Determining the period of a function is the main step in Shor’s factorization algorithm which is a cornerstone in the theory of quantum computing and a primary motivation for developing quantum computers. This paper investigates whether it is possible to have a universal Turing machine that is able to compute the minimum (or fundamental) period of a given periodic computable continuous function. It is shown that for every periodic computable continuous function, its fundamental period is always a computable number. Therefore, there always exists a specific Turing machine for computing the period of this function. Nevertheless, it is also shown that there exists no universal algorithm that is able to compute the period for all functions having periods that are known to be smaller than a given upper bound.

This paper studies the effective convergence of iterative methods for solving convex minimization problems using block Gauss–Seidel algorithms. It investigates whether it is always possible to algorithmically terminate the iteration in such a way that the outcome of the iterative algorithm satisfies any predefined error bound. It is shown that the answer is generally negative. Specifically, it is shown that even if a computable continuous function which is convex in each variable possesses computable minimizers, a block Gauss-Seidel iterative method might not be able to effectively compute any of these minimizers. This means that it is impossible to algorithmically terminate the iteration such that a given performance guarantee is satisfied. The paper discusses two reasons for this behavior and gives simple and concrete examples.

This paper investigates the complexity of computing the minimum mean square prediction error for wide-sense stationary stochastic processes. It is shown that if the spectral density of the stationary process is a strictly positive, computable continuous function then the minimum mean square error (MMSE) is always a computable number. Nevertheless, we also show that the computation of the MMSE is a$\# P_{1}$complete problem on the set of strictly positive, polynomial-time computable, continuous spectral densities. This means that if, as widely assumed,$FP_{1} \neq \# P_{1}$, then there exist strictly positive, polynomial-time computable continuous spectral densities for which the computation of the MMSE is not polynomial-time computable. These results show in particular that under the widely accepted assumptions of complexity theory, the computation of the MMSE is generally much harder than an$NP_{1}$complete problem.

It is known that there exist mathematical problems of practical relevance which cannot be computed on a Turing machine. An important example is the calculation of the first derivative of continuously differentiable functions. This paper precisely classifies the non-computability of the first derivative, and of the maximum-norm of the first derivative in the Zheng-Weihrauch hierarchy. Based on this classification, the paper investigates whether it is possible that a Turing machine detects this non-computability of the first derivative by observing the data of the problem, and whether it is possible to detect upper bounds for the peak value of the first derivative of continuously differentiable functions. So from a practical point of view, the question is whether it is possible to implement an exit-flag functionality for observing non-computability of the first derivative. This paper even studies two different types of exit-flag functionality. A strong one, where the Turing machine always has to stop, and a weak one, where the Turing machine stops if and only if the input lies within the corresponding set of interest. It will be shown that non-computability of the first derivative is not detectable by a Turing machine for two concrete examples, namely for the problem of computing the input–output behavior of simple analog circuits and for solutions of the three-dimensional wave equation. In addition, it is shown that it is even impossible to detect an upper bound for the maximum norm of the first derivative. In particular, it is shown that all three problems are not even semidecidable. Finally, we briefly discuss implications of these results for analog and quantum computing.

This paper presents a new method on transmitting data over linear time-variant (LTV) channels when no channel state estimation (CSI) is accessible. The considered receiver is equipped with multiple antennas and observes a superposition of delay-Doppler shifted versions of the transmitted signal. The messages are coded with known waveforms and are estimated by the receiver using a modified version of the multiple signal classification (MUSIC) algorithm. Although, the transmission scheme is designed for a multi-antenna receiver, the suggested method does not utilize the spatial signatures of multipath scatterers. Hence, the array response of the antenna setup is not required to be known in order to obtain a reliable estimate of the message. The effectiveness of the proposed transmission scheme is illustrated by numerical simulations.

