Free Probability based Capacity Calculation of Multiantenna Gaussian Fading Channels with Cochannel Interference

During the last decade, it has been well understood that communication over multiple antennas can increase linearly the multiplexing capacity gain and provide large spectral efficiency improvements. However, the majority of studies in this area were carried out ignoring cochannel interference. Only a small number of investigations have considered cochannel interference, but even therein simple channel models were employed, assuming identically distributed fading coefficients. In this paper, a generic model for a multi-antenna channel is presented incorporating four impairments, namely additive white Gaussian noise, flat fading, path loss and cochannel interference. Both point-to-point and multiple-access MIMO channels are considered, including the case of cooperating Base Station clusters. The asymptotic capacity limit of this channel is calculated based on an asymptotic free probability approach which exploits the additive and multiplicative free convolution in the R- and S-transform domain respectively, as well as properties of the eta and Stieltjes transform. Numerical results are utilized to verify the accuracy of the derived closed-form expressions and evaluate the effect of the cochannel interference.Comment: 16 pages, 4 figures, 1 tabl

A unified complex noncentral Wishart type distribution inspired by massive MIMO systems

Please read abstract in the article.The National Research Foundation of South Africahttps://link.springer.com/journal/40488am2019Statistic

On the Capacity of Communication Channels with Memory and Sampled Additive Cyclostationary Gaussian Noise: Full Version with Detailed Proofs

In this work we study the capacity of interference-limited channels with memory. These channels model non-orthogonal communications scenarios, such as the non-orthogonal multiple access (NOMA) scenario and underlay cognitive communications, in which the interference from other communications signals is much stronger than the thermal noise. Interference-limited communications is expected to become a very common scenario in future wireless communications systems, such as 5G, WiFi6, and beyond. As communications signals are inherently cyclostationary in continuous time (CT), then after sampling at the receiver, the discrete-time (DT) received signal model contains the sampled desired information signal with additive sampled CT cyclostationary noise. The sampled noise can be modeled as either a DT cyclostationary process or a DT almost-cyclostationary process, where in the latter case the resulting channel is not information-stable. In a previous work we characterized the capacity of this model for the case in which the DT noise is memoryless. In the current work we come closer to practical scenarios by modelling the resulting DT noise as a finite-memory random process. The presence of memory requires the development of a new set of tools for analyzing the capacity of channels with additive non-stationary noise which has memory. Our results show, for the first time, the relationship between memory, sampling frequency synchronization and capacity, for interference-limited communications. The insights from our work provide a link between the analog and the digital time domains, which has been missing in most previous works on capacity analysis. Thus, our results can help improving spectral efficiency and suggest optimal transceiver designs for future communications paradigms.Comment: accepted to the IEEE Transactions on Information Theor

A Bootstrap Method for Spectral Statistics in High-Dimensional Elliptical Models

Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to Mar\v{c}enko-Pastur (MP) models -- in which observations are represented as linear transformations of random vectors with independent entries. By contrast, less is known in the context of elliptical models, which violate the independence structure of MP models and exhibit quite different statistical phenomena. In particular, very little is known about the scope of bootstrap methods for doing inference with spectral statistics in high-dimensional elliptical models. To fill this gap, we show how a bootstrap approach developed previously for MP models can be extended to handle the different properties of elliptical models. Within this setting, our main theoretical result guarantees that the proposed method consistently approximates the distributions of linear spectral statistics, which play a fundamental role in multivariate analysis. Lastly, we provide empirical results showing that the proposed method also performs well for a variety of nonlinear spectral statistics

Extreme eigenvalues of sample covariance matrices under generalized elliptical models with applications

We consider the extreme eigenvalues of the sample covariance matrix $Q=YY^*$ under the generalized elliptical model that $Y=\Sigma^{1/2}XD.$ Here $\Sigma$ is a bounded $p \times p$ positive definite deterministic matrix representing the population covariance structure, $X$ is a $p \times n$ random matrix containing either independent columns sampled from the unit sphere in $\mathbb{R}^p$ or i.i.d. centered entries with variance $n^{-1},$ and $D$ is a diagonal random matrix containing i.i.d. entries and independent of $X.$ Such a model finds important applications in statistics and machine learning. In this paper, assuming that $p$ and $n$ are comparably large, we prove that the extreme edge eigenvalues of $Q$ can have several types of distributions depending on $\Sigma$ and $D$ asymptotically. These distributions include: Gumbel, Fr\'echet, Weibull, Tracy-Widom, Gaussian and their mixtures. On the one hand, when the random variables in $D$ have unbounded support, the edge eigenvalues of $Q$ can have either Gumbel or Fr\'echet distribution depending on the tail decay property of $D.$ On the other hand, when the random variables in $D$ have bounded support, under some mild regularity assumptions on $\Sigma,$ the edge eigenvalues of $Q$ can exhibit Weibull, Tracy-Widom, Gaussian or their mixtures. Based on our theoretical results, we consider two important applications. First, we propose some statistics and procedure to detect and estimate the possible spikes for elliptically distributed data. Second, in the context of a factor model, by using the multiplier bootstrap procedure via selecting the weights in $D,$ we propose a new algorithm to infer and estimate the number of factors in the factor model. Numerical simulations also confirm the accuracy and powerfulness of our proposed methods and illustrate better performance compared to some existing methods in the literature.Comment: 90 pages, 6 figures, some typos are correcte

