Adaptive crosstalk cancellation and Lattice aided detection in multi-user communications

Digital subscriber lines (DSL) have revolutionised the provision of high speed data over the ‘last mile’. Subscribers demand even more bandwidth and the penetration of the service is now nearly universal. While it is feasible to provide improved broadband services on the new very high speed DSL, such as VDSL2/3, one of the greatest challenges to further improvements in speed is the problem of crosstalk. Operating over the unused higher frequencies of the twisted pair network, this technology is subjected to electromagnetic coupling among the wires, limiting the DSL data rate and service reach. Crosstalk suppression methods such as zero-forcing or decision feedback mainly use block processing. However, to cope with the time-varying VDSL environment huge computational costs can be incurred. In contrast, adaptive processing approaches are much simpler and are more beneficial to track such a channel environment. An adaptive canceller uses a training sequence and the convergence speed depends on the number of crosstalk coefficients it has to estimate. In a populated DSL binder, only a few of the crosstalking neighbours to a particular user are significant. With the aim to reduce the computational complexity in such environments, this thesis introduces the concept of detection-guided adaptive crosstalk cancellation for DSL. We propose a least-squares test feature to detect and concentrate the adaptation only on the dominant crosstalking coefficients. In comparison to conventional adaptive cancellers, the cancellers proposed in this thesis demonstrate early convergence. Thus, by incorporating the test feature, these cancellers have to detect only the most significant canceller coefficients and therefore, the length of the training sequence is reduced. Together with enhanced adaptive cancellation with a low run-time complexity and improved convergence, the greatest advantage obtained here is in the bandwidth efficiency. While enhanced adaptive cancellation is a bandwidth-efficient approach, the frequent re-transmission of training sequences may still be required for a rapidly changing VDSL channel. Again, this can be a disadvantage in terms of bandwidth consumption. To overcome this difficulty, we propose fast-converging unsupervised cancellers with an aim to improve the bandwidth efficiency by not transmitting a training sequence. An added advantage obtained here is that this would enable Internet service providers to include multiple or improved broadband services within a single subscription. Certain properties of the DSL channel ensure the communication channel is properly conditioned. This ensures the basis vectors of the channel matrix are near-orthogonal and hence, the linear cancellers, such as zero-forcing perform near-optimally. However, this is not the case with wireless channels. We investigate user detection in wireless channels using the principle of lattice reduction. User detection can also be seen as a search for the closest vector point in the lattice of received symbols. Though a maximum likelihood (ML) detector facilitates optimal user-detection, it has exponential complexity. We identify that the closest vector problem can be cast as a non-linear optimisation problem. Using the periodicity of the maximum likelihood function, we first present a novel algorithm that approximates the ML function using the Taylor series expansion of a suitable cosine function. With the aim of minimising the approximation error, we represent the ML function as a Fourier Series expansion and later, propose another approximation using Jacobi theta functions. We study the performance of these approximations when subjected to a suitable unconstrained optimisation algorithm. Through simulations, we demonstrate that the newly-developed approximations perform better than the conventional cancellers, close to the ML and, importantly, converging in polynomial time