A Turing machine is a model describing the fundamental limits of any realizable computer, digital signal processor (DSP), or field programmable gate array (FPGA). This paper shows that there exist very simple linear time-invariant (LTI) systems which can not be simulated on a Turing machine. In particular, this paper considers the linear system described by the voltage-current relation of an ideal capacitor. For this system, it is shown that there exist continuously differentiable and computable input signals such that the output signal is a continuous function which is not computable. Moreover, for this particular system, we present sharp results characterizing computable input signals which guarantee that the output signal is computable. Additionally, it is shown that the computability of the step response of an LTI system does not necessarily imply that the impulse response is computable.

Although the Hilbert transform and the spectral factorization are of central importance in signal processing, both operations can generally not be calculated in closed form. Therefore, algorithmic solutions are prevalent which provide an approximation of the true solution. Then it is important to effectively control the approximation error of these approximate solutions. This paper characterizes for both operations precisely those signal spaces of differentiable functions for which such an effective control of the approximation error is possible. In other words, the paper provides a precise characterization of signal spaces of smooth functions on which these two operations are computable on Turing machines.

It is common to model rapidly varying communication channels by time-varying linear systems. The output of a time-varying linear system can be described by a superposition of time-frequency (delay-Doppler) shifts of the input signal. This paper investigates a novel message transmission scheme over time-varying linear channels which are sufficiently sparse in the delay-Doppler domain. In order to deal with the time-varying nature of the channel the usual training stage for channel estimation is skipped. The channel state information and the transmitted message, both are estimated by the receiver simultaneously. The main contribution of this paper is that the suggested message transmission scheme over time-variant communication channels enables data transmission in scenarios where previously no communication was possible.

Spectral factorization is an operation which appears in many different engineering applications. This paper studies whether spectral factorization can be algorithmically computed on an abstract machine (a Turing machine). It is shown that there exist computable spectral densities with very good analytic properties (i.e. smooth with finite energy) such that the corresponding spectral factor cannot be determined on a Turing machine. Further, it will be proved that it is impossible to decide algorithmically whether or not a given computable density possesses a computable spectral factor. This negative result has consequences for applications of spectral factorization in computer-aided design, because there it is necessary that this problem be decidable. Conversely, this paper will show that if the logarithm of a computable spectral density belongs to certain Sobolev space of sufficiently smooth functions, then the spectral factor is always computable. As an application, the paper discusses the possibility of calculating the optimal causal Wiener filter on an abstract machine.

This paper considers the problem of approximating continuous functions of finite Dirichlet energy from samples of these functions. It will be shown that there exists no sampling-based method which is able to approximate every function in this space from its samples. Specifically, we are going to show that for any sampling based approximation method, the energy of the approximation tends to infinity as the number of samples is increased for almost every continuous function of finite energy. As an application, we study the problem of solving the Dirichlet problem on a bounded region. It will be shown that if only samples of the boundary function can be processed then the energy of the solution can not be controlled for any function from a non-meager dense set.

The spectral factorization is an important operation in many different applications. This paper studies whether the spectral factor of a given computable spectral density can always be computed on an abstract machine (a Turing machine). It is shown that there are computable spectral densities with very comfortable analytic properties (smoothness and finite energy) such that the corresponding spectral factor can not be determined on a Turing machine. As an application, the paper discusses the possibility of calculating the optimal Wiener filter from computable spectral densities.

In many different applications, it is important to determine the Hilbert transform of a given function. However, it is generally impossible to calculate it in closed form. Therefore Hilbert transform approximations are used. This paper studies the convergence and divergence behavior of general classes of such approximation methods. These classes are characterized by two very natural axioms and they include basically all known traditional numerical algorithms. The convergence of these methods is investigated on a family of signal spaces of continuous functions with finite energy. These spaces are parametrized by a number which measures the energy concentration in the low frequency components of the signal. It is shown that stable methods only exist on signal spaces with a sufficient energy concentration and this paper gives some explicit examples of convergent methods. On all other spaces in the family of signal spaces, every sampling-based Hilbert transform approximation shows a blowup behavior of its peak value, i.e., on these spaces, every sampling-based Hilbert transform approximation diverges.

