Introduction to VIDI
Reliable Wireless Communications over Rapidly Time-Varying Channels

 

Research Topic

Aim and Objectives

Wireless communications are strongly present in nowadays society, and are receiving an ever growing attention. Billions of people own a mobile cell phone to communicate with anyone, at any time, anywhere in the world. Wireless local area networks (WLANs) are being considered to provide broadband access in an office or a classroom, without having to pull wires everywhere. Wireless ad hoc networks are envisioned to connect a multitude of terminals, sensors, and actuators, e.g., for conferencing, home networking, emergency services, personal area networks, and embedded computing applications. Most of these systems have been designed assuming that the wireless channel can be regarded as constant over a block of data. This has a number of important implications:

• Mobility: Mobility introduces Doppler shifts and makes the channel time-varying. Consequently, the assumption that the channel is constant over some period only holds approximately, and will affect wireless systems that are designed based on this assumption:
  • Many wireless applications, such as the third generation system UMTS, can adapt their data rate to the link quality. Because the system design is based on the time-invariance assumption, mobility will reduce the link quality and hence the data rate will drop.
  • For some systems, the violation of the time-invariance assumption can even have disastrous consequences. This is for instance true for digital video broadcasting (DVB-T) systems, which were originally developed for fixed receivers. Currently, they are also envisioned for mobile use, but due to the highly time-varying nature of the propagation environment, they basically break down at high speeds, e.g., in a car or a high-speed train.
• Carrier frequency offsets: Current wireless systems are very sensitive to carrier frequency offsets, and require expensive oscillators and/or complex carrier frequency offset cancellation algorithms to combat this effect. Especially so-called orthogonal frequency division multiplexing (OFDM) systems, which modulate data on different parallel subcarriers, suffer from this problem. Some wireless systems that rely on OFDM are DVB-T and the wireless local area network (WLAN) standards IEEE 802.11 and HIPERLAN/2.

Reducing the block size over which the channel is assumed constant is often not an appropriate solution to these problems, because the absolute amount of redundancy per block (e.g., for synchronization, channel estimation, inter block interference removal, ...) is usually fixed, and as a result, the spectral efficiency will drop considerably if we reduce the block size. On the other hand, a judicious and innovative wireless system design that takes the time-varying nature of the channel (due to mobility or carrier frequency offsets) into account is the key to solve the above problems. This is one of the objectives of this project. The trend toward higher carrier frequencies increases the Doppler shifts due to mobility and carrier frequency offsets, and therefore considerably increases the time-variation of the channel. Consequently, in future wireless systems, the time-varying nature of the channels will become more and more important. That is why this project also aims at providing guidelines for future wireless system design that may even exploit the time-varying behavior of the environment to improve the performance.

Scientific Background

Past and current research in wireless communications mainly studies transmissions over time-invariant channels, only considering the frequency-selectivity of the channel, which arises at high data rates and causes subsequently transmitted data symbols to interfere with each other. This project aims at extending and unifying these concepts to time-varying frequency-selective channels, which will allow us to improve current wireless systems, as well as to provide guidelines for future designs employing high carrier frequencies. In the following, we will provide some scientific background on how channel time-variations due to mobility or carrier frequency offsets will affect communication aspects such as channel modeling, channel estimation, channel equalization, multiple-access, and multiple-input multiple-output (MIMO) communications, and we will indicate possible directions on how to handle, or even exploit these time-varying effects.

Channel modeling: Time-invariant frequency-selective channels are usually modeled as a finite impulse response (FIR) filter with time-invariant taps. We can simply extend this model to time-varying channels by considering an FIR filter with time-varying taps. Assuming no correlation among the tap values at different time instances, we would obtain a huge amount of unknown channel parameters, which would be impossible to estimate in practice. Fortunately, physical motivations indicate that the tap values are highly correlated in time, which allows us to reduce the number of unknowns. More specifically, the time-evolution of each tap can be expressed as a weighted superposition of complex exponentials with frequencies corresponding to the different Doppler shifts. In case of mobility, the number of different Doppler shifts can be very large (each group of scatterers generally corresponds to a different Doppler shift), again leading to a difficult if not impossible identification problem. It is therefore very crucial to develop simplified, yet accurate channel models to mimic the time-variation of a channel tap.

