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Jozsa, CM.; Domene Oltra, F.; Vidal Maciá, AM.; Piñero Sipán, MG.; González Salvador, A. (2014). High performance lattice reduction on heterogeneous computing platform. Journal of Supercomputing. 70(2):772-785. doi:10.1007/s11227-014-1201-2. Abstract The lattice reduction (LR) technique has become very important in many engineering fields. However, its high complexity makes difficult its use in real-time applications, especially in applications that deal with large matrices. As a solution, the Modified Block LLL (MB-LLL) algorithm was introduced in [10], where several levels of parallelism were exploited: (i.) coarse-grained parallelism was achieved by applying the block-reduction concept presented in [15] and (ii.) fine-grained parallelism was achieved through the Cost Reduced All-Swap LLL (CR-AS-LLL) algorithm introduced in [10].In this paper, we present the Cost Reduced MB-LLL (CR-MB-LLL) algorithm, which allows to significantly reduce the computational complexity of the MB-LLL by allowing the relaxation of the first LLL condition while executing the LR of submatrices, resulting in the delay of the GS coefficients update and by using less costly procedures during the boundary checks. The effects of complexity reduction and implementation details are analyzed and discussed for several architectures. A mapping of the CR-MB-LLL on a heterogenenous platform is proposed and it is compared with implementations running on a dynamic parallelism enabled GPU and a multi-core CPU. The mapping on the architecture proposed allows a dynamic scheduling of kernels where the overhead introduced is hidden by the use of several CUDA streams. Results show that the execution time of the CR-MB-LLL algorithm on the heterogeneous platform outperforms the multi-core CPU and it is more efficient than the CR-AS-LLL algorithm in case of large matrices.

Multiuser multiple-input multiple-output (MU-MIMO) techniques, such as scheduling and precoding, have shown to improve the spectral efficiency of wireless communication systems. However, these techniques require an accurate knowledge of the channel of the different users at the transmitter. In frequency division duplex systems, this information has to be provided by the different users, motivating the research of efficient limited feedback schemes. This paper presents a novel statistical characterization of the spatial multiple-input single-output (MISO) channel. In this characterization, one antenna is selected as the reference and the channel fading experienced from this antenna is also considered as reference. The conditional probability density functions (CPDF) of the envelope and phase of the channel fading coefficients from the rest of the antennas (denoted as non-reference channel fading and nonreference antennas) are obtained given the reference one. Based on this statistical characterization, this paper proposes a channel quantization scheme that individually quantizes the channel fading coefficient of each transmit antenna that is seen by each user. The envelope and phase of the reference channel fading are quantized considering a Rayleigh distribution and a uniform distribution, respectively. The non-reference channel fading coefficients are quantized according to their respective CPDFs, which in turn depend on the spatial correlation between each channel fading and the reference channel fading.

It is well known that precoding techniques in multiuser multiple-input multiple-output (MU-MIMO) communication systems improve the whole data throughput since they allow for spatial multiplexing of different users. However, these techniques require a precise knowledge of the channel information at the transmitter. In most of the current systems, transmitter can not estimate the channel so feedback information has to be provided by the receiver. In this paper, we propose a new limited feedback approach where Vector Quantization (VQ) is applied over the channel frequency response. Different configurations of feedback bits per subcarrier in a multiuser MIMO-OFDM system have been simulated. Additionally, different precoding schemes based on the estimated channel information have been tested and BER performance has been evaluated. Results show that, for a similar cost of feedback information (bits/subcarrier), better channel estimates are achieved using longer vectors in the VQ codebook, whereas optimal non-linear precoding schemes perform well even for large channel estimation errors.