Approximating the transfer function of stable causal linear systems by a basis expansion is a common task in signal- and system theory. This paper characterizes a scale of signal spaces, containing stable causal transfer functions, with a very simple basis (the Fourier basis) but which is not computable. Thus it is not possible to determine the coefficients of this basis expansion on any digital computer such that the approximation converges to the desired function. Since the Fourier basis is not computable, the second part of the paper investigates whether there exist better bases. To this end, the notion of a computational basis is introduced and it is shown that there exists no computational basis in these spaces. The paper characterizes also subspaces on which computational bases do exist.

This paper considers the problem of determining the sparse covariance matrix X of an unknown data vector x by observing the covariance matrix Y of a compressive measurement vector y = Ax. We construct deterministic sensing matrices A for which the recovery of a k-sparse covariance matrix X from m values of Y is guaranteed with high probability. In particular, we show that the number of measurements m scales linearly with the sparsity k.

We study support patterns for covariance matrices that appear in the problem of stochastic time-varying channel identification. The problem reduces to solving a linear system that is associated with a matrix in the form of a Kronecker product of a Gabor system matrix with itself, and therefore solvability of the linear system depends on the choice of generating window for the Gabor system and the support pattern of the object vector. In this paper, we investigate support patterns that allows the linear system to be solvable with some window. We present several classes of permissible patterns and also provide how the corresponding windows need to be chosen.

We investigate the impact of having additional information in a form of linear constraints in the channel identification problem. With those constraints taken into account, the problem turns into solving a linear system that is associated with a block matrix where each submatrix is either a Gabor system matrix or a matrix prescribed by the linear constraints. So, the identifiability hinges on whether one can find some generating windows of the Gabor systems for which the full linear system is solvable. We show that in single-input single-output (SISO) settings as well as in multiple-input multiple-output (MIMO) settings, linear constraints consisting of a single equation are beneficial for channel identification, as there always exist windows for which the corresponding full linear system is solvable. Concerning multiple linear constraints, however, there exists a set of linear constraints with two equations for which the full linear system is singular for all choices of windows. In the SISO case, we also provide some sufficient conditions on the linear side constraints under which the full linear system is solvable.

It was recently shown that on a large class of important Sobolev-like Banach spaces there exist no linear methods which are able to approximate the Hilbert transform from samples of the given function. This implies that there exists no linear algorithm for calculating the Hilbert transform which can be implemented on a digital computer and which converges for all functions from the corresponding Banach spaces. The present paper develops a much more general framework which includes also non-linear approximation methods. Algorithms within this framework have to satisfy only an axiom which guarantees the computability of the algorithm on a digital computer based on given samples of the function. Then the paper investigates whether there exists an algorithm within this general framework which converges to the Hilbert transform for all functions in the Sobolev-like Banach spaces. It is shown that non-linear methods give actually no improvement over linear methods.

The Hilbert transform plays an important role in many different applications. Especially in the area of detection and estimation it is closely related to the calculation of the spectral factorization. Generally, it is not possible to calculate the Hilbert transform in closed form. Therefore approximation methods are applied. This paper studies the stability of a general class of approximation algorithms for the Hilbert transform which contains all traditional numerical integration methods. To this end, the paper introduces a scale of signal spaces with finite energy in which a factor (log n)βmeasures the concentration of the signal energy in its Fourier coefficients cn. It will be shown that if the energy concentration is too weak, i.e. if 0 ≤ β ≤ 1, then every approximation method diverges. Conversely, if the energy concentration is sufficiently good, i.e. if β > 1, convergent approximation methods do exist and we give a natural characterization of all convergent methods.

Many important non-adaptive approximation methods are know to diverge for almost all functions from certain Banach space X. One can show that a corresponding adaptive method will improve this behavior in the sense that it converges to the desired result for almost all functions in X. However, even though an adaptive method tries to find an optimal approximation for any given function, the search horizon (i.e. the search set) has to be finite in practical applications. This paper shows that an adaptive method with finite search horizon either converges for all f ϵ X or it diverges for almost all f ϵ X. As an example, we show that there exists no realizable adaptive method which can calculate the Hilbert transform of a continuous function f based on samples of f.

