Wireless Communication over Wideband Channels

Authors

Ulrich G. Schuster

Reference

Series in Communication Theory, ISSN 1865-6765, Hartung-Gorre Verlag Konstanz, ISBN-13 978-3-86628-245-2, pp. 386, 2009.

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Abstract

The amount of data that can be reliably transmitted per second over a given channel, called the channel capacity, depends on the received power and on the number of degrees of freedom (DOF) per second that the combination of transmitter, channel, and receiver allows for. An increase in either power or DOFs increases channel capacity, everything else being equal. Bandwidth and time are the main sources of DOFs in wireline as well as wireless communication systems; directional transmission and reception, i.e., the use of space, can offer additional DOFs in wireless systems. While the radiated power is strictly regulated for most applications of wireless communications, DOFs abound in so-called ultrawideband (UWB) channels of several gigahertz bandwidth, the license-free use of which has been permitted recently in the United States of America. Similar regulations for the use of UWB communications are expected for many other countries in the near future. Therefore, the focus of this thesis is on wireless channels with many DOFs and the performance of communication systems that operate over such channels. Wireless channels change over time, space, and frequency in a seemingly random manner; therefore, each DOF in a wireless channel is commonly described by random coefficient. To communicate reliably, the receiver not only needs to resolve the uncertainty caused by the noise of all electronic components but also the uncertainty introduced by the random channel. We quantify the latter uncertainty through the number of degrees of uncertainty (DOUs) - effectively the number of DOFs with uncorrelated coefficients. Resolution of channel uncertainty requires DOFs and power, which are then no longer available for communication. For example, we can send known pilot symbols over some DOFs to estimate the channel. It is not guaranteed that channel uncertainty can always be resolved. If the number of DOUs increases at the same rate as we add DOFs, e.g., by enlarging the bandwidth, adding more bandwidth might actually be detrimental after some point. While the capacity under channel uncertainty is an information-theoretic problem, the relation between the number of DOFs and DOUs depends on the physical channel and its mathematical model. In the first part of this thesis, we review standard channel models and their physical foundation, all with special emphasis on channels of wide bandwidth. Of particular importance for information-theoretic analysis is a suitable stochastic channel model, i.e., a joint distribution for the time-variant channel impulse response that is accurate yet mathematically tractable. As common modeling assumptions for channels of small bandwidth might no longer hold for UWB channels, we complement the theoretical modeling considerations with statistical analysis of measured wideband channels. We describe two channel measurement campaigns in the band from 2 GHz to 5 GHz conducted in a public space; in the first campaign we moved the transmit antenna on a regular grid and kept the environment static, and in the second campaign we fixed the antennas while people were moving about the environment. On the basis of the measured channel impulse responses, we select marginal amplitude distributions from the Rayleigh, Rice, Nakagami, lognormal, and Weibull families by means of information criteria and use tools from multivariate statistical analysis to obtain a stochastic channel description of second order. While the channel with moving terminals can be sensibly modeled as zero-mean jointly proper Gaussian (JPG) distributed, measurement data for the channel with static terminals does not seem to contain sufficient evidence to unequivocally select a single stochastic channel model. But physical considerations, like a strong mean component in every channel tap, and the need for a parsimonious mathematical model prompt us to advocate the JPG distribution with nonzero mean to describe the latter type of channel. An analysis of channel correlation matrices for the second measurement campaign shows that their number of significant eigenvalues scales linearly with increasing bandwidth. We interpret this scaling behavior as an indication that the number of DOUs increases linearly with the number of DOFs over the measured frequency band. These modeling considerations indicate that a JPG linear time-variant description might be adequate for channels with several gigahertz bandwidth. Hence, we use a discretized version of the standard proper Gaussian wide-sense-stationary uncorrelated-scattering (WSSUS) channel model for the information-theoretic analysis. We extend said model to the spatially correlated multiantenna setting and use it to derive bounds on channel capacity under a constraint on the transmit signal's peak power and under the assumption that neither the transmitter nor the receiver know the instantaneous channel realization but both know the channel law. The bounds are useful for a large range of bandwidth and allow to coarsely identify the capacity-optimal combination of bandwidth and number of transmit antennas. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of large bandwidth. From this expression, we conclude that in the wideband regime: (i) it is optimal to use only one transmit antenna when the channel is spatially white; (ii) one should transmit along the strongest channel eigenmode if the channel is spatially correlated; (iii) spatial correlation is beneficial.

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