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 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

Joint optimization of transceivers with fractionally spaced equalizers

In this paper we propose a method for joint optimization of transceivers with fractionally spaced equalization (FSE). We use the effective single-input multiple-output (SIMO) model for the fractionally spaced receiver. Since the FSE is used at the receiver, the optimized precoding scheme should be changed correspondingly. Simulation shows that the proposed method demonstrates remarkable improvement for jointly optimal linear transceivers as well as transceivers with decision feedback

An Investigation of Orthogonal Wavelet Division Multiplexing Techniques as an Alternative to Orthogonal Frequency Division Multiplex Transmissions and Comparison of Wavelet Families and Their Children

Recently, issues surrounding wireless communications have risen to prominence because of the increase in the popularity of wireless applications. Bandwidth problems, and the difficulty of modulating signals across carriers, represent significant challenges. Every modulation scheme used to date has had limitations, and the use of the Discrete Fourier Transform in OFDM (Orthogonal Frequency Division Multiplex) is no exception. The restriction on further development of OFDM lies primarily within the type of transform it uses in the heart of its system, Fourier transform. OFDM suffers from sensitivity to Peak to Average Power Ratio, carrier frequency offset and wasting some bandwidth to guard successive OFDM symbols. The discovery of the wavelet transform has opened up a number of potential applications from image compression to watermarking and encryption. Very recently, work has been done to investigate the potential of using wavelet transforms within the communication space. This research will further investigate a recently proposed, innovative, modulation technique, Orthogonal Wavelet Division Multiplex, which utilises the wavelet transform opening a new avenue for an alternative modulation scheme with some interesting potential characteristics. Wavelet transform has many families and each of those families has children which each differ in filter length. This research consider comprehensively investigates the new modulation scheme, and proposes multi-level dynamic sub-banding as a tool to adapt variable signal bandwidths. Furthermore, all compactly supported wavelet families and their associated children of those families are investigated and evaluated against each other and compared with OFDM. The linear computational complexity of wavelet transform is less than the logarithmic complexity of Fourier in OFDM. The more important complexity is the operational complexity which is cost effectiveness, such as the time response of the system, the memory consumption and the number of iterative operations required for data processing. Those complexities are investigated for all available compactly supported wavelet families and their children and compared with OFDM. The evaluation reveals which wavelet families perform more effectively than OFDM, and for each wavelet family identifies which family children perform the best. Based on these results, it is concluded that the wavelet modulation scheme has some interesting advantages over OFDM, such as lower complexity and bandwidth conservation of up to 25%, due to the elimination of guard intervals and dynamic bandwidth allocation, which result in better cost effectiveness

Joint bit allocation and precoding for filterbank transceivers in NOFDM systems

Recently, the non orthogonal frequency division multiplexing (NOFDM) systems have attracted increased interest. They have several advantages over traditional OFDM systems: higher bandwidth efficiency; reduced sensitivity to carrier frequency offsets, oscillator phase noise and narrowband interference; and reduced intersymbol/intercarrier interference (ISI/ICI). In particular, low ISI/ICI will be important for future systems where Doppler frequencies will be larger (equivalently, channel variations will be faster) due to higher carrier frequencies and higher mobile velocities. In the first part of this thesis the duality of multicarrier systems and Gabor frames is discussed and applied to the design of a generalized multicarrier system based on a filterbank structure. The efficient polyphase implementation is also discussed. In this thesis the channel capacity of a GMC systems is evaluated through the diagonalization of an equivalent matrix model where intersymbol and intercarrier interferences have been included. Exploiting the majorization theory, the mutual information can be represented as a Schur-concave function and it is maximized through a joint transceiver design adding a linear precoder at the transmitter and a LMMSE equalizer at the receiver. The capacity is derived by the eigenvalue decomposition of the global system matrix including the noise colored by the receiver filtering and employing a power allocation of the transmitted power according to the well-known water-filling solution. This thesis investigates also the behaviour of the NOFDM systems when a power and bit allocation algorithm (like the Campello one) is employed in order to satisfy a certain QoS constrain. A comparison of the performances with OFDM systems is included. Finally a simple application of the cognitive radio paradigm employing filterbankbased multicarrier systems is developed and some interesting results are showed

Investigation, Design and Implementation of MIMO Antennas for Mobile Phones. Simulation and Measurement of MIMO Antennas for Mobile Handsets and Investigations of Channel Capacity of the Radiating Elements Using Spatial and Polarisation Diversity Strategies.

The objectives of this work were to investigate, design and implement Multiple-Input Multiple-Output (MIMO) antenna arrays for mobile phones. Several MIMO antennas were developed and tested over various wireless-communication frequency bands. The radiation performance and channel capacity of these antennas were computed and measured: the results are discussed in the context of the frequency bands of interest. A comprehensive study of MIMO antenna configurations such as 2 × 1, 3 × 1, 2 × 2 and 3 × 3, using polarisation diversity as proposed for future mobile handsets, is presented. The channel capacity is investigated and discussed, as applying to Rayleigh fading channels with different power spectrum distributions with respect to azimuth and zenith angles. The channel capacity of 2 × 2 and 3 × 3 MIMO systems using spatial polarisation diversity is presented for different antenna designs. The presented results show that the maximum channel capacity for an antenna contained within a small volume can be reached with careful selection of the orthogonal spatial fields. The results are also compared against planar array MIMO antenna systems, in which the antenna size considered was much larger. A 50% antenna size reduction method is explored by applying magnetic wall concept on the symmetry reference of the antenna structure. Using this method, a triple dual-band inverted-F antenna system is presented and considered for MIMO application. Means of achieving minimum coupling between the three antennas are investigated over the 2.45 GHz and 5.2 GHz bands. A new 2 2 MIMO dual-band balanced antenna handset, intended to minimise the coupling with the handset and human body was proposed, developed and tested. The antenna coupling with the handset and human hand is reported in terms the radiation performance and the available channel capacity. In addition, a dual-polarisation dipole antenna is proposed, intended for use as one of three collocated orthogonal antennas in a polarisation-diversity MIMO communication system. The antenna actually consists of two overlaid electric and magnetic dipoles, such that their radiation patterns are nominally identical but they are cross-polarised and hence only interact minimally