Matrix Differential Calculus with Applications in Statistics and Econometrics

The fifth generation (5G) wireless network technology is to be standardized by 2020, where main goals are to improve capacity, reliability, and energy efficiency, while reducing latency and massively increasing connection density. An integral part of 5G is the capability to transmit touch perception type real-time communication empowered by applicable robotics and haptics equipment at the network edge. In this regard, we need drastic changes in network architecture including core and radio access network (RAN) for achieving end-to-end latency on the order of 1 ms. In this paper, we present a detailed survey on the emerging technologies to achieve low latency communications considering three different solution domains: 1) RAN; 2) core network; and 3) caching. We also present a general overview of major 5G cellular network elements such as software defined network, network function virtualization, caching, and mobile edge computing capable of meeting latency and other 5G requirements.

A Survey on Low Latency Towards 5G: RAN, Core Network and Caching Solutions

A hybrid antenna is proposed for future 4G/5G multiple input multiple output (MIMO) applications. The proposed antenna is composed of two antenna modules, namely, 4G antenna module and 5G antenna module. The 4G antenna module is a two-antenna array capable of covering the GSM850/900/1800/1900, UMTS2100, and LTE2300/2500 operating bands, while the 5G antenna module is an eight-antenna array operating in the 3.5-GHz band capable of covering the $C$ -band (3400–3600 MHz), which could meet the demand of future 5G application. Compared with ideal uncorrelated antennas in an $8 \times 8$ MIMO system, the 5G antenna module has shown good ergodic channel capacity of $\sim 40$ b/s/Hz, which is only 6 b/s/Hz lower than ideal case. This multi-mode hybrid antenna is fabricated, and typically, experimental results such as S-parameter, antenna efficiency, radiation pattern, and envelope correlation coefficient are presented.

4G/5G Multiple Antennas for Future Multi-Mode Smartphone Applications

In this paper, we create a framework for training-based channel estimation under different channel and interference statistics. The minimum mean square error (MMSE) estimator for channel matrix estimation in Rician fading multi-antenna systems is analyzed, and especially the design of mean square error (MSE) minimizing training sequences. By considering Kronecker-structured systems with a combination of noise and interference and arbitrary training sequence length, we collect and generalize several previous results in the framework. We clarify the conditions for achieving the optimal training sequence structure and show when the spatial training power allocation can be solved explicitly. We also prove that spatial correlation improves the estimation performance and establish how it determines the optimal training sequence length. The analytic results for Kronecker-structured systems are used to derive a heuristic training sequence under general unstructured statistics. The MMSE estimator of the squared Frobenius norm of the channel matrix is also derived and shown to provide far better gain estimates than other approaches. It is shown under which conditions training sequences that minimize the non-convex MSE can be derived explicitly or with low complexity. Numerical examples are used to evaluate the performance of the two estimators for different training sequences and system statistics. We also illustrate how the optimal length of the training sequence often can be shorter than the number of transmit antennas.

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A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels With Rician Disturbance

A new direction-of-arrival (DOA) estimation method is proposed based on a novel data model using the concept of a sparse representation of array covariance vectors (SRACV), in which DOA estimation is achieved by jointly finding the sparsest coefficients of the array covariance vectors in an overcomplete basis. The proposed method not only has high resolution and the capability of estimating coherent signals based on an arbitrary array, but also gives an explicit error-suppression criterion that makes it statistically robust even in low signal-to-noise-ratio (SNR) cases. Simulation experiments are conducted to validate the effectiveness of the proposed method. The performance is compared with several existing DOA estimation methods and the Cramer-Rao lower bound (CRLB).

Direction-of-Arrival Estimation Using a Sparse Representation of Array Covariance Vectors

The estimation of signal covariance matrices is a crucial part of many signal processing algorithms. In some applications, the structure of the problem suggests that the underlying, true covariance matrix is the Kronecker product of two valid covariance matrices. Examples of such problems are channel modeling for multiple-input multiple-output (MIMO) communications and signal modeling of EEG data. In applications, it may also be that the Kronecker factors in turn can be assumed to possess additional, linear structure. The maximum-likelihood (ML) method for the associated estimation problem has been proposed previously. It is asymptotically efficient but has the drawback of requiring an iterative search for the maximum of the likelihood function. Two methods that are fast and noniterative are proposed in this paper. Both methods are shown to be asymptotically efficient. The first method is a noniterative variant of a well-known alternating maximization technique for the likelihood function. It performs on par with ML in simulations but has the drawback of not allowing for extra structure in addition to the Kronecker structure. The second method is based on covariance matching principles and does not suffer from this drawback. However, while the large sample performance is the same, it performs somewhat worse than the first estimator in small samples. In addition, the Cramer-Rao lower bound for the problem is derived in a compact form. The problem of estimating the Kronecker factors and the problem of detecting if the Kronecker structure is a good model for the covariance matrix of a set of samples are related. Therefore, the problem of detecting the dimensions of the Kronecker factors based on the minimum values of the criterion functions corresponding to the two proposed estimation methods is also treated in this work.

On Estimation of Covariance Matrices With Kronecker Product Structure

Estimating MIMO channel covariances from training data under the Kronecker model

5G radio access technology is envisioned to operate from sub-1 GHz to 100 GHz using a wide range of deployment options and to support diverse services. This paper proposes OFDM numerology and frame structure for 5G radio access. The numerology is proposed keeping in view realistic propagation channel measurements, mobility, effect of phase noise, and implementation complexity. The frame structure is proposed for both FDD and TDD. The proposed frame structure is flexible, scalable, and fulfills low latency requirements.

Numerology and frame structure for 5G radio access

The 3GPP LTE standard for mobile broadband includes multi-antenna transmission modes that improve performance, both in terms of coverage, spectral efficiency and peak throughput. The antenna system design, both at the eNB and at the UE is critical to a well performing system; it should be designed with the intended performance profile in mind. Field trials were performed in order to investigate the relative performance of several four and two transmit antenna setups in an LTE system. In general, multi-antenna technology gave substantial performance gains over single antenna transmission. A closely spaced co-polarized configuration gave the best performance for users with poor channel quality while dual-polarized and well-spaced antenna configurations gave better performance for users with good channel quality. The trial also shows that UE antenna polarization is an important parameter that must be kept in mind when designing the eNB antenna system.

Antenna Configurations for 4x4 MIMO in LTE - Field Measurements

Techniques are disclosed for allocating time-frequency resources in a system that uses multiple multicarrier modulation numerologies. According to one aspect, a method in a first wireless node comprises allocating (1310) time-frequency resources for use by a second wireless node, where said allocating comprises selecting, for use in multicarrier modulation in the allocated time-frequency resources, one of two or more subcarrier bandwidths that the second wireless node is adapted to use for modulating or demodulating of data. In some embodiments, the method further comprises sending (1320) resource allocation information to the second wireless node, the resource allocation information identifying the allocated time-frequency resources.

Karl Werner

Papers

On Estimation of Covariance Matrices With Kronecker Product Structure

Estimating MIMO channel covariances from training data under the Kronecker model

Numerology and frame structure for 5G radio access

Antenna Configurations for 4x4 MIMO in LTE - Field Measurements

Resource allocation for data transmission in wireless systems