Lattice Sphere Decoding Research Articles

Spatial Lattice Modulation for MIMO Systems

This paper proposes spatial lattice modulation (SLM), a spatial modulation method for multipleinput-multiple-output (MIMO) systems. The key idea of SLM is to jointly exploit spatial, in-phase, and quadrature dimensions to modulate information bits into a multi-dimensional signal set that consists oflattice points. One major finding is that SLM achieves a higher spectral efficiency than the existing spatial modulation and spatial multiplexing methods for the MIMO channel under the constraint ofM-ary pulseamplitude-modulation (PAM) input signaling per dimension. In particular, it is shown that when the SLM signal set is constructed by using dense lattices, a significant signal-to-noise-ratio (SNR) gain, i.e., a nominal coding gain, is attainable compared to the existing methods. In addition, closed-form expressions for both the average mutual information and average symbol-vector-error-probability (ASVEP) of generic SLM are derived under Rayleigh-fading environments. To reduce detection complexity, a low-complexity detection method for SLM, which is referred to as lattice sphere decoding, is developed by exploiting lattice theory. Simulation results verify the accuracy of the conducted analysis and demonstrate that the proposed SLM techniques achieve higher average mutual information and lower ASVEP than do existing methods.

Regularized Lattice Sphere Decoding for Block Data Transmission Systems

This paper presents Lattice Sphere Decoding (LSD) with regularization techniques for block data transmission systems. It has shown that a small condition number ($$\tau $$?) results in better detection performance. This paper aims to reduce this value to its smallest possible value. Regularization technique offers reduction in condition number ($$\tau $$?) that improves LSD performance. In this work, two regularization techniques are utilized on LSD. First, $$\hbox {L}_{1}$$L1-regularization method is introduced, which sums the mixed norms. Second, $$\hbox {L}_{2}$$L2- regularization method, which is the most commonly used method of regularization for ill-conditioned problems in mathematics. We derive the exact relationship between the LSD performance and condition number ($$\tau $$?) as well as the relationship between LSD initial radius (d) and condition number ($$\tau $$?). The derived equations show their convergence to the fact that the performance increases as the radius (d) increases. Simulation results show that the LSD with $$\hbox {L}_{1}$$L1-regularization technique offers smaller condition number ($$\tau $$?), and therefore, produces better system performance. From the performance results and the complexity analysis, it is apparent that the proposed techniques achieve a good balance between complexity and performance.

Lattice Sphere Decoding for Data Transmission Systems with Special Channel Matrices

This paper presents the effects of condition number ( $$\tau $$ ? ) in communication system performance. It has been shown that a small condition number ( $$\tau $$ ? ) results a better performance. The proposed scheme is using special kind of matrices with Lattice Sphere Decoding (LSD) technique for Block Data Transmission Systems (BDTS). Hankel and Toeplitz matrices are used separately as a channel matrix (H) while circulant matrix is used in the previous works. The proposed scheme reduced the condition number ( $$\tau $$ ? ) and, therefore, improve the system performance. As a result; LSD-based BDTS with Toeplitz/Hankel matrix outperforms the LSD-based BDTS with circulant matrix. Complexity analysis is also done which based on lattice dimension and initial radius selection.

Reduced complexity optimum detector for block data transmission systems using Lattice Sphere Decoding technique

The complexity of the exhaustive search decoding technique such as Maximum Likelihood Block Detection (MLBD) grows exponentially with the size of transmitted data. In this paper, a Lattice Sphere Decoding (LSD) technique is proposed for detection in block data transmission systems (BDTS). Simulation results at 10dB channel SNR of BDTS with LSD using block size of 20 performs are near Hybrid Micro Genetic Algorithm (HMGA) and slightly inferior than the exhaustive search technique using the channels with spectral nulls. In term of complexity, the proposed LSD technique requires only 460 and 126 objective functions evaluation using radius selection based on Babai Estimation (BE) and off-line observation respectively, while the HMGA and exhaustive search requires 3750 and 220 objective functions evaluation respectively.