Gerald Matz

Survey of channel and radio propagation models for wireless MIMO systems

This paper provides an overview of the state-of-the-art radio propagation and channel models for wireless multiple-input multiple-output (MIMO) systems. We distinguish between physical models and analytical models and discuss popular examples from both model types. Physical models focus on the double-directional propagation mechanisms between the location of transmitter and receiver without taking the antenna configuration into account. Analytical models capture physical wave propagation and antenna configuration simultaneously by describing the impulse response (equivalently, the transfer function) between the antenna arrays at both link ends. We also review some MIMO models that are included in current standardization activities for the purpose of reproducible and comparable MIMO system evaluations. Finally, we describe a couple of key features of channels and radio propagation which are not sufficiently included in current MIMO models.

MMSE and adaptive prediction of time-varying channels for OFDM systems

We propose decision-directed channel predictors for orthogonal frequency-division multiplexing (OFDM) communications over time-varying channels. Channel prediction is capable of yielding up-to-date channel state information even without regular transmission of pilot symbols. It is thus potentially useful for delay-free equalization, antenna combining, space-time decoding, adaptive modulation, adaptive power control, and adaptive transmit antenna diversity. We derive a minimum mean-square error channel predictor and its efficient discrete Fourier transform implementation. Furthermore, we develop adaptive predictors that do not require any statistical prior knowledge and are able to track nonstationary channel and noise statistics. Simulation results involving an OFDM receiver in which channel prediction is used for delay-free equalization demonstrate the excellent performance of the proposed techniques even for fast time-varying channels.

On non-WSSUS wireless fading channels

We propose a novel framework for the statistical characterization of fading dispersive channels that do not satisfy the assumption of wide-sense stationary uncorrelated scattering (WSSUS). The local scattering function (LSF) and the channel correlation function (CCF) are introduced and shown to characterize, respectively, the mean power and the correlation of non-WSSUS scatterers. Furthermore, the practically important class of doubly underspread (DU) channels is introduced, and it is shown that for DU channels, the LSF has numerous useful properties. The practical relevance of our approach is illustrated via application examples and numerical experiments.

Worst- and average-case complexity of LLL lattice reduction in MIMO wireless systems

Lattice reduction by means of the LLL algorithm has been previously suggested as a powerful preprocessing tool that allows to improve the performance of suboptimal detectors and to reduce the complexity of optimal MIMO detectors. The complexity of the LLL algorithm is often cited as polynomial in the dimension of the lattice. In this paper we argue that this statement is not correct when made in the MIMO context. Specifically, we demonstrate that in typical communication scenarios the worst-case complexity of the LLL algorithm is not even finite. For i.i.d. Rayleigh fading channels, we further prove that the average LLL complexity is polynomial and that the probability for an atypically large number of LLL iterations decays exponentially.

Pulse-shaping OFDM/BFDM systems for time-varying channels: ISI/ICI analysis, optimal pulse design, and efficient implementation

This paper considers practically relevant aspects and advantages of pulse-shaping orthogonal/biorthogonal frequency division multiplexing (OFDM/BFDM) systems. We analyze the intersymbol/intercarrier interference (ISI/ICI) in such systems when they operate over time-varying channels. Two methods for an ISI/ICI-minimizing pulse design are proposed, and efficient FFT-based modulator and demodulator implementations are presented. Simulations show that for fast time-varying channels, optimized BFDM systems can outperform conventional OFDM systems with respect to ISI/ICI.

Non-WSSUS vehicular channel characterization in highway and urban scenarios at 5.2GHz using the local scattering function

The fading process in high speed vehicular traffic telematic applications at 5 GHz is expected to fulfill the wide-sense stationarity uncorrelated scattering (WSSUS) assumption for very short time-intervals only. In order to test this assumption we apply the concept of a local time- and frequency-variant scattering function, which we estimate from measurements of vehicle-to-vehicle wave propagation channels by means of a multi-window spectrogram. The obtained temporal sequence of local scattering functions (LSF) is used to calculate a collinearity measure. We define the stationarity time as the support of the region where the collinearity exceeds a certain threshold. The stationarity time is the maximum time duration over which the WSSUS assumption is valid. Measurements from an highway with vehicles driving in opposite directions show stationarity times as small as 23 ms whereas vehicles driving in the same direction show stationarity times of 1479 ms.

