Christoph Krall

Equivalent system model and equalization of differential impulse radio UWB systems

A discrete-time equivalent system model is derived for differential and transmitted reference (TR) ultra-wideband (UWB) impulse radio (IR) systems, operating under heavy intersymbol-interference (ISI) caused by multipath propagation. In the systems discussed, data is transmitted using differential modulation on a frame-level, i.e., among UWB pulses. Multiple pulses (frames) are used to convey a single bit. Time hopping and amplitude codes are applied for multi user communications, employing a receiver front-end that consists of a bank of pulse-pair correlators. It is shown that these UWB systems are accurately modeled by second-order discrete-time Volterra systems. This proposed nonlinear equivalent system model is the basis for developing optimal and suboptimal receivers for differential UWB communications systems under ISI. As an example, we describe a maximum likelihood sequence detector with decision feedback, to be applied at the output of the receiver front-end sampled at symbol rate, and an adaptive inverse modeling equalizer. Both methods significantly increase the robustness in presence of multipath interference at tractable complexity.

Time-Interleaved Digital-to-Analog Converters for UWB Signal Generation

In this paper, a differentially encoded time-interleaved digital-to-analog converter (TIDAC) structure for ultra-wideband (UWB) signal generation is presented. We show that the output spectrum of the TIDAC is identical to the output of a DAC running at a higher sampling rate. To support the mathematical derivations, the UWB signal generator has been implemented on FPGA hardware and measurements have been taken for a sinusoidal wave, a Gaussian UWB pulse shape and for a UWB OFDM signal. The measurements show that, compared to the single-channel DAC, the mirror images around the sampling frequency can be reduced by about 30 dB and the analog interpolation filter design is simplified.

Minimum Mean-Square Error Equalization for Second-Order Volterra Systems

In this paper, a novel nonlinear Volterra equalizer is presented. We define a framework for nonlinear second-order Volterra models, which is applicable to different applications in engineering. We use this framework to define the channel and to model the equalizer. We then solve the minimum mean-square error (MMSE) problem explicitly for the tandem connection of the two second-order Volterra systems. Optimal solutions for a simplified, linear version of the MMSE equalizer are also presented. The novel equalizer was tested when applied to a nonlinear ultra-wideband transmitted reference receiver front end. As a comparison, a least mean squares (LMS) equalizer with a training sequence has been used to verify the performance of the newly proposed equalizer. The simulation results show that the LMS equalizer is only able to attain the proposed MMSE equalizer after very long training, which might not be desirable in a communication system.

Nonlinear equalization for frame-differential IR-UWB receivers

This paper shows equalization approaches for high-data-rate transmitted-reference (TR) IR-UWB systems employing an autocorrelation receiver front-end. Using a maximum likelihood sequence detector (MLSD) with decision feedback (in the back-end of the TR-receiver), a significant improvement of the receiver performance is possible. To avoid the high complexity of the MLSD detector, alternative equalizer structures are evaluated. If the parameters of the channel are not known a priori, an equalizer has to be adapted during the transmission of training data. Such an adaptive equalizer is presented as a reference. Furthermore, we study the design of minimum mean square error (MMSE) equalizers assuming knowledge of the channel. A linear MMSE equalizer is designed using the linear and nonlinear channel coefficients. Then the concept of the linear equalizer is extended to a nonlinear Volterra equalizer which further improves the performance of the IR-UWB receiver structure. All proposed methods are discussed and the effects are shown with computer simulations.

Compensation of distortions caused by periodic nonuniform holding signals

We investigate the compensation of distortions caused by periodic nonuniform holding signals in digital-to-analog converters (DACs). Such holding signals can introduce additional distortions, which reduce the DAC performance considerably. A discrete-time model of such holding signals is introduced and the design of a time-varying filter to compensate them is elaborated. For two periodic nonuniform holding signals, we exemplify the filter design. The designed filter reduces the in-band distortions significantly, which is verified by simulations and measurements.

Parallel OFDM Signal Generation for UWB Systems

A parallel signal generation scheme for OFDM signals is presented. Conventionally, the generation of OFDM signals is implemented by computing an inverse discrete Fourier transform (IDFT). If the bandwidth is very large, as in ultra-wide band (UWB) systems, preferably integrated solutions are used to generate the communication signals. Additionally, the output of the IDFT is protected against multipath propagation effects with either a cyclic extension or zero-padding. The system described in this paper enables the implementation of a UWB OFDM signal on low complexity and low cost hardware by generating subband OFDM signals. We show that additional errors are introduced on the subband edges, however. A performance study in terms of symbol error rate (SER) has been conducted. The results show that similar SER performance is achieved when either using a highly integrated solution or our parallel signal generation approach