurements and find it suitable to distinguish between diffuse and discrete scattering contributions. The time-variant contribution from discrete scatterers is tracked over time and delay using a high resolution algorithm, and our observations motivate their power being modeled as a combination of a (deterministic) distance decay and a slowly varying stochastic process. The paper gives a full parameterization of the channel model and supplies an implementation recipe for simulations. The model is verified by comparison of MIMO antenna correlations derived from the channel model to those obtained directly from the measurements