The detection in multiuser (MUD) and multiple-input multiple-output (MIMO) systems can increase the
spectral efficiency, and therefore is of great interest. Although multiuser and MIMO detection is mature in
theory, the real-time implementation is still an open issue. Many suboptimal detection schemes have been
proposed, possessing low computational load, but also having poorer detection performance compared to
the optimal detector. Multiuser detection can be described as a solution of an optimisation problem; in
most cases it is the quadratic optimisation problem. Unconstrained quadratic optimisation is known to result
in decorrelating and MMSE multiuser detection, which cannot provide high detection performance.
The optimal detection is equivalent to the solution of a constrained problem. However, such detection is
too complex for practical systems. In this work, we propose several detectors which possess low complexity
and high detection performance. These detectors are based on Dichotomous Coordinate Descent
(DCD) iterations, which are multiplication and division free, and therefore are attractive for real-time implementation.
We propose a box-constrained DCD algorithm, and apply it to multiuser detection. We also
design an FPGA architecture of the box-constrained DCD detector and implement it in an FPGA. This
design requires a very small area usage. The fixed-point implementation offers a constant throughput over
the signal-to-noise ratio (SNR) and provides almost same detection performance as that of a floating-point
implementation. We further exploit the box-constrained DCD algorithm and propose a complex-valued
box-constrained DCD algorithm. A box-constrained MIMO detector based on the DCD algorithm shows
a better detection performance than the MMSE detector. The proposed FPGA design requires a small area
usage, which is significantly less than that required by known designs of the MMSE MIMO detector. Since
the box-constrained DCD algorithm could not offer the optimal detection performance, while the sphere
decoder encounters high complexity at low SNRs, we suggest a combination of the box-constrained DCD
algorithm with the sphere decoder (fast branch and bound algorithm). The combined detection results in
reduced complexity at low SNRs while retaining outstanding detection performance at all SNRs. As the
box-constrained DCD algorithm is efficient for hardware implementation, we apply it to the nonstationary
iterative Tikhonov regularization and propose a DCD-BTN detector. The DCD-BTN detector shows the
detection performance very close to the optimal performance. It also shows the lowest complexity among
the most advanced detectors. An architecture of the detector has been developed. This detector has been
implemented on an FPGA platform. The design requires a small number of FPGA slices. Numerical results
have shown that the fixed-point FPGA implementation and a floating-point implementation have similar
detection performance. The DCD-BTN detector can only be applied in systems with BPSK modulation.
Therefore, we also propose a multiple phase decoder (MPD), which is based on a phase descent search
(PDS) algorithm. The PDS algorithm uses coordinate descent iterations, where coordinates are unknown
symbol phases, while constraining the symbols to have a unit magnitude. The MPD is investigated in application
to detection of M-PSK symbols in multiuser and MIMO systems. In the multiuser detection, the
MPD is applied to highly loaded scenarios and numerical results show that it provides the near-optimal performance
at low complexity. The MPD significantly outperforms such advanced detector as the semidefinite
relaxation detector in both the detection performance and complexity. In MIMO systems, the MPD exhibits
more favorable performance/complexity characteristics and can be considered as a promising alternative
to the sphere decoder. The matrix inversion is required in many applications. The complexity of matrix
inversion is too high and makes its implementation difficult. To overcome the problem, we propose an
approach based on the DCD algorithm to simplify the matrix inversion. This approach obtains separately
the individual columns of the inverse matrix and costs a very small number of slices, which is suitable for
application, e.g. in MIMO-OFDM systems.
