Karol Schober

System-level performance of LTE-Advanced with joint transmission and dynamic point selection schemes

In this article, we present a practical coordinated multipoint (CoMP) system for LTE-Advanced. In this CoMP system, cooperation is enabled for cell-edge users via dynamic switching between the normal single-cell operation and CoMP. We first formulate a general CoMP system model of several CoMP schemes. We then investigate a practical finite-rate feedback design that simultaneously supports interference coordination, joint transmission (JT), and dynamic point selection (DPS) with a varying number of cooperating transmission points while operating a single-cell transmission as a fallback mode. We provide both link-level and system-level results for the evaluation of different feedback options for general CoMP operation. The results show that there are substantial performance gains in cell-edge throughputs for both JT and DPS CoMP over the baseline Release 10 LTE-Advanced with practical feedback options. We also show that CoMP can enable improved mobility management in real networks.

Beamforming Codebooks for Two Transmit Antenna Systems Based on Optimum Grassmannian Packings

Precoding codebook design for limited feedback MIMO systems is known to reduce to a discretization problem on a Grassmann manifold. The case of two-antenna beamforming is special in that it is equivalent to quantizing the real sphere. The isometry between the Grassmannian G2,1ℂ and the real sphere S2 shows that discretization problems in the Grassmannian G2,1ℂ are directly solved by corresponding spherical codes. Notably, the Grassmannian line packing problem in ℂ2, namely maximizing the minimum distance, is equivalent to the Tammes problem on the real sphere, so that optimum spherical packings give optimum Grassmannian packings. Moreover, a simple isomorphism between G2,1ℂ and S2 enables to analytically derive simple codebooks in closed-form having low implementation complexity. Using the simple geometry of some of these codebooks, we derive closed-form expressions of the probability density function of the relative SNR loss due to limited feedback. We also investigate codebooks based on other spherical arrangements, such as solutions maximizing the harmonic mean of the mutual distances among the codewords, which is known as the Thomson problem. We find that in some special cases, Grassmannian codebooks based on these other spherical arrangements outperform codebooks from Grassmannian packing.

Geodesical codebook design for precoded MIMO systems

We propose a numerical method for finding packings of multiple-input and multiple-output (MIMO) semi-unitary precoding matrices in Grassmannian manifolds with different metrics. The proposed expansion-compression algorithm (ECA) is practical, simple and produces efficient packings without the need for a sophisticated initialization. With chordal distance metric, the algorithm tends to converge into a degenerated point constellation, where two points contain identical as well as orthogonal columns and distance between them cannot increase further along geodesic. Therefore, we alternate between max-min and min-max clustering parts of ECA algorithm, where the latter prevents degenerated constellations. With Fubini-Study distance metric, the algorithm converges to best known packings without extra min-max processing.

Reference Signal Design for Flexible MIMO Operation in LTE-Advanced Downlink

In this paper we address the issue of demodulation reference signal design for LTE-Advanced downlink. Practical systems such as LTE-Advanced should operate in highly time-frequency selective environment. Hence, they impose a very tight trade-off between the radio resources available for reference signals used for channel estimation and spectral efficiency targets to be met. As an additional constraint, LTE-Advanced brings to real deployments state-of-the-art multi-antenna technologies such as multi-user MIMO and cooperative MIMO. The difficult radio environment and the multitude of different multi-antenna techniques set very high challenges to the reference signal design. In this paper we discuss selected issues of realistic demodulation reference signal design for LTE-Advanced. We highlight the trade-offs that are needed for enabling advanced MIMO technologies, while at the same time allowing low complexity channel estimation at the receiver side without increasing related signaling overhead. Based on the analysis we propose a certain reference signal design for LTE-Advanced that fulfills all the required design criteria.

Precoder partitioning in closed-loop MIMO systems

We study unitary precoding for multistream MIMO systems with partial channel state information at the transmitter. We introduce a quantization scheme in which the full space of non-equivalent precoding matrices is partitioned into Grassmannian and orthogonalization parts. The Grassmannian part is used for maximizing the power after precoding and the orthogonalization part is used for removing cross talk between the data streams. We show that orthogonalization improves the attainable capacity when the receiver is linear. We give a parametrization for the non-equivalent orhogonalization matrices and a metric which measures the orthogonality of the transmission. Optimal orthogonalization codebooks for two-stream transmission are presented. When feedback is limited, the optimal partitioning of feedback bits between Grassmannian and orthogonalization parts becomes an issue. In correlated scenarios, the number of feedback bits may be significantly reduced by investing bits into the orthogonalization part.

MIMO-OFDM Channel Estimation with Eigenbeamforming and User-Specific Reference Signals

MIMO-OFDM systems with channel reciprocity allow spatial multiplexing using Eigenbeamforming. However, Eigenbeamforming requires singular value decomposition, which is phase ambiguous and causes the precoded channel to become phase discontinuous in frequency domain. This changes statistical properties of channel components, which degrades the perfor- mance of channel estimation. In this paper we propose phase unifying method to improve channel statistics and consequently decrease the error in channel estimation. In addition, we investigate the 2D-Wiener channel estimation with respect to different channel frequency correla- tion functions. The performance is evaluated using LTE link simulator.

Layer arrangement for single-user coordinated multi-point transmission

Coordinated multi point transmission is an attractive technology to minimize interference in single frequency networks and such to improve data rates. In this paper, we study closed-loop single user joint transmission (JT-MIMO) system. We propose to feedback a layer arrangement matrix together with per transmission point channel state information (CSI). In case of two layers, we provide a simple method to find an optimal layer arrangement. Furthermore, we propose a low complexity algorithm when an exhaustive search over the different layer arrangements becomes unbearable. System level simulation results show that the flexible layer arrangement outperforms traditional rank adaptation with only small amount of additional feedback.

Refinement of MIMO limited-feedback using second best codeword

This paper presents a new low complexity method of providing improved channel state information at the transmitter within closed-loop MIMO systems. We propose to feedback the second best codeword in addition to the best codeword. At the transmitter, these two precoding codewords are interpolated using geodesic. The optimal interpolation parameter is derived in closed-form for single-stream transmission. The performance of the proposed method with b-bit codewords is shown to be close to a codebook with 2b-bit codewords, while our method has significantly lower computational complexity.

Improved User-Specific Channel Estimation Using Geodesical Interpolation at the Transmitter

In this letter we study a precoding matrix (PM) interpolation in the context of user-specific channel estimation. We interpolate the fed-back PMs at the transmitter by the means of geodesic to enable continuous channel estimation across continuously scheduled frequency clusters in the receiver. The proposed scheme is compared to the case where a single PM is used for all sub-carriers within a frequency cluster and channel estimation can be performed only within that cluster. We compare the performance of geodesical interpolation on Grassmann, Stiefel, and Flag manifolds. For this purpose, we provide an iterative framework to obtain geodesics on Stiefel and Flag manifolds based on boundary conditions. We show by monte-carlo simulations that the interpolation of fed-back PMs at the transmitter improves significantly the quality of channel estimation.

MIMO adaptive codebook for cross-polarized antenna arrays

In this paper we address the design of MIMO double codebook structure for cross-polarized antenna arrays. Double codebooks consist of two codebook components, a wide-band long-term component and a short-term sub-band component. Herein we study particularly the two layer short-term sub-band component and provide the complete set of structure types leading to orthogonal constant modulus codewords and cross-polarization phase of M-PSK alphabet. By 3GPP LTE system simulations we show that a novel, two layer structure type, provides significant improvements in channels with large angular spreads.