A Normalization Model for Analyzing Multi-Tier Millimeter Wave Cellular Networks

Based on the distinguishing features of multi-tier millimeter wave (mmWave) networks such as different transmit powers, different directivity gains from directional beamforming alignment and path loss laws for line-of-sight (LOS) and non-line-of-sight (NLOS) links, we introduce a normalization model to simplify the analysis of multi-tier mmWave cellular networks. The highlight of the model is that we convert a multi-tier mmWave cellular network into a single-tier mmWave network, where all the base stations (BSs) have the same normalized transmit power 1 and the densities of BSs scaled by LOS or NLOS scaling factors respectively follow piecewise constant function which has multiple demarcation points. On this basis, expressions for computing the coverage probability are obtained in general case with beamforming alignment errors and the special case with perfect beamforming alignment in the communication. According to corresponding numerical exploration, we conclude that the normalization model for multi-tier mmWave cellular networks fully meets requirements of network performance analysis, and it is simpler and clearer than the untransformed model. Besides, an unexpected but sensible finding is that there is an optimal beam width that maximizes coverage probability in the case with beamforming alignment errors.Comment: 7 pages, 4 figure

PCR-Independent Detection of Bacterial Species-Specific 16S rRNA at 10 fM by a Pore-Blockage Sensor.

A PCR-free, optics-free device is used for the detection of Escherichia coli (E. coli) 16S rRNA at 10 fM, which corresponds to ~100-1000 colony forming units/mL (CFU/mL) depending on cellular rRNA levels. The development of a rapid, sensitive, and cost-effective nucleic acid detection platform is sought for the detection of pathogenic microbes in food, water and body fluids. Since 16S rRNA sequences are species specific and are present at high copy number in viable cells, these nucleic acids offer an attractive target for microbial pathogen detection schemes. Here, target 16S rRNA of E. coli at 10 fM concentration was detected against a total RNA background using a conceptually simple approach based on electromechanical signal transduction, whereby a step change reduction in ionic current through a pore indicates blockage by an electrophoretically mobilized bead-peptide nucleic acid probe conjugate hybridized to target nucleic acid. We investigated the concentration detection limit for bacterial species-specific 16S rRNA at 1 pM to 1 fM and found a limit of detection of 10 fM for our device, which is consistent with our previous finding with single-stranded DNA of similar length. In addition, no false positive responses were obtained with control RNA and no false negatives with target 16S rRNA present down to the limit of detection (LOD) of 10 fM. Thus, this detection scheme shows promise for integration into portable, low-cost systems for rapid detection of pathogenic microbes in food, water and body fluids