This paper considers the problem of recovering a k-sparse, N-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very high probability whenever M ≳ 4k log2(N/k) random Fourier intensity measurements are available. The proposed algorithm is comprised of two stages: An algebraic phase retrieval stage and a compressive sensing step subsequent to it. Simulation results are provided to demonstrate the applicability of the algorithm for noiseless and noisy scenarios.

This paper considers the problem of signal recovery from magnitude measurements for signals in modulation invariant spaces. It proposes a measurement setup such that almost every signal in such a signal space can be reconstructed from its amplitude measurements up to a global constant phase and with a sampling rate of four times the rate of innovation of the signal space. The applicability of the proposed scheme under noise measurements is demonstrated by computer simulations.

This paper provides a quantitative notion of the sparsity for infinite dimensional atomic spaces, which play an important role in many signal processing applications. This notion of sparsity is defined as the ratio of the number of redundant samples (not necessary to recover any signal in the atomic space) to the number of all available samples of a particular canonical sampling system. It is shown that the so defined sparsity can be expressed in terms of the support of the spectral density of the sequence which generates the atomic space.

Given a U-invariant sampling scheme on an arbitrary Hilbert space ℋ. This paper characterizes atomic subspaces A of ℋ such that every signal x ∈ A can be reconstructed from its samples acquired with this sampling scheme. If signal recovery is possible a linear filter is derived which reconstructs the signal from the samples.

Causal processing of a signal's samples is crucial in on-line applications such as audio rate conversion, compression, tracking and more. This paper addresses the problem of causally reconstructing continuous-time signals from their samples. We treat a rich variety of sampling mechanisms encountered in practice, namely in which each sampling function is obtained by applying a unitary operator on its predecessor. Examples include pointwise sampling at the output of an anti-aliasing filter and magnetic resonance imaging, which correspond respectively to the translation and modulation operators. Such sequences of functions were studied extensively in the context of stationary random processes. We thus utilize powerful tools from this discipline, to derive a causal interpolation method that best approximates the commonly used non-causal reconstruction formula.

This paper studies conditions under which a signal can be reconstructed from partial frequency content. We focus on signals in shift-invariant spaces generated by multiple generators. For these signals, we derive a lower bound on the necessary signal bandwidth as well as sufficient conditions on the generators such that signal recovery is possible. When the available frequency content is not sufficient to recover the signal, we propose appropriate pre-processing that can improve the reconstruction ability.

This paper considers the problem of estimating a stationary sequenceyfrom the observation of a stationary correlated sequencexby means of a causal linear filter. Thereby, it is assumed that the spectral density Φxofxvanishes on a subset of the unit circle of positive Lebesgue measure such that the classical derivation of the estimation filter, based on the spectral factorization of Φx, can not be applied. The paper derives the transfer function of such an estimation filter, discusses its stability behavior, and applies the result to the causal reconstruction of deterministic signals from its samples.

Common methods for the calculation of the spectral factorization rely on an approximation of the given spectral density by a polynomial and a subsequent factorization of this polynomial. It is known that the regularity of the stochastic sequence determines the achievable approximation rate of its spectrum. However, since the approximative polynomial should be factorized, it has to be positive. It is shown that this restriction on the approximation polynomial implies a limitation on the approximation rate for linear methods whereas for nonlinear methods the optimal approximation rate can still be achieved. This has also consequences for the rate of convergence of the spectral factor, which is investigated in the second part. There, a lower and an upper bound for the error in the spectral factor is derived, which shows the dependency on the approximation degree and on the regularity of the stochastic sequence. Finally, if the spectral density is given only on a finite set of sampling points, no linear approximation method exists such that the error in the spectral factor can be controlled by the approximation degree.