Mathematical optimization techniques for resource allocation and spatial multiplexing in spectrum sharing networks

Due to introduction of smart phones with data intensive multimedia and interactive applications and exponential growth of wireless devices, there is a shortage for useful radio spectrum. Even though the spectrum has become crowded, many spectrum occupancy measurements indicate that most of the allocated spectrum is underutilised. Hence radically new approaches in terms of allocation of wireless resources are required for better utilization of radio spectrum. This has motivated the concept of opportunistic spectrum sharing or the so-called cognitive radio technology that has great potential to improve spectrum utilization. The cognitive radio technology allows an opportunistic user namely the secondary user to access the spectrum of the licensed user (known as primary user) provided that the secondary transmission does not harmfully affect the primary user. This is possible with the introduction of advanced resource allocation techniques together with the use of wireless relays and spatial diversity techniques. In this thesis, various mathematical optimization techniques have been developed for the efficient use of radio spectrum within the context of spectrum sharing networks. In particular, optimal power allocation techniques and centralised and distributed beamforming techniques have been developed. Initially, an optimization technique for subcarrier and power allocation has been proposed for an Orthogonal Frequency Division Multiple Access (OFDMA) based secondary wireless network in the presence of multiple primary users. The solution is based on integer linear programming with multiple interference leakage and transmission power constraints. In order to enhance the spectrum efficiency further, the work has been extended to allow multiple secondary users to occupy the same frequency band under a multiple-input and multiple-output (MIMO) framework. A sum rate maximization technique based on uplink-downlink duality and dirty paper coding has been developed for the MIMO based OFDMA network. The work has also been extended to handle fading scenarios based on maximization of ergodic capacity. The optimization techniques for MIMO network has been extended to a spectrum sharing network with relays. This has the advantage of extending the coverage of the secondary network and assisting the primary network in return for the use of the primary spectrum. Finally, instead of considering interference mitigation, the recently emerged concept of interference alignment has been used for the resource allocation in spectrum sharing networks. The performances of all these new algorithms have been demonstrated using MATLAB based simulation studies

