Wireless Communications

Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communication-theoretic results accounting for the networks geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs -including point process theory, percolation theory, and probabilistic combinatorics-have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.

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Stochastic geometry and random graphs for the analysis and design of wireless networks

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well-known zero-forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite-rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signal-to-noise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to point-to-point multiple-input multiple-output (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR

MIMO Broadcast Channels With Finite-Rate Feedback

Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple-input multiple-output (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector; both are hard to realize. In this article, a quantized maximum signal-to-noise ratio (SNR) beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter. By using the distribution of the optimal beamforming vector in independent and identically distributed Rayleigh fading matrix channels, the codebook design problem is solved and related to the problem of Grassmannian line packing. The proposed design criterion is flexible enough to allow for side constraints on the codebook vectors. Bounds on the codebook size are derived to guarantee full diversity order. Results on the density of Grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or SNR loss. Monte Carlo simulations are presented that compare the probability of error for different quantization strategies.

Grassmannian beamforming for multiple-input multiple-output wireless systems

As of today, orthogonal frequency division multiplexing (OFDM) has been the dominant technology for broadband multicarrier communications. However, in certain applications such as cognitive radios and uplink of multiuser multicarrier systems, where a subset of subcarriers is allocated to each user, OFDM may be an undesirable solution. In this article, we address the shortcomings of OFDM in these and other applications and show that filter bank multicarrier (FBMC) could be a more effective solution. Although FBMC methods have been studied by a number of researchers, and some even before the invention of OFDM, only recently has FBMC been seriously considered by a few standard committees.

OFDM Versus Filter Bank Multicarrier

The focus of this paper is on the performance of orthogonal frequency division multiplexing (OFDM) signals in mobile radio applications, such as 802.11a and digital video broadcasting (DVB) systems, e.g., DVB-CS2. The paper considers the evaluation of the error probability of an OFDM system transmitting over channels characterized by frequency selectivity and Rayleigh fading. The time variations of the channel during one OFDM symbol interval destroy the orthogonality of the different subcarriers and generate power leakage among the subcarriers, known as inter-carrier interference (ICI). For conventional modulation methods such as phase-shift keying (PSK) and quadrature-amplitude modulation (QAM), the bivariate probability density function (pdf) of the ICI is shown to be a weighted Gaussian mixture. The large computational complexity involved in using the weighted Gaussian mixture pdf to evaluate the error probability serves as the motivation for developing a two-dimensional Gram-Charlier representation for the bivariate pdf of the ICI. It is demonstrated that its truncated version of order 4 or 6 provides a very good approximation in the evaluation of the error probability for PSK and QAM in the presence of ICI. Based on Jakes' model for the Doppler effects, and an exponential multipath intensity profile, numerical results for the error probability are illustrated for several mobile speeds

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Performance degradation of OFDM systems due to Doppler spreading

We exploit the one-to-one correspondences between the recursive least-squares (RLS) and Kalman variables to formulate extended forms of the RLS algorithm. Two particular forms of the extended RLS algorithm are considered: one pertaining to a system identification problem and the other pertaining to the tracking of a chirped sinusoid in additive noise. For both of these applications, experiments are presented that demonstrate the tracking superiority of the extended RLS algorithms compared with the standard RLS and least-mean-squares (LMS) algorithms.

Adaptive tracking of linear time-variant systems by extended RLS algorithms

This paper describes a transformation technique aimed at solving the peak-to-average power ratio (PAPR) problem associated with OFDM (orthogonal frequency-division multiplexing). Constant envelope OFDM (CE-OFDM) transforms the OFDM signal, by way of phase modulation, to a signal designed for efficient power amplification. At the receiver, the inverse transformation - phase demodulation - is applied prior to the conventional OFDM demodulator. The performance of CE-OFDM is analyzed in additive white Gaussian noise (AWGN) and fading channels. CE-OFDM is shown to achieve good performance in dense multipath with the use of cyclic prefix transmission in conjunction with a frequency- domain equalizer (FDE). By way of computer simulation and hardware realization, CE-OFDM is shown to compare favorably to conventional OFDM.

Constant Envelope OFDM

This work studies the performance of dimensional least mean square (TDLMS) adaptive filters as prewhitening filters for the detection of small objects in image data. The object of interest is assumed to have a very small spatial spread and is obscured by correlated clutter of much larger spatial extent. The correlated clutter is predicted and subtracted from the input signal, leaving components of the spatially small signal in the residual output. The receiver operating characteristics of a detection system augmented by a TDLMS prewhitening filter are plotted using Monte-Carlo techniques. It is shown that such a detector has better operating characteristics than a conventional matched filter in the presence of correlated clutter. For very low signal-to-background ratios, TDLMS-based detection systems show a considerable reduction in the number of false alarms. The output energy in both the residual and prediction channels of such filters is shown to be dependent on the correlation length of the various components in the input signal. False alarm reduction and detection gains obtained by using this detection scheme on thermal infrared sensor data with known object positions is presented. >

Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data

A class of constant envelope OFDM phase modulated (OFDM-PM) signals is studied. The motivation behind OFDM-PM is to alleviate the high peak-to-average power ratio of conventional OFDM systems. Power density spectrum plots and fractional out-of-band power curves are given. For small modulation indices, the OFDM-PM signals are shown to be more spectrally contained than conventional OFDM. The signal space is studied by considering the correlation properties of the OFDM-PM signals. A performance bound on the optimum OFDM-PM receiver is compared to simulation results. Also, a sub-optimum phase demodulator receiver is analyzed and an AWGN performance approximation is compared to simulation results. It is shown that for a small modulation index and high signal-to-noise ratio, the sub-optimum receiver performs close to the optimum receiver.

James R. Zeidler

Papers

Performance degradation of OFDM systems due to Doppler spreading

Adaptive tracking of linear time-variant systems by extended RLS algorithms

Constant Envelope OFDM

Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data

Constant envelope OFDM phase modulation: spectral containment, signal space properties and performance