Analysis, Optimization, and Implementation of Low-Interference Wireless Multicarrier Systems

This paper considers pulse-shaping multicarrier (MC) systems that transmit over doubly dispersive fading channels. We provide exact and approximate expressions for the intersymbol and intercarrier interference occurring, in such systems. This analysis reveals that the time and frequency concentration of the transmit and receive pulses is of paramount importance for low interference. We prove the (nonobvious) existence of such jointly concentrated pulse pairs by adapting recent mathematical results on Weyl-Heisenberg frames to the MC context. Furthermore, pulse optimization procedures are proposed that aim at low interference and capitalize on the design freedom existing for redundant MC systems. Finally, we present efficient FFT-based modulator and demodulator implementations. Our numerical results demonstrate that for realistic system and channel parameters, optimized pulse-shaping MC systems can outperform conventional cyclic-prefix OFDM systems

Time-frequency formulation, design, and implementation of time-varying optimal filters for signal estimation

This paper presents a time-frequency framework for optimal linear filters (signal estimators) in nonstationary environments. We develop time-frequency formulations for the optimal linear filter (time-varying Wiener filter) and the optimal linear time-varying filter under a projection side constraint. These time-frequency formulations extend the simple and intuitive spectral representations that are valid in the stationary case to the practically important case of underspread nonstationary processes. Furthermore, we propose an approximate time-frequency design of both optimal filters, and we present bounds that show that for underspread processes, the time-frequency designed filters are nearly optimal. We also introduce extended filter design schemes using a weighted error criterion, and we discuss an efficient time-frequency implementation of optimal filters using multiwindow short-time Fourier transforms. Our theoretical results are illustrated by numerical simulations.

An efficient MMSE-based demodulator for MIMO bit-interleaved coded modulation

In bit-interleaved coded modulation (BICM) systems employing maximum-likelihood decoding, a demodulator (demapper) calculates a log-likelihood ratio (LLR) for each coded bit, which is then used as a bit metric for Viterbi decoding. In the MIMO case, the computational complexity of LLR calculation tends to be excessively high, even if the log-sum approximation is used. Thus, there is a strong demand for efficient suboptimum MIMO-BICM demodulation algorithms with near-optimum performance. We propose an efficient MIMO-BICM demodulator that is derived by means of a Gaussian approximation for the post-detection interference. Our derivation results in an MMSE equalizer followed by per-layer LLR calculation (i.e., LLRs are calculated separately for each layer). The novel demodulator can be interpreted as an MMSE analogue of a recently proposed ZF-equalization based demodulator, as well as an extension of ZF-equalization based demodulation to correlated post-detection interference. Because it performs per-layer LLR calculation, it has the same (low) computational complexity as the ZF-equalization based demodulator. Simulation results demonstrate that the performance of our demodulator is close to that of LLR calculation using all layers jointly, and significantly better than that of the ZF-equalization based demodulator.

Dispersion encoded full range frequency domain optical coherence tomography

We propose an iterative algorithm that exploits the dispersion mismatch between reference and sample arm in frequency-domain optical coherence tomography (FD-OCT) to effectively cancel complex conjugate mirror terms in individual A-scans and thereby generate full range tomograms. The resulting scheme, termed dispersion encoded full range (DEFR) OCT, allows distinguishing real structures from complex conjugate mirror artifacts. Even though DEFR-OCT has higher post-processing complexity than conventional FD-OCT, acquisition speed is not compromised since no additional A-scans need to be measured, thereby rendering this technique robust against phase fluctuations. The algorithm uses numerical dispersion compensation and exhibits similar resolution as standard processing. The residual leakage of mirror terms is further reduced by incorporating additional knowledge such as the power spectrum of the light source. The suppression ratio of mirror signals is more than 50 dB and thus comparable to complex FD-OCT techniques which use multiple A-scans.