Sandesh Rao Mattu

Sandesh Rao Mattu, Nishant Mehrotra, Venkatesh Khammammetti et al.

This tutorial derives the mathematical foundations of what it means for a carrier waveform to be predictable and non-selective. We focus on Zak-OTFS, where each carrier waveform is a pulse in the delay-Doppler (DD) domain, formally a quasi-periodic localized function with specific periods along delay and Doppler. Viewed in the time domain, the Zak-OTFS carrier is realized as a pulse train modulated by a tone (termed a pulsone). We start by providing physical intuition, describing what it means for the Zak-OTFS carrier waveforms to be geometric modes of the Heisenberg-Weyl (HW) group of discrete delay and Doppler shifts that define the discrete-time communication model. In fact, we show that these geometric modes are common eigenvectors of a maximal commutative subgroup of our discrete HW group. When the channel delay spread is less than the delay period, and the channel Doppler spread is less than the Doppler period, we show that the Zak-OTFS input-output (I/O) relation is predictable and non-selective. Given the I/O response at one DD point in a frame, it is possible to predict the I/O response at all other points, without recourse to some mathematical model of the channel. While it may be intuitive that geometric modes of the HW group are predictable and non-selective wireless carriers, this is not a requirement. We provide a necessary and sufficient condition that depends on the ambiguity properties of the basis of carrier waveforms. In fact, we show that the structure of a pulse train modulated by a Hadamard matrix is common to several families of waveforms proposed for 6G, including Zak-OTFS, AFDM, OTSM and ODDM.

Nishant Mehrotra, Sandesh Rao Mattu, Robert Calderbank

Conventional delay-Doppler (DD) communication and sensing systems require transmitting pilot frames at every channel coherence time interval in order to keep track of channel variations at the cost of spectral efficiency. In this paper, we propose an approach to utilize data transmissions modulated using arbitrary waveforms for DD channel estimation without requiring pilot transmissions in every coherence time interval. Numerical evaluation over practical doubly-selective channel models demonstrate $\sim 1.8 \times$ improvement in spectral efficiency with our proposed data-based approach over conventional pilot-based approaches across various 6G modulation schemes.

Jaswanth Bodempudi, Batta Siva Sairam, Madepalli Haritha et al.

Carrier aggregation (CA) is a technique that allows mobile networks to combine multiple carriers to increase user data rate. On the uplink, for power constrained users, this translates to the need for an efficient resource allocation scheme, where each user distributes its available power among its assigned uplink carriers. Choosing a good set of carriers and allocating appropriate power on the carriers is important. If the carrier allocation on the uplink is such that a harmonic of a user's uplink carrier falls on the downlink frequency of that user, it leads to a self coupling-induced sensitivity degradation of that user's downlink receiver. In this paper, we model the uplink carrier aggregation problem as an optimal resource allocation problem with the associated constraints of non-linearities induced self interference (SI). This involves optimization over a discrete variable (which carriers need to be turned on) and a continuous variable (what power needs to be allocated on the selected carriers) in dynamic environments, a problem which is hard to solve using traditional methods owing to the mixed nature of the optimization variables and the additional need to consider the SI constraint. We adopt a reinforcement learning (RL) framework involving a compound-action actor-critic (CA2C) algorithm for the uplink carrier aggregation problem. We propose a novel reward function that is critical for enabling the proposed CA2C algorithm to efficiently handle SI. The CA2C algorithm along with the proposed reward function learns to assign and activate suitable carriers in an online fashion. Numerical results demonstrate that the proposed RL based scheme is able to achieve higher sum throughputs compared to naive schemes. The results also demonstrate that the proposed reward function allows the CA2C algorithm to adapt the optimization both in the presence and absence of SI.