Fernando Domene

A reconfigurable GPU implementation for Tomlinson-Harashima precoding

Fast parallel processing capability of general purpose Graphic Processing Units (GPU) can be exploited to accelerate the precoding calculation needed in spatially multiplexed wireless communication systems. In this paper, a GPU-based implementation of the well-known multiuser Tomlinson-Harashima precoding (THP) scheme combined with a lattice-reduction (LR) stage is presented. The proposed approach allows the LR stage to be switched off when user requirements are achieved by using only THP. Moreover, our GPU implementation provides scalability in the number of sub-carriers per symbol, which is a key factor in LTE and 4G wireless standards. Simulation results show that the GPU-based THP implementation performs up to 7 times faster than its CPU-equivalent whereas the LR stage implementation only achieves a speedup of 3. Despite the fact that the LR cannot be as efficiently parallelized as the THP, a speedup of nearly 6 is achieved when both are combined.

An evaluation of precoding techniques for multiuser communication systems

The lattice reduction method proposed by Lenstra, Lenstra and Lovasz (LLL algorithm) is employed to perform signal precoding in multiuser downlink communications. Efficient implementations of this method have been well investigated, which, as the original algorithm, provide a matrix that contains the transformations to be done over the initial channel matrix in order to get a transformed matrix with less correlated columns. Since there are several precoding algorithms that also make use of the inverse of the channel transformation matrix, in this work we use an efficient way to calculate the inverse of the transformation matrix inside the LLL algorithm. The impact of the preprocessing computational cost reduction in the overall cost of some well-known precoding algorithms is also discussed. In addition, both a computational cost and a performance comparison among the algorithms is included.

A limited feedback scheme based on spatially correlated channels for coordinated multipoint systems

High spectral efficiency can be achieved in the downlink of multi-antenna coordinated multi-point systems provided that the multiuser interference is appropriately managed at the transmitter side. For this sake, downlink channel information needs to be sent back by the users, thus reducing the rate available at the uplink channel. The amount and type of feedback information required has been extensively studied and many limited feedback schemes have been proposed lately. A common pattern to all of them is that achieving low rates of feedback information is possible at the cost of increasing complexity at the user side and, sometimes, assuming that some statistics of the channel are known. In this article, we propose a simple and versatile limited feedback scheme that exploits the spatial correlation at each multi-antenna base station (BS) without requiring any previous statistical information of the channel and without adding significant computational complexity. It is based on the separate quantization of the channel impulse response modulus and phase and it shows better mean square error performance than the standard scheme based on quantization of real and imaginary parts. In order to evaluate the performance of the downlink regarding multiuser interference management, different precoding techniques at the BSs, such as zero-forcing (ZF), Tomlinson-Harashima precoding (THP) and lattice reduction Tomlinson- Harashima precoding (LRTHP), have been evaluated. Simulations results show that LRTHP and THP present a higher robustness than ZF precoding against channel quantization errors but at the cost of a higher complexity at the BS. Regarding sum-capacity and bit error rate performances, our versatile scheme achieves better results than the standard one in the medium and high SNR regime, that is, in the region where quantization errors are dominant against noise, for the same feedback cost measured in bits per user.

Channel Quantization Based on the Statistical Characterization of Spatially Correlated Fading

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 (FDD) 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 to be the reference. The conditional probability density functions (CPDFs) of the envelope and phase of the channel fading coefficients from the rest of the antennas (denoted as nonreference 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 nonreference 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. Numerical simulations have been carried out to compare the performance of the proposed conditional quantization (CQ) scheme with a polar quantization (PQ) and with a quantization based on the Karhunen-Loève (KL) transform. PQ does not consider spatial correlation, CQ needs one spatial correlation coefficient per nonreference antenna, and the KL scheme makes use of the full spatial correlation matrix. The results show that CQ achieves a lower quantization mean square error (MSE) than the other two schemes in highly and moderately correlated environments. When the spatial channel model (SCM) is considered, the proposed scheme allows the spatial correlation to be successfully exploited in arrays with N = 4 and N = 8 transmit antennas for antenna separations that are lower than d= 1.3λ and d=0.75λ, respectively.

High performance lattice reduction on heterogeneous computing platform

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, where several levels of parallelism were exploited: (a) fine-grained parallelism was achieved through the cost-reduced all-swap LLL (CR-AS-LLL) algorithm introduced together with the MB-LLL by Józsa et al. (Proceedings of the tenth international symposium on wireless communication systems, 2013) and (b) coarse-grained parallelism was achieved by applying the block-reduction concept presented by Wetzel (Algorithmic number theory. Springer, New York, pp 323–337, 1998). 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 Gram–Schmidt 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 heterogeneous 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.

Performance of multiuser MIMO-OFDM precoding techniques with quantized channel information

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.

A Channel Quantization Scheme Based on the Karhunen-Loève Transform

Spatial multiplexing techniques in multiuser multiple-input multiple-output orthogonal frequency- division multiplexing (MU-MIMO-OFDM) systems have increased the spectral efficiency of wireless communications systems. However, these systems require an accurate knowledge of the channel at the transmitter, which usually has to be provided by receivers through a low-rate feedback channel. In this paper, we present a channel quantization scheme based on the Karhunen-Loève (KL) transform. This scheme outperforms the scheme based on time-domain quantization in terms of mean square error for a given amount of quantization bits. The comparison has been carried out in a system that presents some unmodulated subcarriers. The computational complexity of both schemes has also been analyzed showing that, when efficient eigendecomposition is used, the scheme based on KL transform has only a slightly higher computational complexity.

A low-complexity joint power control and beamforming algorithm for the downlink of multi-user W-CDMA coordinated systems

The downlink of a system with phase coherent coordination between several base stations is considered throughout this paper. Within the framework of the power minimization problem, two Joint Power Control and Optimal Beamforming (JPCOB) algorithms have already been proposed in previous works. However, one of the major challenges associated with network coordination is the design of algorithms which result in low-complexity requirements as the number of users increases. In this paper, one of the previous JPCOB algorithms is modified in order to obtain a low-complexity solution by reducing the amount of feedback required from single antenna users in the system. The performance of this algorithm is then compared with the previous JPCOB solutions. Simulation results in a W-CDMA scenario show that the low-complexity algorithm equals the performance of the previous solutions for a given number of coordinated base stations. However, it suffers a severe penalty for scenarios with high SINR requirements at the users. In order to overcome this drawback, two iterative schemes based on the particular structure of the matrices involved in the power control updating step are proposed. Moreover, these schemes could be seen as efficient and computationally simple scheduling techniques.

Block diagonalization aided precoding algorithm for large MU-MIMO systems

Large Multi-User Multiple-Input Multiple-Output (MU-MIMO) system is considered as a potential technique to serve a high number of users simultaneously increasing the achievable data rates. By large we mean a large number of transmit antennas (Nt) at the base station (BS) and a large number of downlink users terminals (UTs). In large MU-MIMO systems, the complexity of precoding algorithms becomes a bottleneck. In this work, we propose a low complexity precoder scheme with two steps. In the proposed scheme the UTs are classified into B blocks. Thereby, in the first step, the interference between block users block is mitigated using a Block Diagonalization (BD) method. In the second step, the interference between users belonging to the same block is palliated employing a more complex precoding. Simulation results show that the proposed scheme can achieve suitable performance while offering lower computational complexity than a nonlinear precoding.