Multiple-input multiple-output (MIMO) technology in conjunction with orthogonal frequency division multiplexing (OFDM) transmission is widely adopted in fifth-generation mobile networks to support multiple users. However, in these mobile communication systems, high power amplifiers (HPAs) at user terminals’ transmitters are driven into their saturation regions, which makes the multiuser frequency-selective MIMO-OFDM uplink channel nonlinear and renders the standard multiuser detection (MUD) at the base station (BS) ineffective. In this paper machine learning is employed to combat the distortions in the uplink of this multiuser frequency-selective MIMO-OFDM communication system. More specifically, a powerful complex-valued B-spline neural network (BSNN) based design is developed to simultaneously identify the system’s channel impulse response (CIR) matrix and the BSNN model for the nonlinear transmitters’ HPA together with the BSNN inversion for the nonlinear HPA at transmitters. This enables the BS to effectively implement MUD by utilizing the estimated MIMO-OFDM CIR matrix as well as to compensate for the transmitter HPAs’ saturation distortions using the estimated BSNN inversion. A simulation study is included to evaluate the effectiveness of this novel BSNN assisted design in combating multiuser and dispersive channel interference as well as nonlinear distortions for multiuser MIMO-OFDM nonlinear uplink.

The plethora of ways of data representation and their applications to system modeling is inherently associated with dimensionality reduction. In a nutshell, the result of dimensionality reduction should support efficient ways of constructing ensuing models (classifiers and predictors) as well as an interpretation of the data themselves. Furthermore, there should be a suitable measure quantifying the quality of data positioned in the reduced space. We advocate that what makes the reduced data interpretable goes hand in hand with revealing a logic fabric of the data, suppressing redundancy, and finally arriving at a logic description of data. The anticipation is that the reduced data can be described in the form of logic expressions formed over the original highly dimensional data. Evidently, having these above-stated points in mind, the aim of this article is twofold: 1) to develop a logic-oriented data representation with the aid of autoencoders; and 2) to quantify the quality of results of this dimensionality reduction by incorporating a facet of information granularity. In other words, we argue that the result of dimensionality reduction gives rise to information granules whose level of granularity associates with the quality of processing completed by the autoencoder. In light of the recent surge of architectures of deep learning, the study is focused on the construction and analysis of logic-oriented autoencoders. We propose a two-level architecture composed of the logic-oriented processing units organized in two layers of logic processing units. As data representation provided by the autoencoder is not ideal, we augment the original architecture by granular parameters, which give rise to granular logic-oriented autoencoders. A suite of experiments is also reported.

Multicriteria group decision-making environments that have a high number of criterion values can be difficult for the experts to handle. This is due to the fact that the experts have to take too much information into account. Thus, they get lost among all the possibilities and have difficulties making the right decision. In order to solve this problem, we present a novel multicriteria group decision-making method that reduces the initial set of criterion values in an organized way. Hierarchical clustering methods are used in order to generate a new reduced criteria set that can be handled by the experts. Fuzzy ontologies are used as an aid system that stores how much each alternative fulfills each criterion. The presented method makes it possible for the experts to carry out the group decision-making process by focusing on ranking the reduced set of criterion values. As a result, a comfortable decision environment is generated, in which the experts can make decisions by managing a fair amount of information. The aid provided by fuzzy ontologies allows the experts to focus on establishing the importance of the criterion values, leaving the rest to the computational system.

For the multiple-input multiple-output (MIMO) uplink employing high-order quadrature amplitude modulation (QAM) signaling and with nonlinear high power amplifiers (HPAs) at mobile users' transmitters, the existing multiuser detection methods can no longer be applied. We propose a novel nonlinear multiuser detection scheme for the nonlinear MIMO uplink. Specifically, we adopt an effective B-spline parameterization of the nonlinear transmit HPAs and derive an efficient and accurate algorithm to identify the nonlinear MIMO uplink channel, including the nonlinear B-spline model of the nonlinear transmit HPAs and the estimate of the linear MIMO channel matrix. Moreover, as the direct result of this nonlinear MIMO channel identification, the B-spline inverse model of nonlinear transmit HPAs can readily be identified. The nonlinear multiuser detection can be effectively implemented by the zero-forcing linear detection based on the estimated linear MIMO channel and followed by compensating the nonlinear distortion of the nonlinear transmit HPAs based on the estimated B-spline inverse model. An extensive simulation investigation is performed to demonstrate the effectiveness of our proposed nonlinear multiuser detection scheme for nonlinear MIMO uplink with high-order QAM signaling.

