9 research outputs found
Polynomial matrix eigenvalue decomposition techniques for multichannel signal processing
Polynomial eigenvalue decomposition (PEVD) is an extension of the eigenvalue decomposition (EVD) for para-Hermitian polynomial matrices, and it has been shown to be a powerful tool for broadband extensions of narrowband signal processing problems. In the context of broadband sensor arrays, the PEVD allows the para-Hermitian matrix that results from the calculation of a space-time covariance matrix of the convolutively mixed signals to be diagonalised. Once the matrix is diagonalised, not only can the correlation between different sensor signals be removed but the signal and noise subspaces can also be identified. This process is referred to as broadband subspace decomposition, and it plays a very important role in many areas that require signal separation techniques for multichannel convolutive mixtures, such as speech recognition, radar clutter suppression, underwater acoustics, etc. The multiple shift second order sequential best rotation (MS-SBR2) algorithm, built on the most established SBR2 algorithm, is proposed to compute the PEVD of para-Hermitian matrices. By annihilating multiple off-diagonal elements per iteration, the MS-SBR2 algorithm shows a potential advantage over its predecessor (SBR2) in terms of the computational speed. Furthermore, the MS-SBR2 algorithm permits us to minimise the order growth of polynomial matrices by shifting rows (or columns) in the same direction across iterations, which can potentially reduce the computational load of the algorithm. The effectiveness of the proposed MS-SBR2 algorithm is demonstrated by various para-Hermitian matrix examples, including randomly generated matrices with different sizes and matrices generated from source models with different dynamic ranges and relations between the sources’ power spectral densities. A worked example is presented to demonstrate how the MS-SBR2 algorithm can be used to strongly decorrelate a set of convolutively mixed signals. Furthermore, the performance metrics and computational complexity of MS-SBR2 are analysed and compared to other existing PEVD algorithms by means of numerical examples. Finally, two potential applications of theMS-SBR2 algorithm, includingmultichannel spectral factorisation and decoupling of broadband multiple-input multiple-output (MIMO) systems, are demonstrated in this dissertation
Enhanced multi-user DMT spectrum management using polynomial matrix decomposition techniques
This thesis researches the increasingly critical roles played by intelligent resource management
and interference mitigation algorithms in present-day input multiple output (MIMO)
communication systems. This thesis considers the application of polynomial matrix decomposition
(PMD) algorithms, an emerging broadband factorisation technology for broadband
MIMO access networks. Present DSL systems’ performance is constrained by the presence
of interference (crosstalk) between multiple users sharing a common physical cable bundle.
Compared to the traditional static spectrum management methods that define their survival
to the worst-case scenarios, DSM methods provides some degree of flexibility to both direct
channel and noise parameters to improve evolvability and robustness significantly. A novel
crosstalk-aware DSM algorithm is proposed for the efficient management of multi-user DSL
systems. Joint power allocation procedures are considered for the proposed single-channel
equalisation method in DSL access networks.
This thesis then shows that DSM can also benefit overdetermined precoding-equalisation
systems, when the channel state information (CSI) parameters call for a specific decision
feedback criterion to achieve a perfect reconstruction. A reasonable redundancy is introduced
to reformulate the original multi-user MIMO problem into the simplest case of power
management problem. DSM algorithms are primarily applied to solve the power allocation
problem in DSM networks with the aim of maximising the system attribute rather than
meeting specific requirements. Also, a powerful PMD algorithm known as sequential
matrix diagonalisation (SMD) is used for analysing the eigenvalue decomposition problem
by quantifying the available system resource including the effects of the crosstalk and its
parameters. This analysis is carried out through joint precoding and equalisation structures.
The thesis also investigates dynamic interference mitigation strategies for improving
the performance of DSL networks. Two different mitigation strategies through a decision
feedback equalisation (DFE) criterion are considered, including zero-forcing (ZF) and
minimum mean square error (MMSE) equalisers. The difference between ZF and MMSE
equalisations is analysed. Some experimental simulation results demonstrate the performance
of both ZF and MMSE equalisation under the DFE equalisation constraint settings. Model reduction on the MMSE equalisation is thus applied to balance the crosstalk interference and
enhance the data-rate throughput.
Finally, the thesis studies a multi-user MIMO problem under the utility maximisation
framework. Simulation results illustrate that the power allocation of multi-user DSL transmission
can be jointly controlled and the interference can often be mitigated optimally on
a single user basis. Driven by imperfect CSI information in current DSL networks, the
research presents a novel DSM method that allows not only crosstalk mitigation, but also the
exploitation of crosstalk environments through the fielding of versatile, flexible and evolvable
systems. The proposed DSM tool is presented to achieve a robust mitigating system in any
arbitrary overdetermined multi-user MIMO environment. Numerical optimisation results show that the mitigation of crosstalk impairment using the proposed DSM strategy. The design and implementation of the proposed DSM are carried out in the environment of
MATLAB
Polynomial matrix algebra with applications
[Abstract unavailable
Characterizations of Families of Rectangular, Finite Impulse Response, Para-Unitary Systems
We here study Finite Impulse Response (FIR) rectangular, not necessarily causal, systems which are (para)-unitary on the unit circle (=the class U). First, we offer three characterizations of these systems. Then, introduce a description of all FIRs in U, as copies of a real polytope, parametrized by the dimensions and the McMillan degree of the FIRs.