The so-called basis expansion model (BEM) is such a simplified time-varying channel model. In the BEM, the time-variation of each tap is expressed as a superposition of a few fixed basis functions. Some examples are the complex exponential BEM (CE-BEM) and the complex polynomial BEM (CP-BEM), where the basis functions consist of fixed complex exponentials and fixed complex polynomials, respectively. Another interesting channel model is the Gauss-Markov model (GMM), which models the time-variation of each tap by a Gauss-Markov process (usually only a first-order process is considered). Only few results exist on the accuracy of these simplified channel models. It is further not clear which model is the best and whether improved models can be developed. Answering these questions is one of the goals of the project.

Channel estimation: The simplest way to estimate a channel is by means of training, i.e., some transmitted data symbols are known at the receiver and based on this knowledge the channel is estimated. In this context, optimal placement of training symbols plays a crucial role. For time-invariant frequency-selective channels, training-based channel estimation and optimal training have been studied extensively. To extend these ideas to time-varying frequency-selective channels, we need at least as many training symbols as there are unknown channel parameters. Hence, simplified time-varying channel models with few unknown parameters are essential. Some initial results in this area are reported, but either the channel model is restricted and not accurate, optimal training designs are unknown, or the frequency-selectivity is ignored. The objective of this project is to fill in these research gaps as well as to compare and improve the different approaches. To gain bandwidth-efficiency, so-called blind channel estimation techniques can also be used. These do not rely on the use of training symbols, and exploit some specific system properties, such as spatial or temporal oversampling properties, statistical properties, or the finite alphabet property of the data symbols. For time-invariant frequency-selective channels, a plethora of blind channel estimation techniques has been developed. Extensions to time-varying frequency-selective channels are understudied, but it is clear that they should rely on simplified channel models such as the BEM or the GMM in order to reduce the number of unknown channel coefficients.

To avoid explicit channel estimation, one can also explore differential encoding and detection techniques. These techniques have only recently been proposed for time-invariant frequency-selective channels, but extensions to time-varying frequency-selective channels are unknown. Note that such extensions would be of great importance, since they would avoid the difficult problem of estimating the time-varying frequency-selective channel. Simplified time-varying channel models such as the BEM or the GMM will again be the key tools to realize this.

Channel Equalization: To combat the distortive channel effects, or in other words, invert the FIR filter (time-invariant or time-varying) representing the channel, a so-called equalizer is needed. One can basically distinguish between serial equalizers and block equalizers. Serial equalizers estimate the data sequence symbol by symbol, whereas block equalizers estimate a whole block of data symbols in one step.

In orthogonal frequency division multiplexing (OFDM) systems, such as digital video broadcasting (DVB-T) and the WLAN standards IEEE 802.11a and HIPERLAN/2, for example, block equalizers are used. In case of time-invariant channels, these block equalizers can be simplified significantly, relying on the fact that a time-invariant FIR filter can be diagonalized by means of FFT processing. Such simplified block equalizers cannot be used in the presence of time-varying channels, because it is not possible to diagonalize a time-varying FIR filter by means of FFT processing. As a consequence, other types of block equalizers have to be developed for OFDM over time-varying frequency-selective channels.

Serial equalizers for time-varying frequency-selective channels have to adapt to the time-variation of the channel. We could for instance use the traditional maximum likelihood, linear, or decision feedback serial equalizers, and re-compute the coefficients of the equalizer at each symbol period, but this would lead to a very large equalizer complexity. Therefore, we suggest to restrict the time-variation of the equalizer, e.g., using the BEM or the GMM. In that case, the model for the equalizer is usually chosen to fit the simplified model that is adopted for the channel. Some preliminary results exist where the equalizer as well as the channel are modeled by the CE-BEM, but extensions to the CP-BEM or the GMM have not yet been developed.

