Nearly Optimal Computations with Structured Matrices

We estimate the Boolean complexity of multiplication of structured matrices by a vector and the solution of nonsingular linear systems of equations with these matrices. We study four basic most popular classes, that is, Toeplitz, Hankel, Cauchy and Van-der-monde matrices, for which the cited computational problems are equivalent to the task of polynomial multiplication and division and polynomial and rational multipoint evaluation and interpolation. The Boolean cost estimates for the latter problems have been obtained by Kirrinnis in \cite{kirrinnis-joc-1998}, except for rational interpolation, which we supply now. All known Boolean cost estimates for these problems rely on using Kronecker product. This implies the $d$-fold precision increase for the $d$-th degree output, but we avoid such an increase by relying on distinct techniques based on employing FFT. Furthermore we simplify the analysis and make it more transparent by combining the representation of our tasks and algorithms in terms of both structured matrices and polynomials and rational functions. This also enables further extensions of our estimates to cover Trummer's important problem and computations with the popular classes of structured matrices that generalize the four cited basic matrix classes.Comment: (2014-04-10

Analysis of Candidate Waveforms for 5G Cellular Systems

Choice of a suitable waveform is a key factor in the design of 5G physical layer. New waveform/s must be capable of supporting a greater density of users, higher data throughput and should provide more efficient utilization of available spectrum to support 5G vision of “everything everywhere and always connected” with “perception of infinite capacity”. Although orthogonal frequency division multiplexing (OFDM) has been adopted as the transmission waveform in wired and wireless systems for years, it has several limitations that make it unsuitable for use in future 5G air interface. In this chapter, we investigate and analyse alternative waveforms that are promising candidate solutions to address the challenges of diverse applications and scenarios in 5G

Finite precision arithmetic in Polyphase Filterbank implementations

The MeerKAT is the most sensitive radio telescope in its class, and it is important that systematic effects do not limit the dynamic range of the instrument, preventing this sensitivity from being harnessed for deep integrations. During commissioning, spurious artefacts were noted in the MeerKAT passband and the root cause was attributed to systematic errors in the digital signal path. Finite precision arithmetic used by the Polyphase Filterbank (PFB) was one of the main factors contributing to the spurious responses, together with bugs in the firmware. This thesis describes a software PFB simulator that was built to mimic the MeerKAT PFB and allow investigation into the origin and mitigation of the effects seen on the telescope. This simulator was used to investigate the effects in signal integrity of various rounding techniques, overflow strategies and dual polarisation processing in the PFB. Using the simulator to investigate a number of different signal levels, bit-width and algorithmic scenarios, it gave insight into how the periodic dips occurring in the MeerKAT passband were the result of the implementation using an inappropriate rounding strategy. It further indicated how to select the best strategy for preventing overflow while maintaining high quantization effciency in the FFT. This practice of simulating the design behaviour in the PFB independently of the tools used to design the DSP firmware, is a step towards an end-to-end simulation of the MeerKAT system (or any radio telescope using nite precision digital signal processing systems). This would be useful for design, diagnostics, signal analysis and prototyping of the overall instrument

Low Complexity Time-Concatenated Turbo Equalization for Block Transmission Without Guard Interval: Part 1—The Concept

This paper proposes a novel time-concatenated turbo equalization technique, chained turbo equalization (CHATUE), that allows block transmission systems to eliminate the guard interval (GI), while achieving excellent performance. The proposed CHATUE algorithm connects turbo equalizers neighboring in time, so that they exchange information about their inter-block-interference components in the form of a posteriori log-likelihood ratio. The latest version of the low complexity sub-optimal turbo equalization technique for block-wise single carrier transmission, frequency domain soft cancellation and minimum mean squared error, is fully exploited in developing the CHATUE algorithm. Results of extrinsic information transfer chart analysis as well as a series of bit-error rate (BER) simulations show that excellent performances can be achieved without imposing heavy computational burden in multipath-rich (quasi-static) block Rayleigh fading channels. It is shown that, if the information bit-rate is kept identical (because it may be unpreferable for the industry to change the frame structure), the CHATUE algorithm achieves lower BER than that with block transmission with GI, because lower rate (strong) code for error protection can be used by utilizing the time-duration made available by eliminating the GI. In addition, by combining the proposed structure with a simple rate-1 doped accumulator, further BER improvement exhibiting clear turbo cliff can be achieved. A sister paper (a Part-2 paper) applies the proposed CHATUE algorithm to single carrier frequency division multiple access systems Hui et al. (Wirel Pers Commun, 2011)

Hybrid receiver study

The results are presented of a 4 month study to design a hybrid analog/digital receiver for outer planet mission probe communication links. The scope of this study includes functional design of the receiver; comparisons between analog and digital processing; hardware tradeoffs for key components including frequency generators, A/D converters, and digital processors; development and simulation of the processing algorithms for acquisition, tracking, and demodulation; and detailed design of the receiver in order to determine its size, weight, power, reliability, and radiation hardness. In addition, an evaluation was made of the receiver's capabilities to perform accurate measurement of signal strength and frequency for radio science missions

FFT and FIR Filter implementations for the DSL MODEMS

Broad band digital communication that operates over a standard copper wires. It requires the DSL modems which splits the transmissions into 2 frequency bands. The lower frequencies for voice and the higher frequencies for digital data (internet) in order to transmit the data to larger distances through a copper cable we need modulation techniques. Generally in this DSL modems modulation used is QAM technique. The output of the QAM is complex data this complex data we cannot transfer directly through a copper cable because the data should be in time domain or otherwise the phase of the data which is in frequency domain can be lost, in copper cable so this data should be converted in time domain by using IDFT technique. As IDFT requires more number of complex multiplications and more number of complex additions in comparison to IFFT so to reduce the additions and multiplications IFFT technique is used. At the receiver side we can retrieve the same data by using FFT technique. In this section the implemented FFT architecture is fully efficient and this architecture will require less area. And before we have to transmit through the copper line we have to do interpolation or decimation by using the Filtering operation. The implemented poly phase architecture for the filtering is fully efficient, symmetrical and it requires less number of multipliers

Microprocessor- Oriented Algorithms for Data Communications

Data modem design has attracted a lot of scientific and commercial interest for more than three decades now. The field is important from a scientific point of view, since reliable data communications require very sophisticated solutions to many associated problems. From a commercial point of view its importance arises from the ever- rising needs for Computer networking and distributed processing in general. Modem algorithms are real-time in nature, so adequate technological support is important for modem design development. Advances in VLSI are opening new possibilities in this area and current trends toward integration of computing and communications are placing new demands on its further development. One can say that data modem design is entering its renaissance and this fact was our motivation in preparing this text. The objective is to bridge the gap between the increasing number of published papers on modem design and implementation, and the rapidly growing interest in the field. Included in the text are topics to introduce and familiarize the reader with modem design. Topics covered include: microprocessor applications in communications, data modem types, microprocessor and VLSI types, and technological impacts on design. Finally, we address the hardware issues such as the processor elements and interfacing, and software issues like the digital filter implementation. A comprehensive bibliography on modem design and implementation is also provided. With this bibliography one can research VLSI/microprocessor-based data modem design easily and thoroughly