Uplink Non-Orthogonal Multiple Access with Finite-Alphabet Inputs

This paper focuses on the non-orthogonal multiple access (NOMA) design for a classical two-user multiple access channel (MAC) with finite-alphabet inputs. We consider practical quadrature amplitude modulation (QAM) constellations at both transmitters, the sizes of which are assumed to be not necessarily identical. We propose to maximize the minimum Euclidean distance of the received sum-constellation with a maximum likelihood (ML) detector by adjusting the scaling factors (i.e., instantaneous transmitted powers and phases) of both users. The formulated problem is a mixed continuous-discrete optimization problem, which is nontrivial to resolve in general. By carefully observing the structure of the objective function, we discover that Farey sequence can be applied to tackle the formulated problem. However, the existing Farey sequence is not applicable when the constellation sizes of the two users are not the same. Motivated by this, we define a new type of Farey sequence, termed punched Farey sequence. Based on this, we manage to achieve a closed-form optimal solution to the original problem by first dividing the entire feasible region into a finite number of Farey intervals and then taking the maximum over all the possible intervals. The resulting sum-constellation is proved to be a regular QAM constellation of a larger size. Moreover, the superiority of NOMA over time-division multiple access (TDMA) in terms of minimum Euclidean distance is rigorously proved. Furthermore, the optimal rate allocation among the two users is obtained in closed-form to further maximize the obtained minimum Euclidean distance of the received signal subject to a total rate constraint. Finally, simulation results are provided to verify our theoretical analysis and demonstrate the merits of the proposed NOMA over existing orthogonal and non-orthogonal designs.Comment: Submitted for possible journal publicatio

Additional file 16: of The human jejunum has an endogenous microbiota that differs from those in the oral cavity and colon

O. Illumina abundance summary file. Distribution of microbiota from raw Illumina file. (CSV 95 kb

Additional file 14: of The human jejunum has an endogenous microbiota that differs from those in the oral cavity and colon

M. Illumina abundance summary file. Distribution of microbiota from raw Illumina file. (CSV 111 kb

Additional file 20: of The human jejunum has an endogenous microbiota that differs from those in the oral cavity and colon

S. Illumina abundance summary file. Distribution of microbiota from raw Illumina file. (CSV 115 kb

Additional file 6: of The human jejunum has an endogenous microbiota that differs from those in the oral cavity and colon

E. Illumina abundance summary file. Distribution of microbiota from raw Illumina file. (CSV 103 kb

A Spontaneous Missense Mutation in Branched Chain Keto Acid Dehydrogenase Kinase in the Rat Affects Both the Central and Peripheral Nervous Systems - Fig 6

<p><b>A</b>. Brains from wild type (left) and <i>frogleg</i> (right) were of similar size. Scale is in centimeters. <b>B</b>. Brain weights, however, differed in wild type (+/+) and homozygote (<i>frogleg</i>) rats of 4 weeks, 10 weeks and 7 months of age, being considerably smaller in the <i>frogleg</i> rats compared to their littermates at all ages tested (mean+SEM).</p

Transmission electron microscopy images of cross sections of hind limb nerves from a <i>frogleg</i> rat.

<p>A. Sciatic nerve showing evidence of rare active demyelination (arrow). In the ventral root (B) of the sciatic nerve (as well as in the nerve itself) there were axons that were thinly myelinated (arrows in B). In the sural nerve, there was evidence of rare Wallerian-like degeneration, intra-axonal inclusions, and denervated Schwann cells. Scale bar = 2 microns.</p

Electrophoresis and western analysis of protein lysates from the brains of <i>frogleg</i> and littermate rats.

<p>In panel A are shown the staining patterns for 5 individual rats: lane 1 is lysate from a wild type, lanes 2 and 3 are from rats heterozygous for the <i>Bckdk</i> mutation, and lanes 4 and 5 are from homozygotes. In panel B equal aliquots of the same 5 samples were electrophoresed, transferred to nitrocellulose and probed with an antibody to BCKDH subunit E1α. It is evident that similar amounts of the total enzyme are present in all 5 samples. In panel C the amount of BCKDH phosphorylated at Ser293 of the E1α subunit is determined by probing the same 5 lysates with an antibody specific for the phosphorylated form of the enzyme. While the wildtype and heterozygous animals have a clear band, no immunoreactivity is detected in the 2 samples homozygous for the mutation. To demonstrate that the bands present on panel C represent the phosphorylated enzyme, aliquots of the same lysates were treated with calf intestinal alkaline phosphatase before electrophoresis. The bands present in lanes 1–3 of panel C are no longer visible.</p

Wild type and <i>frogleg</i> testes and epididymis, paraffin, 5μ sections, H and E.

<p>A. Wild type testis, with normal spermatogenesis. B. <i>Frogleg</i> testis, multiple seminiferous tubules with no spermatogenesis; only 1 tubule (arrow) with active spermatogenesis. C. <i>Frogleg</i> epididymis, reduced sperm (oligospermia) with clumped and degenerating cells. Scale bars = 100μm in A and B; 200μm in C.</p

Linkage map of the <i>frogleg</i> locus on rat chromosome 1.

<p>Ideogram of rat chromosome 1, showing polymorphic markers in the region of the <i>Bckdk</i> gene. Nucleotide sequence positions were determined by locating original marker amplimer sequences to the RGSC 6.0 / rn6 July 2014 assembly of the rat genome. MLINK-derived maximum LOD scores and corresponding theta values indicate linkage distance to the disease locus. The analysis was based on 11 affected and 10 unaffected individuals. Significant linkage scores identifying the initial disease interval (> 3.0) are enclosed in the box.</p