Equalizers for time-varying frequency-selective channels are even capable of exploiting the time-variability of the environment in order to improve the performance, in a similar way as the frequency-selectivity of a channel can be exploited. In other words, the time-varying behavior of the channel can be viewed as an additional level of diversity that can be exploited rather than being seen as a nuisance.

Since the equalizer performance critically depends on the channel knowledge, it is also of significant importance to study equalization in conjunction with channel estimation. We could further try to bypass channel estimation using direct equalizer designs. For time-varying channels, these might hold new promise for achieving a desirable bit-error-rate performance, since direct equalization methods do not rely on a specific time-varying channel model.

Multiple-Access: If multiple users want to communicate in the same area, the transmission medium has to be shared by all the users. This is achieved by a so-called multiple-access technique, such as frequency-division multiple-access (FDMA) and time-division multiple-access (TDMA), which simply assign a different frequency band (FDMA) or time slot (TDMA) to each user. A combination of FDMA and TDMA is for instance used in GSM. More recently, code-division multiple-access (CDMA) has been proposed as an alternative to FDMA and TDMA. In CDMA, all users are simultaneously active over the total available bandwidth, but each user spreads out its data using a different code. Because CDMA has some interesting capacity and implementation advantages over FDMA and TDMA, it has been adopted in UMTS. To separate the different users in a CDMA system, a so-called multi-user detector is required. In time-invariant frequency-selective channels, this multi-user detector also has to suppress the undesirable frequency-selective channel effects.

Since the blocks of data over which the channel is assumed constant are usually large in CDMA systems (the more users can be accommodated, the larger the blocks), problems arise when adopting CDMA in a time-varying environment. Third generation wireless CDMA systems like UMTS, can for instance not offer large data rates at high mobility, due to the poor quality of the link. Hence, it is important to improve the performance of CDMA systems in time-varying frequency-selective channels. Some initial results exist, but these assume that the multi-user detector is recomputed each symbol period. We could again reduce the complexity of such multi-user detectors by restricting their time-variation to for instance a BEM or GMM. We additionally have to investigate the effect of channel estimation on the performance of these time-varying multi-user detectors. Direct multi-user detection approaches are also of great importance, since they bypass the estimation of the time-varying channels.

MIMO Communications: Finally, a popular new trend in the field of wireless communications is the use of multiple antennas at the transmitter and receiver, leading to so-called multiple-input multiple-output (MIMO) systems. The growing interest in these systems started after the pioneering work of G. J. Foschini (Bell Labs, USA) in this field. His work shows that the capacity of a wireless communication system equipped with as many transmit as receive antennas grows linearly with the number of antennas (in an ideal environment). To achieve this capacity boost in practice, space-time coding is required, which transforms the data signal such that the transmitted signals are correlated both in space and in time. The redundancy implied by this correlation can then be exploited at the receiver. In time-invariant frequency-selective channels, the design of space-time codes is rather complicated due to the additional frequency-selective channel effects, but many researchers recently succeeded in developing relatively simple space-time codes for this purpose.

For time-varying frequency-selective channels, almost no results are available, even though MIMO techniques are particularly important in this context, since the time-varying nature of the channel already puts a high burden on the quality of the link. Some initial proposals rely on the idea to transform multiple time-varying frequency-selective channels into one longer or faster time-invariant frequency-selective channel, and to use an appropriate transmission scheme developed for such a channel. Since these approaches still suffer from a low coding gain, we aim at developing improved space-time codes, not only relying on a CE-BEM channel model, but possibly also using the CP-BEM or the GMM. Trade-offs among complexity, data rate, and performance will play a crucial role in this design.

Significance and Potential Contributions

The proposed project aims at providing a unifying view on wireless communications, which does not ignore but rather exploit the time-varying nature of the environment. It holds great potential to have an impact on current and future wireless communication systems, such as digital video broadcasting (DVB-T), wireless local area networks (WLANs), and the third generation wireless system UMTS. More specifically, we expect to solve the following problems for current wireless systems:

• We aim at improving the link quality and hence also the data rate of currently proposed UMTS systems at high mobile speeds, by taking the time-varying structure of the channel into account in the system design.
• We expect to extend current DVB-T receivers in order to avoid a break down at high speeds, which will allow for high-quality video reception, even at high mobility, e.g., in a car or a high-speed train.
• Our goal is to make current OFDM systems, such as DVB-T and the WLAN standards IEEE 802.11 and HIPERLAN/2, more robust against carrier frequency offsets, thereby significantly reducing the cost of local oscillators and/or complexity of carrier frequency offset cancellation algorithms.