In this study, we present a methodology of building a hierarchical framework of system modeling by engaging concepts and design methodology of granular computing. We demonstrate that it arises as a result of designing and using locally constructed models to develop a model of a global nature. Two main categories of development of hierarchical models are proposed and discussed. In the first one, given a collection of local models, designed is a granular output space and the ensuing hierarchical model produces information granules of the corresponding type depending upon the depth of the hierarchy of the overall hierarchical structure. The crux of the second category of modeling is about selecting one of the original models and elevating its level of information granularity so that it becomes representative of the entire family of local models. The formation of the most “promising” granular model identified in this way involves mechanisms of allocation of information granularity. The focus of the study is on information granules represented as intervals and fuzzy sets (which in case of type-2 information granules lead to so-called granular intervals and interval-valued fuzzy sets) while the detailed models come as rule-based architectures and neural networks. A series of experiments is presented along with a comparative analysis.

We propose a nonlinear hybrid decision feedback equalizer (NHDFE) for single-carrier (SC) block transmission systems with nonlinear transmit high power amplifier (HPA), which significantly outperforms our previous nonlinear SC frequency-domain equalization (NFDE) design. To obtain the coefficients of the channel impulse response (CIR) as well as to estimate the nonlinear mapping and the inverse nonlinear mapping of the HPA, we adopt a complex-valued (CV) B-spline neural network approach. Specifically, we use a CV B-spline neural network to model the nonlinear HPA, and we develop an efficient alternating least squares scheme for estimating the parameters of the Hammerstein channel, including both the CIR coefficients and the parameters of the CV B-spline model. We also adopt another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can be estimated using the least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. The effectiveness of our NHDFE design is demonstrated in a simulation study, which shows that the NHDFE achieves a signal-to-noise ratio gain of 4dB over the NFDE at the bit error rate level of 10-4.

The study is focused on a development of a global structure in a family of distributed data realized on a basis of locally discovered structures. The local structures are revealed by running fuzzy clustering (Fuzzy C-Means), whereas building a global view is realized by forming global proximity matrices on a basis of the local proximity matrices implied by the partition matrices formed for the individual data sets. To capture the diversity of local structures, a global perspective at the structure of the data is captured in terms of a granular proximity matrix, which is built by invoking a principle of justifiable granularity with regard to the aggregation of individual proximity matrices. The three main scenarios are investigated: (a) designing a global structure among the data through building a granular proximity matrix, (b) refining a local structure (expressed in the form of a partition matrix) by engaging structural knowledge conveyed at the higher level of the hierarchy and provided in the form of the granular proximity matrix, (c) forming a consensus-building scheme and updating all local structures with the aid of the proximity dependences available at the upper layer of the hierarchy. While the first scenario delivers a passive approach to the development of the global structure, the two others are of an active nature by facilitating a structural feedback between the local and global level of the hierarchy of the developed structures. The study is illustrated through a series of experiments carried out for synthetic and publicly available data sets.

In this study, we introduce a concept of hierarchical granular clustering and establish its algorithmic framework. We show that the proposed model naturally gives rise to information granules that are both of higher order and higher type, offering a compelling justification behind their emergence. In a concise way, we can capture the overall architecture of information granules as a hierarchy exhibiting conceptual layers of increasing abstraction: numeric data → information granules → information granules of type-2, order-2 → ... information granules of higher type/order. The elevated type of information granules is reflective of the visible hierarchical facet of processing and the inherent diversity of the individual locally revealed structures in data. While the concept and the methodology deliver some general settings, the detailed algorithmic aspects are discussed in detail when using fuzzy clustering realized by means of fuzzy c-means. Furthermore, for illustrative purposes, we mainly focus on interval-valued fuzzy sets and granular interval fuzzy sets arising at the higher level of the hierarchy. Higher type fuzzy sets are formed with the help of the principle of justifiable granularity. The conceptually sound hierarchy is established in a general way, which makes it equally applicable to various formalisms of representation of information granules. Experiments are reported for synthetic and publicly available datasets.

