Analysis of Degrees of Freedom of Wideband Random Multipath Fields Observed Over Time and Space Windows

In multipath systems, available degrees of freedom can be considered as a key performance indicator, since the channel capacity grows linearly with the available degrees of freedom. However, a fundamental question arises: given a size limitation on the observable region, what is the intrinsic number of degrees of freedom available in a wideband random multipath wavefield observed over a finite time interval? In this paper, we focus on answering this question by modelling the wavefield as a sum of orthogonal waveforms or spatial orders. We show that for each spatial order, (i) the observable wavefield is band limited within an effective bandwidth rather than the given bandwidth and (ii) the observation time varies from the given observation time. These findings show the strong coupling between space and time as well as space and bandwidth. In effect, for spatially diverse multipath wavefields, the classical degrees of freedom result of "time-bandwidth" product does not directly extend to "time-space-bandwidth" product.Comment: 9 pages, 2 figures, Accepted in 2014 IEEE Workshop on Statistical Signal Processin

Wireless Device-to-Device Caching Networks with Distributed MIMO and Hierarchical Cooperations

© 2017 IEEE. In this paper, we propose a new caching scheme for a random wireless device-to-device (D2D) network of n nodes with local caches, where each node intends to download files from a prefixed library via D2D links. Our proposed caching delivery includes two stages, employing distributed MIMO and hierarchical cooperations respectively. The distributed MIMO is applied to the first stage between source nodes and neighbours of the destination node. The induced multiplexing gain and diversity gain increase the number of simultaneous transmissions, improving the throughput of the network. The hierarchical cooperations are applied to the second stage to facilitate the transmissions between the destination node and its neighbours. The two stages together exploit spatial degrees of freedom as well as spatial reuse. We develop an uncoded random caching placement strategy to serve this cooperative caching delivery. Analytical results show that the average aggregate throughput of the network scales almost linearly with n, with a vanishing outage probability

Band Limited Signals Observed Over Finite Spatial and Temporal Windows: An Upper Bound to Signal Degrees of Freedom

The study of degrees of freedom of signals observed within spatially diverse broadband multipath fields is an area of ongoing investigation and has a wide range of applications, including characterising broadband MIMO and cooperative networks. However, a fundamental question arises: given a size limitation on the observation region, what is the upper bound on the degrees of freedom of signals observed within a broadband multipath field over a finite time window? In order to address this question, we characterize the multipath field as a sum of a finite number of orthogonal waveforms or spatial modes. We show that (i) the "effective observation time" is independent of spatial modes and different from actual observation time, (ii) in wideband transmission regimes, the "effective bandwidth" is spatial mode dependent and varies from the given frequency bandwidth. These findings clearly indicate the strong coupling between space and time as well as space and frequency in spatially diverse wideband multipath fields. As a result, signal degrees of freedom does not agree with the well-established degrees of freedom result as a product of spatial degrees of freedom and time-frequency degrees of freedom. Instead, analogous to Shannon's communication model where signals are encoded in only one spatial mode, the available signal degrees of freedom in spatially diverse wideband multipath fields is the time-bandwidth product result extended from one spatial mode to finite modes. We also show that the degrees of freedom is affected by the acceptable signal to noise ratio (SNR) in each spatial mode.Comment: Submitted to IEEE Transactions on Signal Processin