The study of the spatial aspects of multipath in wireless communications environments is an increasingly important addition to the study of the temporal aspects in the search for ways to increase the utilization of the available wireless channel capacity. Traditionally, multipath has been viewed as an encumbrance in wireless communications, two of the major impairments being signal fading and intersymbol interference. However, recently the potential advantages of the diversity offered by multipath rich environments in multiuser communications have been recognised. Space time coding, for example, is a recent technique which relies on a rich scattering environment to create many practically uncorrelated signal transmission channels. Most often, statistical models have been used to describe the multipath environments in such applications. This approach has met with reasonable success but is limited when the statistical nature of a field is not easily determined or is not readily described by a known distribution.¶ Our primary aim in this thesis is to probe further into the nature of multipath environments in order to gain a greater understanding of their characteristics and diversity potential. We highlight the shortcomings of beamforming in a multipath multiuser access environment. We show that the ability of a beamformer to resolve two or more signals in angle directly limits its achievable capacity.¶ We test the probity of multipath as a source of spatial diversity, the limiting case of which is co-located users. We introduce the concept of separability to define the fundamental limits of a receiver to extract the signal of a desired user from interfering users’ signals and noise. We consider the separability performances of the minimum mean square error (MMSE), decorrelating (DEC) and matched filter (MF) detectors as we bring the positions of a desired and an interfering user closer together. We show that both the MMSE and DEC detectors are able to achieve acceptable levels of separability with the users as close as λ/10.¶ In seeking a better understanding of the nature of multipath fields themselves, we take two approaches. In the first we take a path oriented approach. The effects on the variation of the field power of the relative values of parameters such as amplitude and propagation direction are considered for a two path field. The results are applied to a theoretical analysis of the behaviour of linear detectors in multipath fields. This approach is insightful for fields with small numbers of multipaths, but quickly becomes mathematically complex.¶ In a more general approach, we take a field oriented view, seeking to quantify the complexity of arbitrary fields. We find that a multipath field has an intrinsic dimensionality of (πe)R/λ≈8.54R/λ, for a field in a two dimensional circular region, increasing only linearly with the radius R of the region. This result implies that there is no such thing as an arbitrarily complicated multipath field. That is, a field generated by any number of nearfield and farfield, specular and diffuse multipath reflections is no more complicated than a field generated by a limited number of plane waves. As such, there are limits on how rich multipath can be. This result has significant implications including means: i) to determine a parsimonious parameterization for arbitrary multipath fields and ii) of synthesizing arbitrary multipath fields with arbitrarily located nearfield or farfield, spatially discrete or continuous sources. The theoretical results are corroborated by examples of multipath field analysis and synthesis.

Synchronization between base stations is a fundamental part of any operating telecommunication system. With 5G and future generations of mobile networks, the data speeds are getting higher, which creates the need for fast and accurate synchronization. In wireless systems, the transmitted signals are affected by the environment. Both moving and stationary objects can cause a transmitted signal to be scattered or reflected, causing the receiver to receive multiple instances of one signal. If a synchronization signal is transmitted from one base station and received in multiple instances by another, it is hard for the receiving base station to know which of the received instances that should be used for calculating the synchronization error between the base stations. In this thesis, multiple different algorithms for selecting a synchronization signal pair between two base stations to be used for calculating time alignment error have been tested. The results have been evaluated based on their accuracy of selecting a correct matching signal pair. It is shown that the proposed algorithms in this thesis all perform significantly better than the method currently in use. Further, the advantages and disadvantages of each of the new algorithms are discussed, and finally new concepts for future studies are suggested. / Synkronisering mellan basstationer är en fundamental del av ett fungerande telekommunikationssystem. Med 5G och framtida generationer av mobila nätverk så ökas datahastigheter, vilket skapar behovet av en snabb och precis synkronisering. I trådlösa system påverkas skickade signaler av dess omgivning. Både stationära och icke-stationära objekt i omgivningen kan splittra eller reflektera signaler, vilket ger upphov till en flervägskanal. Detta gör att en mottagare kan ta emot flera instanser av en skickad signal. Om en synkroniseringssignal skickas från en basstation via en flervägskanal till en mottagande basstation, så kommer mottagaren att ta emot flera instanser av den skickade signalen vid olika tidpunkter. Det kan då vara svårt för mottagaren att avgöra vilken av de mottagna signalerna som ska användas vid beräkning av tidsfelet mellan basstationerna. I detta examensarbete testas ett flertal olika algoritmer för att välja vilket synkroniseringssignalpar som ska användas vid beräkning av tidsfelet mellan två basstationer. Resultatet utvärderas baserat på hur hög precision algoritmen har i att välja ett korrekt matchat synkroniseringssignalpar. Resultatet visar att de algoritmer som presenteras i denna uppsats presterar märkbart bättre än den algoritm som används i systemen just nu. Vidare diskuteras fördelar och nackdelar med de olika algoritmerna och förslag på vidareutveckling av algoritmerna läggs fram.