Efficient Integer Coefficient Search for Compute-and-Forward

Integer coefficient selection is an important decoding step in the implementation of compute-and-forward (C-F) relaying scheme. Choosing the optimal integer coefficients in C-F has been shown to be a shortest vector problem (SVP) which is known to be NP hard in its general form. Exhaustive search of the integer coefficients is only feasible in complexity for small number of users while approximation algorithms such as Lenstra-Lenstra-Lovasz (LLL) lattice reduction algorithm only find a vector within an exponential factor of the shortest vector. An optimal deterministic algorithm was proposed for C-F by Sahraei and Gastpar specifically for the real valued channel case. In this paper, we adapt their idea to the complex valued channel and propose an efficient search algorithm to find the optimal integer coefficient vectors over the ring of Gaussian integers and the ring of Eisenstein integers. A second algorithm is then proposed that generalises our search algorithm to the Integer-Forcing MIMO C-F receiver. Performance and efficiency of the proposed algorithms are evaluated through simulations and theoretical analysis.Comment: IEEE Transactions on Wireless Communications, to appear.12 pages, 8 figure

Optimal Lattice-Reduction Aided Successive Interference Cancellation for MIMO Systems

In this letter, we investigated the optimal minimummean-squared-error (MMSE) based successive interference cancellation (SIC) strategy designed for lattice-reduction aided multiple-input multiple-output (MIMO) detectors. For the sake of generating the MMSE-based MIMO symbol estimate at each SIC detection stage, we model the so-called effective symbols generated with the aid of lattice-reduction as joint Gaussian distributed random variables. However, after lattice-reduction, the effective symbols become correlated and exhibit a non-zero mean. Hence, we derive the optimal MMSE SIC detector, which updates the mean and variance of the effective symbols at each SIC detection stage. As a result, the proposed detector achieves a better performance compared to its counterpart dispensing with updating the mean and variance, and performs close to the maximum likelihood detector. Index Terms—Lattice-reduction, multiple antennas, MIMO, symbol detection, SIC detector

Bound-intersection detection for multiple-symbol differential unitary space-time modulation

This paper considers multiple-symbol differential detection (MSD) of differential unitary space-time modulation (DUSTM) over multiple-antenna systems. We derive a novel exact maximum-likelihood (ML) detector, called the bound-intersection detector (BID), using the extended Euclidean algorithm for single-symbol detection of diagonal constellations. While the ML search complexity is exponential in the number of transmit antennas and the data rate, our algorithm, particularly in high signal-to-noise ratio, achieves significant computational savings over the naive ML algorithm and the previous detector based on lattice reduction. We also develop four BID variants for MSD. The first two are ML and use branch-and-bound, the third one is suboptimal, which first uses BID to generate a candidate subset and then exhaustively searches over the reduced space, and the last one generalizes decision-feedback differential detection. Simulation results show that the BID and its MSD variants perform nearly ML, but do so with significantly reduced complexity

Joint data detection and channel estimation for OFDM systems

We develop new blind and semi-blind data detectors and channel estimators for orthogonal frequency-division multiplexing (OFDM) systems. Our data detectors require minimizing a complex, integer quadratic form in the data vector. The semi-blind detector uses both channel correlation and noise variance. The quadratic for the blind detector suffers from rank deficiency; for this, we give a low-complexity solution. Avoiding a computationally prohibitive exhaustive search, we solve our data detectors using sphere decoding (SD) and V-BLAST and provide simple adaptations of the SD algorithm. We consider how the blind detector performs under mismatch, generalize the basic data detectors to nonunitary constellations, and extend them to systems with pilots and virtual carriers. Simulations show that our data detectors perform well

Dual-lattice ordering and partial lattice reduction for SIC-based MIMO detection

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, we propose low-complexity lattice detection algorithms for successive interference cancelation (SIC) in multi-input multi-output (MIMO) communications. First, we present a dual-lattice view of the vertical Bell Labs Layered Space-Time (V-BLAST) detection. We show that V-BLAST ordering is equivalent to applying sorted QR decomposition to the dual basis, or equivalently, applying sorted Cholesky decomposition to the associated Gram matrix. This new view results in lower detection complexity and allows simultaneous ordering and detection. Second, we propose a partial reduction algorithm that only performs lattice reduction for the last several, weak substreams, whose implementation is also facilitated by the dual-lattice view. By tuning the block size of the partial reduction (hence the complexity), it can achieve a variable diversity order, hence offering a graceful tradeoff between performance and complexity for SIC-based MIMO detection. Numerical results are presented to compare the computational costs and to verify the achieved diversity order