This correspondence studies the calculation of the Hilbert transform of continuous functions f with continuous conjugate f from a finite set of sampling points. It shows that there exists no linear operator which approximates f arbitrary well in the uniform norm from a finite number of sampling points for all possible continuous function f with continuous conjugate f. However for smooth functions such linear approximation operators exist and sufficient conditions on the smoothness of the functions are presented. The correspondence also examines the robustness of the calculation of the Hilbert transform from interpolated data and it gives explicit error bounds. It is shown that for a large class of algorithms the error grows at least proportional to the logarithm of the number of sampling points.

This paper studies the approximation of continuous functions in subsets of all causal and stable transfer functions. Such approximations play a central roll in filter design, filter bank analysis, and in sampling, since any filtering can be considered as a kind of approximation in a space defined by the filters. The present paper studies in particular the consequences resulting from the causality and stability constrain imposed on the filter process. It is shown that there exists no linear approximation method which is also causal and stable. Only if either the causality or the stability constrain is left out, a linear approximation method may exist.

Common methods for the calculation of the spectral factorization rely on an approximation of the given spectral density by a trigonometric polynomial and a subsequent spectral factorization of this polynomial. Since the approximative polynomial should be factorized, the approximation method must be positive. The first part of this paper studies such approximation methods and deduces limitation on the approximation rate for linear methods which arise from the required positivity. The second part states a lower and an upper bound on the error in the spectral factor induced by the approximation of the spectral density. They show the dependency of the error on the regularity of the stochastic process and on the approximative degree.

This correspondence investigates the continuity behavior of the spectral factorization mapping for trigonometric polynomials. It is clear that this factorization mapping is continuous on the space of all trigonometric polynomials of a fixed degree N which means that a small perturbation in the given spectrum yields always a bounded error in the spectral factor. The correspondence derives a lower bound on the continuity constant of the spectral factorization mapping which shows that the error in the spectral factor grows at least proportional with the logarithm of the degree N of the given spectrum.

Spectral factorization, Wiener filtering, and many other important operations in information theory and signal processing can be lead back to a Hilbert transform and a Poisson integral. Whereas the Poisson integral causes generally no problems, the Hilbert transform has a much more complicated behavior. This paper investigates the possibility to calculate the Hilbert transformftilde of a given continuous function f based on a finite set of sampling points of f. It shows that even if ftilde is continuous, no linear approximation operator exists which approximates arbitrary well from a finite number of sampling points of f, in general. Moreover, the paper characterizes the set of all functions for which such linear approximation operators exist and discusses some consequences for practical applications

In the investigation of equalizers and precoders for multiple-input multiple-output systems with intersymbol interference, completely new phenomena appear if the causality of theses filters is required. To investigate these phenomena, the inner-outer factorization is an important tool, both for theoretical investigations as well as a practical algorithm to calculate such filters. This paper investigates the properties of the inner-outer factorization operator for matrix valued transfer functions. It derives sufficient conditions on the transfer functions such that the inner and outer factors have the same system theoretical properties as the given transfer function, and such that this factorization operator is bounded. Acomparison to the spectral factorization mapping is provided and possible consequences for numerical algorithms are discussed.

Any Wiener filter can be interpreted as a cascade of a whitening and estimation filter. The whitening filter is determined due to the spectral factorization of the spectral density of the input signal. For the calculation of the estimation filter the spectral factorization as well as the so called plus-operator is needed. This correspondence investigates in detail the behavior of these two operations and studies the corresponding properties of both filters. Then the practical consequences for the overall Wiener Filter are discussed. It is shown that if the given spectral densities are smooth (Houmllder continuous) functions, the resulting Wiener filter will always be stable and can be approximated arbitrarily well by a finite impulse response (FIR) filter. Moreover, the smoothness of the spectral densities characterizes how fast the FIR filter approximates the desired filter characteristic, and the correspondence gives a class of approximation polynomials which actually achieves the optimal approximation behavior. On the other hand, if the spectral densities are continuous, but not Houmllder continuous, the resulting Wiener filter may not be stable