Information granules emerging as a result of an abstract and more condensed and global view at numeric data play an essential role in various pattern recognition pursuits. In this study, we investigate an idea of granular prototypes (representatives) and discuss their role in the realization of classification schemes. A two-stage procedure of a formation of information granules is discussed. We show how the commonly used clustering methods are viewed as a prerequisite for the construction of granular prototypes. In this regard, a certain version of the principle of justifiable granularity is investigated. In the sequel, a characterization of information granules expressed in terms of their information (classification) content is provided and its usage in the realization of a classifier is studied. Experimental studies involving both synthetic and publicly available data are reported.

The study introduces a concept of mappings realized in presence of information granules and offers a design framework supporting the formation of such mappings. Information granules are conceptually meaningful entities formed on a basis of a large number of experimental input–output numeric data available for the construction of the model. We develop a conceptually and algorithmically sound way of forming information granules. Considering the directional nature of the mapping to be formed, this directionality aspect needs to be taken into account when developing information granules. The property of directionality implies that while the information granules in the input space could be constructed with a great deal of flexibility, the information granules formed in the output space have to inherently relate to those built in the input space. The input space is granulated by running a clustering algorithm; for illustrative purposes, the focus here is on fuzzy clustering realized with the aid of the fuzzy C-means algorithm. The information granules in the output space are constructed with the aid of the principle of justifiable granularity (being one of the underlying fundamental conceptual pursuits of Granular Computing). The construct exhibits two important features. First, the constructed information granules are formed in the presence of information granules already constructed in the input space (and this realization is reflective of the direction of the mapping from the input to the output space). Second, the principle of justifiable granularity does not confine the realization of information granules to a single formalism such as fuzzy sets but helps form the granules expressed any required formalism of information granulation. The quality of the granular mapping (viz. the mapping realized for the information granules formed in the input and output spaces) is expressed in terms of the coverage criterion (articulating how well the experimental data are “covered” by information granules produced by the granular mapping for any input experimental data). Some parametric studies are reported by quantifying the performance of the granular mapping (expressed in terms of the coverage and specificity criteria) versus the values of a certain parameters utilized in the construction of output information granules through the principle of justifiable granularity. The plots of coverage–specificity dependency help determine a knee point and reach a sound compromise between these two conflicting requirements imposed on the quality of the granular mapping. Furthermore, quantified is the quality of the mapping with regard to the number of information granules (implying a certain granularity of the mapping). A series of experiments is reported as well.

Most existing databases lack features which allow for the convenient manipulation of text. It is even more difficult to use them if the text language is not based on the Roman alphabet. The Arabic language is a very good example of this case. Many projects have attempted to use conventional database systems for Arabic data manipulation (including text data), but because of Arabic's many differences with English, these projects have met with limited success. In the Bayan project, the approach has been different. Instead of simply trying to adopt an environment to Arabic, the properties of the Arabic language were the starting point and everything was designed to meet the needs of Arabic, thus avoiding the shortcomings of other projects. A text database management system was designed to overcome the shortcomings of conventional database management systems in manipulating text data. Bayan's data model is based on an object-oriented approach which helps the extensibility of the system for future use. In Bayan, we designed the database with the Arabic text properties in mind. We designed it to support the way Arabic words are derived, classified, and constructed. Furthermore, linguistic algorithms (for word generation and morphological decomposition of words) were designed, leading to a formalization of rules of Arabic language writing and sentence construction. A user interface was designed on top of this environment. A new representation of the Arabic characters was designed, a complete Arabic keyboard layout was created, and a window-based Arabic user interface was also designed.