Multi-hop Cooperative Wireless Networks: Diversity Multiplexing Tradeoff and Optimal Code Design

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP)networks and layered networks.KPP networks, can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4.For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks.For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable.Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. We also give alternative and often simpler proofs of several existing results and show that codes achieving full diversity on a MIMO Rayleigh fading channel achieve full diversity on arbitrary fading channels. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes.Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT

Model track studies on fouled ballast using ground penetrating radar and multichannel analysis of surface wave

Ballast fouling is created by the breakdown of aggregates or outside contamination by coal dust from coal trains, or from soil intrusion beneath rail track. Due to ballast fouling, the conditions of rail track can be deteriorated considerably depending on the type of fouling material and the degree of fouling. So far there is no comprehensive guideline available to identify the critical degree of fouling for different types of fouling materials. This paper presents the identification of degree of fouling and types of fouling using non-destructive testing, namely seismic surface-wave and ground penetrating radar (GPR) survey. To understand this, a model rail track with different degree of fouling has been constructed in Civil engineering laboratory, University of Wollongong, Australia. Shear wave velocity obtained from seismic survey has been employed to identify the degree of fouling and types of fouling material. It is found that shear wave velocity of fouled ballast increases initially, reaches optimum fouling point (OFP), and decreases when the fouling increases. The degree of fouling corresponding after which the shear wave velocity of fouled ballast will be smaller than that of clean ballast is called the critical fouling point (CFP). Ground penetrating radar with four different ground coupled antennas (500 MHz, 800 MHz, 1.6 GHz and 2.3 GHz) was also used to identify the ballast fouling condition. It is found that the 800 MHz ground coupled antenna gives a better signal in assessing the ballast fouling condition. Seismic survey is relatively slow when compared to GPR survey however it gives quantifiable results. In contrast, GPR survey is faster and better in estimating the depth of fouling. (C) 2011 Elsevier B.V. All rights reserved.

Robust MMSE Tomlinson-Harashima Precoder for Multiuser MISO Downlink with Imperfect CSI

Non-linear precoding for the downlink of a multiuser MISO (multiple-input single-output) communication system in the presence of imperfect channel state information (CSI) is considered.The base station is equipped with multiple transmit antennas and each user terminal is equipped with a single receive antenna. The CSI at the transmitter is assumed to be perturbed by an estimation error. We propose a robust minimum mean square error (MMSE) Tomlinson-Harashima precoder (THP)design, which can be formulated as an optimization problem that can be solved efficiently by the method of alternating optimization(AO). In this method of optimization, the entire set of optimization variables is partitioned into non-overlapping subsets,and an iterative sequence of optimizations on these subsets is carried out, which is often simpler compared to simultaneous optimization over all variables. In our problem, the application of the AO method results in a second-order cone program which can be numerically solved efficiently. The proposed precoder is shown to be less sensitive to imperfect channel knowledge. Simulation results illustrate the improvement in performance compared to other robust linear and non-linear precoders in the literature.

Generalized Silver Codes

For an n(t) transmit, n(r) receive antenna system (n(t) x n(r) system), a full-rate space time block code (STBC) transmits at least n(min) = min(n(t), n(r))complex symbols per channel use. The well-known Golden code is an example of a full-rate, full-diversity STBC for two transmit antennas. Its ML-decoding complexity is of the order of M(2.5) for square M-QAM. The Silver code for two transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order of M(2). Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (for n(r) >= n(t)) but have a high ML-decoding complexity of the order of M(ntnmin) (for n(r) < n(t), the punctured Perfect codes are considered). In this paper, a scheme to obtain full-rate STBCs for 2(a) transmit antennas and any n(r) with reduced ML-decoding complexity of the order of M(nt)(n(min)-3/4)-0.5 is presented. The codes constructed are also information lossless for >= n(t), like the Perfect codes, and allow higher mutual information than the comparable punctured Perfect codes for n(r) < n(t). These codes are referred to as the generalized Silver codes, since they enjoy the same desirable properties as the comparable Perfect codes (except possibly the coding gain) with lower ML-decoding complexity, analogous to the Silver code and the Golden code for two transmit antennas. Simulation results of the symbol error rates for four and eight transmit antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML-decoding complexity.