A Wiener filter can be interpreted as a cascade of a whitening- and an estimation filter. This paper gives a detailed investigates of the properties of these two filters. Then the practical consequences for the overall Wiener filter are ascertained. It is shown that if the given spectral densities are smooth (Hoelder continuous) functions, the resulting Wiener filter would always be stable and can be approximated arbitrarily well by a finite impulse response (FIR) filter. Moreover, the smoothness of the spectral densities characterizes how fast the FIR filter approximates the desired filter characteristic. If on the other hand the spectral densities are continuous but not smooth enough, the resulting Wiener filter may not be stable

This paper, gives a general framework to investigate the existence and the general structure of causal inverse filters for multiple-input multiple-output (MIMO) systems with intersymbol interference (ISI). It gives necessary and sufficient conditions for the existence of causal and stable inverse filters allowing for further properties of the receive filters such as stability and smoothness of its transfer function. Furthermore, a parametrization and the general structure of all causal inverses is given.

In this paper, we investigate the optimal length of the training and data phase for continuously time-varying channels that maximize the achievable information rate. It is shown that both lengths depend not only on the Doppler spread of the channel but also on the noise power and the number of transmit antennas whereas the number of receive antennas and the channel condition have only a small influence. It turns out that the optimal coherence interval depends strongly on the SNR, whereas the optimal ratio between training and data phase is nearly independent on the SNR.

The rake receiver is investigated for spatial multiplexing (SM) in wide-band code-division multiple access systems. In general, the SM increases the data rate and the diversity order as well. The appropriate maximum likelihood detector is derived in this paper and it is shown that the diversity order is related to the product of the numbers of receive antennas and taps. With realistic numbers similar diversity orders may be achieved also with reduced complexity detection schemes. Finally, a standard-conformal scrambling technique is proposed to enhance the performance and to equalize it among the full set of orthogonal variable spreading factor (OVSF) sequences used in the third generation cellular system.

In this paper we develop a unique framework for evaluating the required repetition rate of channel estimation for multiple-input multiple-output (MIMO) systems in continuous fading radio channels. An analytical formula for the interference due to the temporal variation of the channel coefficients is given. This makes it possible to evaluate the time interval in which the channel has to be estimated again in order to keep the error probability below a desired threshold. This interval depends not only on the Doppler spread of the channel but also on the antenna configuration, detection algorithm and modulation scheme.

The irreducible error, introduced by the time dispersion of the radio channel for multiple-input multiple-output (MIMO) systems with flat fading detection algorithms are investigated analytically and by link level simulations. Using an adequate synchronisation method, the error floor is determined only by the intersymbol interference, for which a formula is derived. The maximal data rate is not only determined by the value of this interference, but also by the modulation scheme, antenna configuration and channel condition.

A high-speed wireless system (/spl ges/100 Mb/s) for indoor infrared (IR) communications via the line of sight is described and feasibility is shown in an experimental demonstrator. A diffuse link is used for connectivity, and tracked directed links are used for high-speed communications. The transmitter is made of a laser diode array in combination with multiple-beam forming optics. For the receiver (Rx), a wide-angle lens, and an avalanche photodiode array are used. For the diffuse link, the signals from all pixels in the array are combined. Pixels are selectively addressed to realize directed links. Fast electronic tracking of a directed link is possible by switching the signal path onto the right pixel in the array. Diffuse link, directed link, position detection, and tracking can be realized with one and the same transceiver hardware. A favorite system design is derived from constraints due to the IR channel, eye safety, lenses, photodetectors, and the overall system complexity. The experimental system shows some key features, namely 155-Mb/s wireless transmission over a distance of nearly 2 m with electronic tracking at an imaging IR Rx. Electronic tracking of IR links, thus, allows both high data rates and high capacity for wireless access in small office and home environments.