In addition, the trend to higher carrier frequencies will increase the Doppler shifts of future wireless systems, making them very sensitive to mobility and carrier frequency offsets. Our project will gather new and insightful results on wireless communications over rapidly time-varying channels that will guide future wireless communication standards. Based on our past experience, and our initial research results in the proposed research field, we also expect substantial scientific contributions in the signal processing field. The proposed channel modeling, for instance, is closely connected to time-frequency analysis, which has been a vast research area for many decades, if not centuries. Time-varying channel estimation and equalization, on the other hand, relate to detection and estimation, and will require advanced linear algebra concepts that could impact other research areas.

Approach

Considering the nature of the problem and the fact that we ask funding for the applicant and only one PhD student, we do not believe it is necessary to split the project into different subprojects, but we will partition the project into five more or less consecutive activities. Each activity will be related to one of the wireless communications problems described earlier (channel modeling, channel estimation, channel equalization, multiple-access, and MIMO communications). The proposed ideas in each activity will be applied to practical systems, such as DVB-T, IEEE 802.11, HIPERLAN/2, and UMTS, in order to solve the current problems that these systems face due to the time-varying nature of the channels (see section on aim and objectives), but they will also be used to derive new criteria for future wireless system designs that can cope with time-varying channels. The five main activities are outlined below.

A1. Channel modeling

• Literature study of simplified models for time-varying channels
• Comparison of the accuracy of these models
• Developing new channel models with improved accuracy
• Application to practical systems
• Guidelines for future wireless system designs

A2. Channel estimation

• Literature study of channel estimation algorithms for time-varying channels
• Developing improved algorithms based on the channel models of A1
• Training-based algorithms
• Blind algorithms
• Comparison of different algorithms
• Application to practical systems
• Guidelines for future wireless system designs

A3. Channel equalization

• Literature study of channel equalizers for time-varying channels
• Developing new equalizers by restricting their time-varying structure
• Equalizer design based on channel knowledge
• Perfect channel knowledge
• Estimated channels
• Direct equalizer design
• Training-based design
• Blind design
• Application to practical systems
• Guidelines for future wireless system designs

A4. Multiple-access

• Studying the behavior of existing multiple-access schemes in time-varying channels
• Deriving new multi-user detectors for CDMA by restricting their time-varying structure
• Application to practical systems
• Guidelines for future wireless system designs

A5. MIMO communications

• Studying space-time coding for time-varying channels based on the channel models of A1
• Improving the coding gain of these codes
• Application to practical systems
• Guidelines for future system design

Innovation

The basic innovative aspect of this project is that we take the time-varying nature of the channel explicitly into account in the wireless system design, as opposed to assuming that the channel is constant over a block of data. To make this feasible, many aspects of wireless communications have to be revisited and rethought, taking both performance and computational complexity considerations into account. In all of the earlier introduced communications aspects, innovative elements will be introduced:

Channel modeling:

• Introduction and study of simplified time-varying channel models
• Development of new improved channel models

Channel estimation:

• Development of channel estimation algorithms based on simplified time-varying channel models
• Studying differential encoding and detection for time-varying channels, in order to avoid channel estimation

Channel equalization:

• Reducing the complexity of time-varying equalizers by restricting their time-varying structure
• Studying the effect of channel estimation on equalization
• Development of direct equalization approaches for time-varying channels, bypassing channel estimation

Multiple-access:

• Improving the link quality of CDMA systems by introducing novel time-varying multi-user detectors
• Restricting the time-varying structure of the multi-user detectors, thereby reducing their complexity

MIMO communications:

• The use of MIMO ideas to improve the link quality of time-varying channels
• Development of novel space-time codes based on the simplified time-varying channel models