Tri-Orthogonal Polarisation Diverse Communications

This thesis investigates improving communication link coverage through triorthogonal polarisation diversity. Tri-orthogonal polarisation diversity exploits radiated electromagnetic energy transmission and reception in three orthogonal spatial directions with an aim to provide enhanced communication link performance. Original contributions to this branch of diversity are presented in areas of both software and hardware design. First, simulations are presented highlighting the benefit of tri-orthogonal polarisation diversity at both the transmitter and receiver over a range of terrestrial channel conditions. The results are presented in an easily understandable graphical format that results from a novel model design considering all antenna orientations. Orientation robustness at the antenna is demonstrated as a consequence of a tri-orthgonal polarisation diverse approach. Second, additional research is performed in order to extend the model into the field of satellite systems. The ionosphere is required to be modelled, and this is performed according to a novel vectorised approach using realtime ionospheric data and terrestrial magnetic field appreciation. Third, ionospheric modelling is incorporated into a non-geosynchronous satellite orbit channel model that provides an insight into the benefit of applying a tri-orthogonal polarisation diverse approach uniquely at the receiver. Novelty is provided in the form of a vectorised approach to simulation covering all antenna orientations in a field-ofview as observed from a satellite transmitter. This is extended over the orbits of three distinct satellite systems. Output is provided in graphical format and conclusions are drawn form the data which suggest that a tri-orthogonal polarisation diverse approach applied at the receiver provides an increase in reception performance. Fourth, an antenna is designed, simulated, constructed and tested that provides three orthogonal polarisations in a phase-centred differentially-fed package. Novelty is provided in the design being planar in nature, with three orthogonal modes being able to be transmitted from a single slot. Results emanating from the testing procedure demonstrate the benefits of the design in terms of diversity and extension to beamforming applications. Fifth, as an extension to the antenna design, a circularly polarised feeding arrangement is used together with an omnidirectional vertically polarised mode feed in an antenna and feed combination. This provides the possibility of a direct comparison with conventional circularly polarised techniques, such as those used in both terrestrial and satellite receive antennas. Sixth, the operational bandwidth of the omnidirectional vertically polarised mode is extended by adapting the design of the cavity wall resonating slots in a substrateintegrated monopole antenna while maintaining a planar structure. The electric monopole design demonstrates an increase in operating bandwidth from 2.5% to 56%. In the thesis, a tri-orthogonal polarisation diverse approach is shown to be beneficial to signal reception over a range of channels, both in the areas of terrestrial and satellite communications. The concept is demonstrated to be feasible in a planar structure. Triorthogonal polarisation diversity is likely to play an increasing role in the future as systems look to cope with an ever increasing data flow. The demand for content on mobile devices has forced massive growth in mobile data over the past two decades. This growth has recently reached saturation point, and so new avenues for extending growth have to be considered. A search for available bandwidth has lead research to focus on the mmWave section of the electromagnetic spectrum. The advent of the next generation of wireless connectivity, dubbed fifth generation or 5G, is now upon us (Rappaport et al. 2013b). With data traffic set to multiply by up to one thousand fold by 2020 (Qualcomm Inc. Accessed: 2014b, Qualcomm Inc. Accessed: 2014a, Li et al. 2014, Chin et al. 2014), as The Internet of Things (Ashton 2009, Cisco Inc. Accessed: 2014, Gubbi et al. 2013) enters into the fray, an overhaul of wireless design is somewhat overdue. For static point-to-point, or LoS systems, challenges exist according to the channel environment and temporal changes that may occur within. For any network that has a mobile component built in, where spatial position and alignment of transmitter and receiver change over time, signal propagation is additionally influenced by link geometry. In an increasingly mobile world, this presents challenges as increased coverage, one of the main focus points of the 5G system, will require efficient use of radiated electromagnetic energy. Conventional techniques for improving data rate have typically aimed at increasing performance at the transmitter. For terrestrial networks, a transmitter is typically stationary. Performance outweighs size constraints and so power amplification and combination may be used to excite antennas that flood a network cell with a strong linearly polarised transmitted signal. For commercial providers, this has proved a very successful technique, mainly as a result of the majority of wireless subscribers living in dense urban environments. For a linearly polarised wave, operating at conventional operating frequencies around 2 GHz, and transmitted with relatively high power, the urban environment typically provides assistance for signal reception at the receiver through diversity brought about by reflection, refraction and scattering or multipath due to the presence of buildings. Small misalignments in transmit and receive antennas are mitigated as the propagating signal wavelength is large and a relatively high transmit power establishes a relatively high signal-to-noise ratio, providing useful multipath effects over the channel. At certain receive positions, channel fading may occur when superposition of received multipath components effectively cancel each other. This may be mitigated through additional transmitters that are spaced appropriately; a concept known as spatial diversity that has been cited at mmWave frequencies (Smulders 2002, Park and Pan 2012). Diversity of signal is important in that it offers a greater possibility of a signal being received due to individuality of uncorrelated channel propagation for each diverse signal component. As more content is demanded by subscribers within an ever shrinking timeframe, a higher frequency of operation is typically required for a carrier wave capable of providing this service. Add in the context of mobility, and issues quickly appear. Beneficial effects on a linearly polarised signal operating at conventional low gigahertz frequencies arising from reflection, refraction, and scattering or multipath effects, assist