Minimum-Energy Bandlimited Time-Variant Channel Prediction with Dynamic Subspace Selection

In current cellular communication systems the time-selective fading process is highly oversampled. We exploit this fact for time-variant flat-fading channel prediction by using dynamically selected predefined low dimensional subspaces spanned by discrete prolate spheroidal (DPS) sequences. The DPS sequences in each subspace exhibit a subspace-specific bandwidth matched to a certain Doppler frequency range. Additionally, DPS sequences are most energy concentrated in a time interval matched to the channel observation interval. Both properties enable the application of DPS sequences for minimum-energy (ME) bandlimited prediction. The dimensions of the predefined subspaces are in the range from one to five for practical communication systems. The subspace used for ME bandlimited prediction is selected based on a probabilistic bound on the reconstruction error. By contrast, time-variant channel prediction based on non-orthogonal complex exponential basis functions needs Doppler frequency estimates for each propagation path which requires high computational complexity. We compare the performance of this technique under the assumption of perfectly known complex exponentials with that of ME bandlimited prediction augmented with dynamic subspace selection. In particular we analyze the mean square prediction error of the two schemes versus the number of discrete propagation paths

Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

Cross-Layer Optimization of Network Performance over MIMO Wireless Mobile Channels

In the information theory, the channel capacity states the maximum amount of information which can be reliably transmitted over the communication channel. In the specific case of multiple-input multiple-output (MIMO) wireless systems, it is well recognized that the instantaneous capacity of MIMO systems is a random Gaussian process. Time variation of the capacity leads to the outages at instances when it falls below the transmission rate. The frequency of such events is known as outage probability. The cross-layer approach proposed in this work focuses on the effects of MIMO capacity outages on the network performance, providing a joint optimization of the MIMO communication system. For a constant rate transmission, the outage probability sensibly affects the amount of information correctly received at destination. Theoretically, the limit of the ergodic capacity in MIMO time-variant channels can be achieved by adapting the transmission rate to the capacity variation. With an accurate channel state information, the capacity evolution can be predicted by a suitable autoregressive model based on the capacity time correlation. Taking into consideration the joint effects of channel outage at the physical layer and buffer overflow at the medium access control (MAC) layer, the optimal transmission strategy is derived analytically through the Markov decision processes (MDP) theory. The adaptive policy obtained by MDP is optimal and maximizes the amount of information correctly received at the destination MAC layer (throughput of the system). Analytical results demonstrate the significant improvements of the optimal variable rate strategy compared to a constant transmission rate strategy, in terms of both system throughput and probability of data loss

Digital data transmission over an HF channel

The thesis is concerned with detection, estimation techniques and a method of the adaptive adjustment of the equaliser, for use in a 4800bit/sec synchronous digital transmission system operating over a voice-band time-varying HF channel. Two main impairments are additive Gaussian noise and inter-symbol interference (ISI), which can be very severe at times. All techniques considered here are algorithms or processes that operate on sequences of sample values. Modern digital modems normally operate in this way, and the techniques described are of direct application to practical systems, and could be implemented using the new technology of high speed real-time digital signal processing (DSP). The performance of the various systems that employ the above techniques are obtained using the computer simulated model of three types of HF channels. The ionospheric propagation medium, the characteristics of HF channel and the signal distortion introduced by the channel are first described. The thesis then presents a suitable base-band model of the HF channel for computer simulation of quadrature amplitude modulation systems. A suitable method for the adjustment of the receiver is described next. This method is suitable both for the adjustment of a conventional decision feedback equaliser (DFE), and also for the adjustment of a linear feedforward filter that is employed ahead of a near-maximum likelihood (NML) detector. This method uses a minimum phase (root-finding) algorithm (MPA) to convert the channel response from being non-minimum phase to at least approximately minimum phase. The results of computer simulation tests of this algorithm are then presented over different types of HF channel models. The results demonstrate the algorithm's capability to make the channel response minimum (or near-minimum) phase. Various NML detectors, derived from the Viterbi detector, are discussed. Each detector is here preceded by an adaptive linear filter that is adjusted adaptively using an MPA. The performance of these detectors is compared with the conventional DFE, whose tap-gains are adjusted adaptively using an MPA, and the detector which gives the best compromise between performance and complexity is selected for combined receivers. These results are obtained using perfect estimation of the channel response. The estimation techniques studied in this thesis include both new and conventional estiniators, which are based on the least- mean-square (LMS) algorithm or recursive least-square(RLS) algorithm. The estimator provides an estimate of the sampled impulse response (SIR) of the channel, necessary for the NML detector or MPA. The performances of these estimators are compared using computer simulation tests. The results also demonstrate that the simpler LMS algorithm with adaptive step size gives a comparable level of accuracy with the more complex RLS algorithm. Finally the most promising of the detectors and estimators are connected with an adaptive equaliser, using an MPA, to form a new combined receiver. The details of the combined system structure with its computational complexity are given. Extensive computer simulation tests have been carried out on the different arrangements of the combined system including DFE, when all the functions of detection, estimation and MPA are present, in order to find the most cost effective system in terms of performance and complexity. A considerable reduction in the equipment complexity can be achieved by allowing a long period between successive adjustment of the adaptive filter and estimator