This thesis investigates signal processing techniques for wireless communication receivers. The aim is to improve the performance or reduce the computationally complexity of these, where the primary focus area is cellular systems such as Global System for Mobile communications (GSM) (and extensions thereof), but also general Multiple-Input Multiple-Output (MIMO) systems are considered. The motivation for a performance improvement is that this is needed to achieve higher capacity in the systems, which can ensure increased bit-rates at the same or lower prices. A reduction in the computationally complexity can potentially lead to limited power consumption, which translates into longer battery life-time in the handsets. The scope of the thesis is more specifically to investigate approximate (nearoptimal) detection methods that can reduce the computationally complexity significantly compared to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum-phase and all-pass filters. This enables us to view Sphere Detection (SD) as an adaptive variant of minimum-phase prefiltered reduced-state sequence estimation. Thus, a novel way of computing the minimum-phase filter and its associated all-pass filter using the numerically stable QL-factorization is suggested. Alternatively, fast QL-factorization methods can be applied which provides a computationally efficient way of obtaining these filers. Additionally, Markov Chain Monte Carlo (MCMC) sampling has been investigated for near-optimal Maximum Likelihood Sequence Detection in MIMO systems. The MCMC method considered in the thesis is the Gibbs sampler, which is proposed as an alternative to the SD in scenarios where the latter type of detector requires an unacceptable high complexity.