signal reception. Relatively long wavelengths are subjected to many scatterers, and due to the relatively high transmit power involved, scattering effects provide diversity at the receiver in the form of many smaller receivable diverse signal components. These signal components are superpositioned either constructively or destructively, after diverse individual propagation through the channel, at the receiver to provide signal reception. At mmWave frequencies, due to a shrinking wavelength, the following issues arise: • increased path loss over a defined range due to spreading loss (Pozar 2011), and increased atmospheric absorption (Liebe et al. 1989). An obvious solution is to provide more transmit power at the transmitter. At higher frequencies, miniaturisation of devices limits this possibility as heat sinking becomes problematic. Amplifier non-linearity and unwanted third order intermodulation impact on system performance (Niknejad and Hashemi 2008, Hashemi and Raman 2016) • the beneficial effect of multipath fading may not exist in a mmWave terrestrial channel (Pi and Khan 2011), as a smaller wavelength typically implies a reduced beamwidth and less scatterers available for the LoS signal to scatter into useful smaller diverse signal components. Due to a relatively low transmit power involved, any scattering of a LoS signal into smaller, weaker diverse signal components may result in no received signal. As a result, cell range is reduced and more transmitters are required to provide coverage over a network • with a shrinking wavelength, relatively lower transmit power, and increased mobility, antenna misalignment becomes problematic. A drive for radiated power efficiency is paramount in providing the next generation of wireless networks. An ability to transmit signals into and receive signals from all angles is necessary (Rappaport et al. 2013b). The terahertz range, for example, offers extremely high transfer rates, although any small misalignment greatly affects rate. The use of dielectric mirrors is required to effectively steer the transmitted signal to its destination. Mitigation of misalignment becomes important in maintaining system performance. For the next generation of mobile wireless systems to operate within the mmWave section of the electromagnetic spectrum, a solution to extend range is to increase radiated energy in a direction of propagation, through beam steering techniques. Within a mobile context, this poses challenges, not least as the link geometry is variable. For terrestrial networks, conventional transmitted waveforms are mainly vertically polarised, or circularly polarised, and as such are mainly one dimensional, or two dimensional at best, in performance. To provide the next generation of wireless networks, a third dimension needs to be considered to provide efficient use of radiated electromagnetic energy. Frequency bands of interest for 5G systems differ from country to country. According to the US Federal Communications Commission (FCC), the mmWave region that will be studied ranges from 24–80 GHz (Rappaport et al. 2013b, Rappaport Accessed: 2014, Above Ground Level Media Group Accessed: 2015). One of the aims of 5G is to improve coverage (Rappaport et al. 2013b). One method that is being considered is the joining of terrestrial and satellite services into one seamless network that may be readily accessed by the subscriber at the receiver (Evans et al. 2005, Evans et al. 2015, Federal Communications Commission Accessed: 2016). Satellite networks provide their own specific challenges, as transmit power is limited to payload specifications, and coverage typically requires a satellite that is moving relative to the Earth’s surface. Once again we find ourselves facing the same three issues that we encountered within the terrestrial context of a mmWave channel. If we are to increase link performance in a satellite channel to complement any improvement in terrestrial channels then the following points need to be considered: • propagation using higher operating frequencies typically suffers from higher path losses (Liebe et al. 1989, Pozar 2011). In some circumstances this can be mitigated by higher transmit power, but not all. A satellite payload is subject to a strict payload capacity and this restricts the size of transmit power devices and hence available transmit power that can be launched into orbit • a lack of beneficial reflectors, refractors, and scatterers is observed during channel propagation as the signal is typically LoS, narrow in beamwidth, and weak due to higher path loss and lower transmit power (Pi and Khan 2011). Multipath effects may degrade system performance as signals are weak • an evolving link geometry that affects antenna alignment. Linear and circular polarised signals are only two dimensional in nature. Three dimensions need to be considered, and beam steering of radiated power to provide the required range is a requirement (Evans et al. 2005, Hong et al. 2014b). To ensure that the next generation of mobile systems are fully mobile, while providing increased data rate, we need to consider diversity in three dimensions. Beam steering of a transmitted signal with high gain in the direction of a receiver is one viable option, and in the context of full mobility, three dimensional signal transmission and reception appears a logical step to achieving this (Hong et al. 2014a). While at a terrestrial transmitter, it is suggested that size is not a constraint, it remains so for a satellite transmitter, as it is at a mobile receiver. This rules out spatial diversity as an approach to increasing system performance. One approach of increasing diversity within a confined volume is through polarisation techniques (Vaughan 1990). In this thesis, we investigate the benefit of a subset of this approach—tri-orthogonal polarisation diversity (Andrews et al. 2001). In effect, the concept provides at least one additional degree of freedom or layer of diversity over conventional techniques such as circular polarisation. Due to orthogonality in three directions, this approach has a wide field of view, and potentially offers diversity and improved system performance through beam steering in any unit direction. Tri-orthogonal polarisation diversity may be applied either at the transmitter, at the receiver, or at both. In Chapter 1 of the thesis, both novel software and hardware aspects of the research are highlighted. Overall, the research outcomes of this thesis from both simulation and measured results suggest that the concept of tri-orthogonal polarisation diversity is: • beneficial to wireless performance over a majority of antenna orientations • plausible for implementation within typical antenna volume constraints.Thesis (Ph.D.) -- University of Adelaide, School of School of Electrical and Electronic Engineering, 201