Equalization in the time domain is a well-known technique for combating intersymbol interference (ISI) in frequency selective channels. We derive the general structure of the linear zero forcing (ZF) equalizing filters for multiple input multiple output (MIMO) communication systems with more outputs than inputs. These filters are finite impulse response (FIR) filters in general and their structure is determined by the number of inputs and outputs. The relation between the spatial diversity of the system and the necessary filter length is worked out and it is shown, that an optimal time lag in the filter will improve the performance considerably.

The paper discusses channel inversion which is a spatial equalization technique when channel state information is available at the transmitter. Channel inversion is a straightforward concept without iterations and it might be useful when the data transmission is critical with time e.g. high data rate applications. We discuss performance degradation caused by channel estimation errors, clipping due to the limited range of the transmitted power and the effect of cochannel interference. These results give an insight into the technical constraints of this transmission technique and show how these critical issues can be limited or reduced.

In this work, we study a single-user MIMO transmission link in flat and frequency selective Rayleigh fading. The impact of the time dispersion in the channel on the performance of the signal separation algorithms is analyzed. We discuss the mismatch case in which the receiver assumes a flat-fading channel but is confronted actually with a frequency-selective MIMO channel. We give an analytical formula for the uncoded bit error rate in the mismatch case for zero-forcing detection. It is shown how to generalize the well known signal detection algorithms for flat-fading MIMO channels to the frequency-selective case. In particular, the performance and complexity of these algorithms is compared. A suboptimal algorithm with reduced complexity is proposed and compared to the optimal algorithms. All theoretical results are confirmed by numerical simulations.

We study the relation between antenna spacing and capacity of MIMO channels for indoor environments using a ray tracing program. It has been confirmed also by measurements that in rich scattering environments an antenna spacing below 0.5/spl lambda/ is sufficient to reach nearly the full capacity predicted for multiple-antenna arrays in ideal and uncorrelated Rayleigh fading channels.

A simple analytical model of the wireless infrared communication channel in indoor environments is presented. The infrared signal is modeled as the combination of a diffuse component and a line-of-sight (LOS) or direct component. For the diffuse component alone, the properties of the channel are found using Ulbricht's integrating sphere. When a LOS component is also present, the transfer function depends upon the Rician factor K given by the ratio of the electrical power in the LOS and diffuse signals after the detector. For small K, the transfer function shows notches down to low frequencies, but due to the nature of light never for zero frequency. We confirm that a K-factor /spl ges/13 dB is required also in infrared wireless links in order to support distortionless data transmission beyond 100 Mbit/s. Increasing the directivity at the receiver and/or at the transmitter improves the effective value of K. Here, we show that a moderate directivity will be sufficient for high-speed infrared communication in typical indoor scenarios.

A multiple-input multiple-output (MIMO) indoor radio system is studied to identify the origin of a typical performance degradation. When the data and overlay pilot-sequences for the channel estimation are transmitted at the same time, an error floor at high signal-to-noise ratio is normally observed. The floor is caused by channel estimation errors due to the interfering data signal. The crosstalk between the data paths can be calculated, approximately, and it is shown that the shape of the bit error curves can be steered both with the amplitude ratio /spl eta/ between pilot and data signals and with the length L of the sequences. Near-optimum performance can be reached in this way. With L = 16383, for instance, an amplitude ratio of /spl eta/ /spl ges/ 0.15 (0.3) is sufficient for BPSK (16-QAM) modulation in a MIMO system with 8 transmit and 12 receive antennas.

Multiple input multiple output (MIMO) systems, being under intensive research nowadays, are discussed under the aspect of bit error rates (BER) that can be achieved in indoor scenarios. This paper focuses on the influence of antenna diversity, a line of sight (LOS) signal and channel estimation errors onto the BER using BPSK and 16-QAM modulation. The developed simulation environment allows us to determine the necessary accuracy for channel estimation to achieve the desired BER performance in a MIMO channel under certain constraints like number of antennas, modulation scheme etc.

An simple analytic model for the light propagation in indoor environments is presented. Ray tracing simulations confirm that the model is applicable to the wireless infrared communication channel in rooms.