Multi-Domain Communication Systems and Networks: A Tensor-Based Approach

IEEE Open J. Commun. Soc.

2023

Modern communication systems employ multi-domain modulation and coding techniques for effectively exploiting all available resources. Hence in such systems the transmit and receive signals have an inherent multi-domain structure which can be represented using tensors. This work considers the capacity of higher order tensor channels associated with such multi-domain communication systems when the elements of the input tensor are constrained to be drawn from discrete signalling constellations. We establish a relationship between the tensor gradient of the mutual information and the error covariance tensor associated with the minimum mean squared error estimator at the receiver. This relation is used to iteratively find a multi-linear precoder at the input which achieves capacity of the tensor channel under the signalling constellation constraints. Through numerical examples, we show the convergence behavior of the proposed precoder, and compare the capacity achieved under different constellations with the capacity when the input is Gaussian. Further, we exploit the tensor formulation of the problem to find the channel capacity under a variety of different power constraints spanning across several domains. At high SNR, the constellation constraints saturates the capacity while at low SNRs, the constellation constraints are not too relevant, and the power constraints dominate and limit the performance. The capacity saturation level depends on the input order and distribution.

Section: A Conditions For Optimal Input Covariancementioning

confidence: 82%

Section: B Capacity Achieving Input Precodermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Capacity Performance of Tensor Multi-Domain Communication Systems With Discrete Signalling Constellations

IEEE Open J. Commun. Soc.

2023

“…The capacity of a MIMO GFDM channel modelled as a sixth order tensor, under sum power constraint is considered in [45]. Further, [46] presents the notion of tensor partial response signalling as a means to generate multi-domain signals with desired spectral and cross-spectral properties. The trade-off between domains of a communication system as revealed through the tensor approach is also studied in [46].…”

Section: Introductionmentioning

confidence: 99%

“…Further, [46] presents the notion of tensor partial response signalling as a means to generate multi-domain signals with desired spectral and cross-spectral properties. The trade-off between domains of a communication system as revealed through the tensor approach is also studied in [46]. In [47], the capacity of tensor channels under a family of power constraints, which includes per antenna or sum power constraints as its specific cases, is considered.…”

Section: Introductionmentioning

confidence: 99%

The Tensor Multi-Linear Channel and Its Shannon Capacity

2022

IEEE Access

Self Cite

Tensors are multi-way arrays which can be used to model systems spanning many domains. This work proposes to use tensors for characterizing, analyzing, and designing multi-domain communication systems. Most modern day communication systems make use of coding and modulation across different domains such as space, frequency, time. Hence a unified mathematical framework characterizing such a multiple-domain system in an intuitive manner is well needed. In this paper, we present such a unified framework that characterizes a communication system with N input domains, M output domains and an M + N domains multi-linear tensor channel. The proposed framework is generic where the physical interpretation of the domains is system specific. We illustrate a few examples from multi-antenna multicarrier and multi-user systems that fit the proposed framework. Assuming a fixed tensor channel, we provide an information theoretic analysis by deriving its Shannon capacity and input power allocation under a variety of power constraints. In this paper we show how the tensor framework's suitability to mathematically describe a family of power constraints can be used to design and analyze various multiple domain communication systems. The tensor based approach extends water-filling from a matrix setting to tensors, encapsulating the effects of multiple domains thereby allowing joint multi-domain precoding. We show that the capacity pre-log for a tensor channel increases exponentially in the number of domains, indicating the potential of tensor based multi-domain communication systems to provide the large information transmission rates envisaged for 5G and beyond systems. We also show the application of the tensor framework in characterizing the capacity and rate regions of multi-user MIMO channels. Both multiple access and interference channels are considered where the tensor based approach leads to a coordinated users transmission scheme. Such a scheme ensures higher achievable sum rates as compared to independent user transmissions.INDEX TERMS Tensors, MIMO channels, multi-user MIMO, Shannon capacity, tensor SVD and EVD.

Tensor Multi-linear MMSE Estimation Using the Einstein Product

Advances in Intelligent Systems and Computing

2021

In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product, known as the Einstein Product and its properties, many of the known concepts from Linear Algebra could be extended to a multi-linear setting. This enables to define the notions of multi-linear system theory where the input, output signals and the system are multi-domain in nature. This paper provides an overview of tensor algebra tools which can be seen as an extension of linear algebra, at the same time highlighting the difference and advantages that the multi-linear setting brings forth. In particular, the notion of tensor inversion, tensor singular value and tensor Eigenvalue decomposition using the Einstein product is explained. In addition, this paper also introduces the notion of contracted convolution in both discrete and continuous multi-linear system tensors. Tensor Networks representation of various tensor operations is also presented. Also, application of tensor tools in developing transceiver schemes for multi-domain communication systems, with an example of MIMO CDMA systems, is presented. Thus this paper acts as an entry point tutorial for graduate students whose research involves multi-domain or multi-modal signals and systems.