Bojan Vrcelj

Transmultiplexers as precoders in modern digital communication: a tutorial review

In this paper we review the recent impact of transmultiplexers in digital communications. Filter banks precoders, conditions for equalization, and multiuser interference cancellation are reviewed. The idea behind blind channel identification is reviewed as well. The emphasis is mostly on the theoretical infrastructure, and the list of references provide a wealth of related information.

MIMO biorthogonal partners and applications

Multiple input multiple output (MIMO) biorthogonal partners arise in many different contexts, one of them being multiwavelet theory. They also play a central role in the theory of MIMO channel equalization, especially with fractionally spaced equalizers. In this paper, we first derive some theoretical properties of MIMO biorthogonal partners. We develop conditions for the existence of MIMO biorthogonal partners and conditions under which FIR solutions are possible. In the process of constructing FIR MIMO biorthogonal partners, we exploit the nonuniqueness of the solution. This will lead to the design of flexible fractionally spaced MIMO zero-forcing equalizers. The additional flexibility in design makes these equalizers more robust to channel noise. Finally, other situations where MIMO biorthogonal partners occur are also considered, such as prefiltering in multiwavelet theory and deriving the vector version of the least squares signal projection problem.

Fast and robust blind-equalization based on cyclic prefix

The cyclic prefix is commonly used in the context of frequency domain equalization in DMT channels. We observe that it can be used in more general contexts and show its advantages in blind equalization, especially for non-minimum phase channels.

Theory of fractionally spaced cyclic-prefix equalizers

The cyclic prefix system is widely used for frequency domain equalization in discrete multitone channels. In this paper we show how the idea of fractionally spaced equalization (FSE) can be adapted to cyclic prefix systems. We derive the condition for a perfect FSE, and show that there is a certain freedom in the choice of the equalizer coefficients. This freedom is then exploited to minimize the effect of additive noise at the detector input. The theory is generally applicable to any deconvolution problem, though the setting used for our development uses the language of digital communication.

On sampling theorems for non bandlimited signals

It is well-known that certain non-bandlimited signals such as splines can be reconstructed from uniformly spaced samples similar to bandlimited signals. This usually requires noncausal IIR filters. We revisit this result and consider extensions such as derivative sampling theorems and pulse sampling theorems. It turns out that spline-like signals can often be reconstructed from joint sampling of amplitude and derivative using only FIR filters. We also briefly consider discrete time versions of these results.

Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners.

Equalization with oversampling in multiuser CDMA systems

Some of the major challenges in the design of new-generation wireless mobile systems are the suppression of multiuser interference (MUI) and inter-symbol interference (ISI) within a single user created by the multipath propagation. Both of these problems were addressed successfully in a recent design of A Mutually Orthogonal Usercode-Receiver (AMOUR) for asynchronous or quasisynchronous code division multiple access (CDMA) systems. AMOUR converts a multiuser CDMA system into parallel single-user systems regardless of the multipath and guarantees ISI mitigation, irrespective of the channel null locations. However, the noise amplification at the receiver can be significant in some multipath channels. In this paper, we propose to oversample the received signal as a way of improving the performance of AMOUR systems. We design Fractionally Spaced AMOUR (FSAMOUR) receivers with integral and rational amounts of oversampling and compare their performance with the conventional method. An important point that is often overlooked in the design of zero-forcing channel equalizers is that sometimes, they are not unique. This becomes especially significant in multiuser applications where, as we will show, the nonuniqueness is practically guaranteed. We exploit this flexibility in the design of AMOUR and FSAMOUR receivers and achieve noticeable improvements in performance.

Theory of MIMO biorthogonal partners and their application in channel equalization

Channel equalization is an important step in most applications of digital communications. In this paper we consider the equalization of multiple input multiple output (MIMO) channels. To that end we derive the theory of MIMO biorthogonal partners, a concept that has already been introduced (only in the scalar case) by the authors. We develop conditions for the existence of an FIR MIMO biorthogonal partners and describe their application in the MIMO channel equalization. We also show that it is possible to exploit the non-uniqueness of FIR MIMO biorthogonal partners in order to design flexible fractionally spaced MIMO equalizers that will be more robust to the channel noise.

Fractional biorthogonal partners and application in signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented in this paper is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers. Hence the name fractional biorthogonal partners. The conditions for the existence of stable and of FIR fractional biorthogonal partners are derived. This result gives rise to an all-FIR spline interpolation technique with the minimum amount of required oversampling. This technique is illustrated by an interpolation example.

Least squares signal approximation using multirate systems: multichannel nonuniform case

The issue of signal approximation has been treated extensively by the signal processing and mathematics communities. The problem is usually that of minimizing an appropriate metric between the given signal and signals described by a certain model. In this paper we consider the general signal model described by multirate systems. Multiple channels with nonuniform interpolation ratios are considered. We show that the solution minimizing the /spl lscr/ /sub 2/ norm of the approximation error involves filtering that is in general time-varying. We also point out the conditions under which LTI filters can be used and consider a special uniform case which provides further insights.