Canonical time-frequency, time-scale, and frequency-scale representations of time-varying channels

Mobile communication channels are often modeled as linear time-varying filters or, equivalently, as time-frequency integral operators with finite support in time and frequency. Such a characterization inherently assumes the signals are narrowband and may not be appropriate for wideband signals. In this paper time-scale characterizations are examined that are useful in wideband time-varying channels, for which a time-scale integral operator is physically justifiable. A review of these time-frequency and time-scale characterizations is presented. Both the time-frequency and time-scale integral operators have a two-dimensional discrete characterization which motivates the design of time-frequency or time-scale rake receivers. These receivers have taps for both time and frequency (or time and scale) shifts of the transmitted signal. A general theory of these characterizations which generates, as specific cases, the discrete time-frequency and time-scale models is presented here. The interpretation of these models, namely, that they can be seen to arise from processing assumptions on the transmit and receive waveforms is discussed. Out of this discussion a third model arises: a frequency-scale continuous channel model with an associated discrete frequency-scale characterization.Comment: To appear in Communications in Information and Systems - special issue in honor of Thomas Kailath's seventieth birthda

The continuous wavelet transform as a maximum entropy solution of the corresponding inverse problem

The continuous wavelet transform is obtained as a maximum entropy solution of the corresponding inverse problem. It is well known that although a signal can be reconstructed from its wavelet transform, the expansion is not unique due to the redundancy of continuous wavelets. Hence, the inverse problem has no unique solution. If we want to recognize one solution as "optimal", then an appropriate decision criterion has to be adopted. We show here that the continuous wavelet transform is an "optimal" solution in a maximum entropy sense.Peer Reviewe

Millimeter-wave Mobile Sensing and Environment Mapping: Models, Algorithms and Validation

Integrating efficient connectivity, positioning and sensing functionalities into 5G New Radio (NR) and beyond mobile cellular systems is one timely research paradigm, especially at mm-wave and sub-THz bands. In this article, we address the radio-based sensing and environment mapping prospect with specific emphasis on the user equipment (UE) side. We first describe an efficient l1-regularized least-squares (LS) approach to obtain sparse range--angle charts at individual measurement or sensing locations. For the subsequent environment mapping, we then introduce a novel state model for mapping diffuse and specular scattering, which allows efficient tracking of individual scatterers over time using interacting multiple model (IMM) extended Kalman filter and smoother. We provide extensive numerical indoor mapping results at the 28~GHz band deploying OFDM-based 5G NR uplink waveform with 400~MHz channel bandwidth, covering both accurate ray-tracing based as well as actual RF measurement results. The results illustrate the superiority of the dynamic tracking-based solutions, compared to static reference methods, while overall demonstrate the excellent prospects of radio-based mobile environment sensing and mapping in future mm-wave networks