Finally, we present six simple ways (along with their combinations) to construct, from any FIR, a large family of FIRs, of various dimensions and McMillan degrees, so that whenever the original system is in U, so is the whole family.
A key role is played by Hankel matrices
Use of frequency response masking technique in designing A/D converter for SDR.
Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2005.Analog-to-digital converters (ADCs) are required in almost all signal processing and communication
systems. They are often the most critical components, since they tend to determine the overall system
performance. Hence, it is important to determine their performance limitations and develop improved
realizations. One of the most challenging tasks for realizing software defined radio (SDR) is to move ND
conversion as close to the antenna as possible, this implies that the ADC has to sample the incoming
signal with a very high sample rate (over 100 MSample/s) and with a very high resolution (14 -to -16 bits).
To design and implement AID converters with such high performance, it is necessary to investigate new
designing techniques.
The focus in this work is on a particular type of potentially high-performance (high-resolution and highspeed)
analog-to-digital conversion technique, utilizing filter banks, where two or more ADCs are used in
the converter array in parallel together with asymmetric filter banks. The hybrid filter bank analog-todigital
converter (HFB ADC) utilizes analog filters (analysis filters) to allocate a frequency band to each
ADC in a converter array and digital synthesis filters to reconstruct the digitized signal. The HFB
improves the speed and resolution of the conversion, in comparison to the standard time-interleaving
technique by attenuating the effect of gain and phase mismatches between the ADCs.
Many of the designs available in the literature are compromising between some metrics: design
complexity, order of the filter bank (computation time) and the sharpness of the frequency response rolloff
(the transition from the pass band to the stop band).
In this dissertation, five different classes of near perfect magnitude reconstruction (NPMR) continuoustime
hybrid filter banks (CT HFBs) are proposed. In each of the five cases, two filter banks are designed;
analysis filter bank and synthesis filter bank. Since the systems are hybrid, continuous time IlR filter are
used to implement the analysis filter bank and digital filters are used for the synthesis filter bank. To
optimize the system, we used a new technique, known in the literature as frequency response masking
(FRM), to design the synthesis filter bank. In this technique, the sharp roll-off characteristics can be
achieved while keeping the complexity of the filter within practical range, this is done by splitting the
filter into two filters in cascade; model filter with relaxed roll-off characteristics followed by a masking
filter.
One of the main factors controlling the overall complexity of the filter is the way of designing the model
filter and that of designing the masking filter.
The dissertation proposes three combinations: use of HR model filter and IlR masking filter, HR model
filter/FIR masking filter and FIR model filter/FIR masking filter. To show the advantages of our designs,
we considered the cases of designing the synthesis filter as one filter, either FIR or IlR. These two filters
are used as base for comparison with our proposed designs (the use of masking response filter). The results showed the following:
1. Asymmetric hybrid filter banks alone are not sufficient for filters with sharp frequency response
roll-off especially for HR/FIR class.
2. All classes that utilize FRM in their synthesis filter banks gave a good performance in general in
comparison to conventional classes, such as the reduction of the order of filters
3. HR/HR FRM gave better performance than HR/FIR FRM.
4. Comparing HR/HR FRM using FIR masking filters and HR/IIR FRM using IIR masking filters,
the latter gave better performance (the performance is generally measured in terms of reduced
filter order).
5. All classes that use the FRM approach have a very low complexity, in terms of reduced filter
order. Our target was to design a system with the following overall characteristics: pass band
ripple of -0.01 dB, stop band minimum attenuation of - 40 dB and of response roll-off of 0.002.
Our calculations showed that the order of the conventional IIR/FIR filter that achieves such
characteristics is aboutN =2000. Using the FRM technique, the order N reduced to
aboutN = 244, N = 179 for IIRJFIR and IIR/IIR classes, respectively. This shows that the
technique is very effective in reducing the filter complexity.
6. The magnitude distortion and the aliasing noise are calculated for each design proposal and
compared with the theoretical values. The comparisons show that all our proposals result in
approximately perfect magnitude reconstruction (NPMR).
In conclusion, our proposal of using frequency-response masking technique to design the synthesis filter
bank can, to large extent, reduce the complexity of the system. The design of the system as a whole is
simplified by designing the synthesis filter bank separately from the design of the analysis filter bank. In
this case each bank is optimized separately. This implies that for SDR applications we are proposing the
use of the continuous-time HFB ADC (CT HFB ADC) structure utilizing FRM for digital filters