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Convex Analysisの二,三の進展について

The increasing demand of mobile Internet and the Internet of Things poses challenging requirements for 5G wireless communications, such as high spectral efficiency and massive connectivity. In this article, a promising technology, non-orthogonal multiple access (NOMA), is discussed, which can address some of these challenges for 5G. Different from conventional orthogonal multiple access technologies, NOMA can accommodate much more users via nonorthogonal resource allocation. We divide existing dominant NOMA schemes into two categories: power-domain multiplexing and code-domain multiplexing, and the corresponding schemes include power-domain NOMA, multiple access with low-density spreading, sparse code multiple access, multi-user shared access, pattern division multiple access, and so on. We discuss their principles, key features, and pros/cons, and then provide a comprehensive comparison of these solutions from the perspective of spectral efficiency, system performance, receiver complexity, and so on. In addition, challenges, opportunities, and future research trends for NOMA design are highlighted to provide some insight on the potential future work for researchers in this field. Finally, to leverage different multiple access schemes including both conventional OMA and new NOMA, we propose the concept of software defined multiple access (SoDeMA), which enables adaptive configuration of available multiple access schemes to support diverse services and applications in future 5G networks.

Non-orthogonal multiple access for 5G: solutions, challenges, opportunities, and future research trends

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Communication at millimeter wave (mmWave) frequencies is defining a new era of wireless communication. The mmWave band offers higher bandwidth communication channels versus those presently used in commercial wireless systems. The applications of mmWave are immense: wireless local and personal area networks in the unlicensed band, 5G cellular systems, not to mention vehicular area networks, ad hoc networks, and wearables. Signal processing is critical for enabling the next generation of mmWave communication. Due to the use of large antenna arrays at the transmitter and receiver, combined with radio frequency and mixed signal power constraints, new multiple-input multiple-output (MIMO) communication signal processing techniques are needed. Because of the wide bandwidths, low complexity transceiver algorithms become important. There are opportunities to exploit techniques like compressed sensing for channel estimation and beamforming. This article provides an overview of signal processing challenges in mmWave wireless systems, with an emphasis on those faced by using MIMO communication at higher carrier frequencies.

An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems

We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.

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CasADi: a software framework for nonlinear optimization and optimal control

We examine and compare the different types of linear transmit processing for multiple input, multiple output systems, where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters. We can identify three filter types similar to receive processing: the transmit matched filter, the transmit zero-forcing filter, and the transmit Wiener filter. We show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power. Moreover, the transmit Wiener filter has similar convergence properties as the receive Wiener filter, i.e., it converges to the matched filter and the zero-forcing filter for low and high signal-to-noise ratio, respectively. We give closed-form solutions for all transmit filters and present the fundamental result that their mean-square errors are equal to the errors of the respective receive filters, if the information symbols and the additive noise are uncorrelated. However, our simulations reveal that the bit-error ratio results of the transmit filters differ from the results for the respective receive filters.

Linear transmit processing in MIMO communications systems

To achieve the full multiplexing gain of MIMO interference networks at high SNRs, the interference from different transmitters must be aligned in lower-dimensional subspaces at the receivers. Recently a distributed “max-SINR” algorithm for precoder optimization has been proposed that achieves interference alignment for sufficiently high SNRs. We show that this algorithm can be interpreted as a variation of an algorithm that minimizes the sum Mean Squared Error (MSE). To maximize sum utility, where the utility depends on rate or SINR, a weighted sum MSE objective is used to compute the beams, where the weights are updated according to the sum utility objective. We specify a class of utility functions for which convergence of the sum utility to a local optimum is guaranteed with asynchronous updates of beams, receiver filters, and utility weights. Numerical results are presented, which show that this method achieves interference alignment at high SNRs, and can achieve different points on the boundary of the achievable rate region by adjusting the MSE weights.

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Minimum Mean Squared Error interference alignment

We present a method for estimating conditionally Gaussian random vectors with random covariance matrices, which uses techniques from the field of machine learning. Such models are typical in communication systems, where the covariance matrix of the channel vector depends on random parameters, e.g., angles of propagation paths. If the covariance matrices exhibit certain Toeplitz and shift-invariance structures, the complexity of the minimum mean squared error (MMSE) channel estimator can be reduced to ${\mathcal O}(M\log M)$ floating point operations, where $M$ is the channel dimension. While in the absence of structure the complexity is much higher, we obtain a similarly efficient (but suboptimal) estimator by using the MMSE estimator of the structured model as a blueprint for the architecture of a neural network. This network learns the MMSE estimator for the unstructured model, but only within the given class of estimators that contains the MMSE estimator for the structured model. Numerical simulations with typical spatial channel models demonstrate the generalization properties of the chosen class of estimators to realistic channel models.

Learning the MMSE Channel Estimator

We derive the transmit Wiener filter for DS-CDMA systems which depends upon the noise power at the receivers. We show that the transmit Wiener filter converges to the transmit matched filter and the transmit zero-forcing filter for low and high signal-to-noise-ratio, respectively. Simulation results show the superiority of the transmit Wiener filter compared to the other two transmit filters. Moreover, we observe that the application of the three transmit filters and the respective receive filters lead to similar results.

Transmit Wiener filter for the downlink of TDDDS-CDMA systems

We investigate the effects of fading correlations on wireless communication systems employing multiple antennas at both the receiver and the transmitter side of the link, so called multiple-input multiple-output (MIMO) systems. It turns out that the amount of transmitter sided channel knowledge plays an important part when dealing with fading correlations. Furthermore, the possible availability of time diversity in a time-selective channel can have essential influence on performance. To study the influence of time-selectivity, the concept of sample-mean outage is introduced and applied to information theoretic measures, like capacity or cutoff rate. It will be shown, that in some cases correlated fading may offer better performance than uncorrelated fading permits, which is due to exploitable antenna gain, that will also be defined in a general form for MIMO systems.

Wolfgang Utschick

Papers

Linear transmit processing in MIMO communications systems

Minimum Mean Squared Error interference alignment

Learning the MMSE Channel Estimator

Transmit Wiener filter for the downlink of TDDDS-CDMA systems

Fading correlations in wireless MIMO communication systems