Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation

In this work, we report a novel high capacity (number of degrees of freedom) open loop adaptive optics method, termed digital optical phase conjugation (DOPC), which provides a robust optoelectronic optical phase conjugation (OPC) solution. We showed that our prototype can phase conjugate light fields with ~3.9 x 10^(−3) degree accuracy over a range of ~3 degrees and can phase conjugate an input field through a relatively thick turbid medium (μ_sl ~13). Furthermore, we employed this system to show that the reversing of random scattering in turbid media by phase conjugation is surprisingly robust and accommodating of phase errors. An OPC wavefront with significant spatial phase errors (error uniformly distributed from – π/2 to π/2) can nevertheless allow OPC reconstruction through a scattering medium with ~40% of the efficiency achieved with phase error free OPC

Outage Capacity and Optimal Transmission for Dying Channels

In wireless networks, communication links may be subject to random fatal impacts: for example, sensor networks under sudden power losses or cognitive radio networks with unpredictable primary user spectrum occupancy. Under such circumstances, it is critical to quantify how fast and reliably the information can be collected over attacked links. For a single point-to-point channel subject to a random attack, named as a \emph{dying channel}, we model it as a block-fading (BF) channel with a finite and random delay constraint. First, we define the outage capacity as the performance measure, followed by studying the optimal coding length $K$ such that the outage probability is minimized when uniform power allocation is assumed. For a given rate target and a coding length $K$, we then minimize the outage probability over the power allocation vector \mv{P}_{K}, and show that this optimization problem can be cast into a convex optimization problem under some conditions. The optimal solutions for several special cases are discussed. Furthermore, we extend the single point-to-point dying channel result to the parallel multi-channel case where each sub-channel is a dying channel, and investigate the corresponding asymptotic behavior of the overall outage probability with two different attack models: the independent-attack case and the $m$-dependent-attack case. It can be shown that the overall outage probability diminishes to zero for both cases as the number of sub-channels increases if the \emph{rate per unit cost} is less than a certain threshold. The outage exponents are also studied to reveal how fast the outage probability improves over the number of sub-channels.Comment: 31 pages, 9 figures, submitted to IEEE Transactions on Information Theor

On Design of Collaborative Beamforming for Two-Way Relay Networks

We consider a two-way relay network, where two source nodes, S1 and S2, exchange information through a cluster of relay nodes. The relay nodes receive the sum signal from S1 and S2 in the first time slot. In the second time slot, each relay node multiplies its received signal by a complex coefficient and retransmits the signal to the two source nodes, which leads to a collaborative two-way beamforming system. By applying the principle of analog network coding, each receiver at S1 and S2 cancels the "self-interference" in the received signal from the relay cluster and decodes the message. This paper studies the 2-dimensional achievable rate region for such a two-way relay network with collaborative beamforming. With different assumptions of channel reciprocity between the source-relay and relay-source channels, the achievable rate region is characterized under two setups. First, with reciprocal channels, we investigate the achievable rate regions when the relay cluster is subject to a sum-power constraint or individual-power constraints. We show that the optimal beamforming vectors obtained from solving the weighted sum inverse-SNR minimization (WSISMin) problems are sufficient to characterize the corresponding achievable rate region. Furthermore, we derive the closed form solutions for those optimal beamforming vectors and consequently propose the partially distributed algorithms to implement the optimal beamforming, where each relay node only needs the local channel information and one global parameter. Second, with the non-reciprocal channels, the achievable rate regions are also characterized for both the sum-power constraint case and the individual-power constraint case. Although no closed-form solutions are available under this setup, we present efficient numerical algorithms.Comment: new version of the previously posted, single column double spacing, 24 page

Digital optical phase conjugation of fluorescence in turbid tissue

We demonstrate a method for phase conjugating fluorescence. Our method, called reference free digital optical phase conjugation, can conjugate extremely weak, incoherent optical signals. It was used to phase conjugate fluorescent light originating from a bead covered with 0.5 mm of light-scattering tissue. The phase conjugated beam refocuses onto the bead and causes a local increase of over two orders of magnitude in the light intensity. Potential applications are in imaging, optical trapping, and targeted photochemical activation inside turbid tissue

Analysis and evaluation of the entropy indices of a static network structure

Although degree distribution entropy (DDE), SD structure entropy (SDSE), Wu structure entropy (WSE) and FB structure entropy (FBSE) are four static network structure entropy indices widely used to quantify the heterogeneity of a complex network, previous studies have paid little attention to their differing abilities to describe network structure. We calculate these four structure entropies for four benchmark networks and compare the results by measuring the ability of each index to characterize network heterogeneity. We find that SDSE and FBSE more accurately characterize network heterogeneity than WSE and DDE. We also find that existing benchmark networks fail to distinguish SDSE and FBSE because they cannot discriminate local and global network heterogeneity. We solve this problem by proposing an evolving caveman network that reveals the differences between structure entropy indices by comparing the sensitivities during the network evolutionary process. Mathematical analysis and computational simulation both indicate that FBSE describes the global topology variation in the evolutionary process of a caveman network, and that the other three structure entropy indices reflect only local network heterogeneity. Our study offers an expansive view of the structural complexity of networks and expands our understanding of complex network behavior.The authors would like to thank the financial support of the National Natural Science Foundation of China (71501153), Natural Science Foundation of Shaanxi Province of China (2016JQ6072), and the Foundation of China Scholarship Council (201506965039, 201606965057). (71501153 - National Natural Science Foundation of China; 2016JQ6072 - Natural Science Foundation of Shaanxi Province of China; 201506965039 - Foundation of China Scholarship Council; 201606965057 - Foundation of China Scholarship Council)Published versio