Ulrich Schuster

Ultrawideband Channel Modeling on the Basis of Information-Theoretic Criteria

We present results of two ultra-wideband (UWB) channel measurement campaigns in the 2-5 GHz frequency band, and use Akaikes Information Criterion (AIC) to determine suitable distributions for the channel impulse response taps. Despite the large bandwidth, AIC supports the complex Gaussian tap distribution, with mean depending on the measurement setting. We estimate the empirical covariance matrix of the channel impulse response, and demonstrate that the number of corresponding significant eigenvalues scales approximately linearly with bandwidth, albeit we find that channel taps are correlated

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 channels delay spread and Doppler spread is small. The underspread assumption is satisfied by virtually all wireless communication channels. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channels 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 channels scattering function. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the infinite-bandwidth limit, 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. Our lower bound is closely related to a result by Viterbi (1967). We find cases where the bounds coincide and, hence, the infinite-bandwidth capacity is characterized exactly. The analysis in this paper is based on a discrete-time discrete-frequency approximation of WSSUS time- and frequency-selective channels. This discretization takes the underspread property of the channel explicitly into account.

Ultra-wideband channel modeling on the basis of information-theoretic criteria

We present results of two indoor ultrawideband channel measurement campaigns in the 2-5 GHz frequency band. In measurement campaign I (MC I), the channel is static and we sample it spatially, while in MCII the transmitting and receiving antennas are fixed and channel variation is induced by people moving in the environment. Transmitter and receiver are separated by up to 27 m in MC I and up to 20 m in MC II. To determine suitable small-scale fading distributions for the tap amplitudes of the discrete-time baseband-equivalent channel impulse response, we use Akaikes information criterion (AIC). Despite the large bandwidth, AIC supports the Rayleigh (MCI) or the Rice distribution (MC II). For data from MC II, we estimate the covariance matrix of the random channel impulse response and demonstrate that the number of corresponding significant eigenvalues, and hence the diversity order of the channel, scales approximately linearly with bandwidth. Contrary to the uncorrected scattering assumption, we find that the channel taps are weakly correlated. The ergodic capacity predicted by the Ricean channel model with parameters estimated from MC II shows good agreement with the ergodic capacity obtained by direct evaluation of the measurement results, while the corresponding outage capacities show a worse fit for low outage probabilities because of shadowing.

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.

Semicoherent PPM for wideband communications

We quantify the impact of coherence on pulse position modulation (PPM) over wideband fading channels by computing achievable rates and an upper bound on uncoded symbol error probability. We study the influence of channel estimation accuracy on the optimum diversity order and furthermore find that a near-optimum receiver typically needs to estimate a few channel taps only

Capacity bounds for peak-constrained multiantenna wideband channels

Bounds are derived on the noncoherent capacity of a very general class of multiple-input multiple-output fading channels that are selective in time and frequency as well as correlated in space. The bounds apply to peak-constrained inputs; they are explicit in the channels scattering function, are useful for a large range of bandwidth, and allow one to coarsely identify the capacity-optimal combination of bandwidth and number of transmit antennas. Furthermore, a closed-form expression is obtained for the first-order Taylor series expansion of capacity in the limit of infinite bandwidth. From this expression, it is concluded that in the wideband regime: (i) it is optimal to use only one transmit antenna when the channel is spatially uncorrelated; (ii) rank-one statistical beamforming is optimal if the channel is spatially correlated; and (iii) spatial correlation, be it at the transmitter, the receiver, or both, is beneficial.