Training-Symbol Embedded, High-Rate, Single-Symbol ML-Decodable, Distributed STBCs for Relay Networks

Distributed space-time block codes (DSTBCs) from complex orthogonal designs (CODs) (both square and nonsquare), coordinate interleaved orthogonal designs (CIODs), and Clifford unitary weight designs (CUWDs) are known to lose their single-symbol ML decodable (SSD) property when used in two-hop wireless relay networks using amplify and forward protocol. For such networks, in this paper, three new classes of high rate, training-symbol embedded (TSE) SSD DSTBCs are constructed: TSE-CODs, TSE-CIODs, and TSE-CUWDs. The proposed codes include the training symbols inside the structure of the code which is shown to be the key point to obtain the SSD property along with the channel estimation capability. TSE-CODs are shown to offer full-diversity for arbitrary complex constellations and the constellations for which TSE-CIODs and TSE-CUWDs offer full-diversity are characterized. It is shown that DSTBCs from nonsquare TSE-CODs provide better rates (in symbols per channel use) when compared to the known SSD DSTBCs for relay networks. Important from the practical point of view, the proposed DSTBCs do not contain any zeros in their codewords and as a result, antennas of the relay nodes do not undergo a sequence of switch on/off transitions within every codeword, and, thus, avoid the antenna switching problem.

A Low ML-Decoding Complexity, Full-Diversity, Full-Rate MIMO Precoder

Precoding for multiple-input multiple-output (MIMO) antenna systems is considered with perfect channel knowledge available at both the transmitter and the receiver. For two transmit antennas and QAM constellations, a real-valued precoder which is approximately optimal (with respect to the minimum Euclidean distance between points in the received signal space) among real-valued precoders based on the singular value decomposition (SVD) of the channel is proposed. The proposed precoder is obtainable easily for arbitrary QAM constellations, unlike the known complex-valued optimal precoder by Collin et al. for two transmit antennas which is in existence for 4-QAM alone and is extremely hard to obtain for larger QAM constellations. The proposed precoding scheme is extended to higher number of transmit antennas on the lines of the E - d(min) precoder for 4-QAM by Vrigneau et al. which is an extension of the complex-valued optimal precoder for 4-QAM. The proposed precoder's ML-decoding complexity as a function of the constellation size M is only O(root M)while that of the E - d(min) precoder is O(M root M)(M = 4). Compared to the recently proposed X- and Y-precoders, the error performance of the proposed precoder is significantly better while being only marginally worse than that of the E - d(min) precoder for 4-QAM. It is argued that the proposed precoder provides full-diversity for QAM constellations and this is supported by simulation plots of the word error probability for 2 x 2, 4 x 4 and 8 x 8 systems.

An Accurate Model for EESM and its Application to Analysis of CQI Feedback Schemes and Scheduling in LTE

The Effective Exponential SNR Mapping (EESM) is an indispensable tool for analyzing and simulating next generation orthogonal frequency division multiplexing (OFDM) based wireless systems. It converts the different gains of multiple subchannels, over which a codeword is transmitted, into a single effective flat-fading gain with the same codeword error rate. It facilitates link adaptation by helping each user to compute an accurate channel quality indicator (CQI), which is fed back to the base station to enable downlink rate adaptation and scheduling. However, the highly non-linear nature of EESM makes a performance analysis of adaptation and scheduling difficult; even the probability distribution of EESM is not known in closed-form. This paper shows that EESM can be accurately modeled as a lognormal random variable when the subchannel gains are Rayleigh distributed. The model is also valid when the subchannel gains are correlated in frequency or space. With some simplifying assumptions, the paper then develops a novel analysis of the performance of LTE's two CQI feedback schemes that use EESM to generate CQI. The comprehensive model and analysis quantify the joint effect of several critical components such as scheduler, multiple antenna mode, CQI feedback scheme, and EESM-based feedback averaging on the overall system throughput.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Joint Performance Analysis of Channel Quality Indicator Feedback Schemes and Frequency-Domain Scheduling for LTE

Frequency-domain scheduling and rate adaptation enable next-generation orthogonal frequency-division multiple access (OFDMA) cellular systems such as Long-Term Evolution (LTE) to achieve significantly higher spectral efficiencies. LTE uses a pragmatic combination of several techniques to reduce the channel-state feedback that is required by a frequency-domain scheduler. In the subband-level feedback and user-selected subband feedback schemes specified in LTE, the user reduces feedback by reporting only the channel quality that is averaged over groups of resource blocks called subbands. This approach leads to an occasional incorrect determination of rate by the scheduler for some resource blocks. In this paper, we develop closed-form expressions for the throughput achieved by the feedback schemes of LTE. The analysis quantifies the joint effects of three critical components on the overall system throughput-scheduler, multiple-antenna mode, and the feedback scheme-and brings out its dependence on system parameters such as the number of resource blocks per subband and the rate adaptation thresholds. The effect of the coarse subband-level frequency granularity of feedback is captured. The analysis provides an independent theoretical reference and a quick system parameter optimization tool to an LTE system designer and theoretically helps in understanding the behavior of OFDMA feedback reduction techniques when operated under practical system constraints.

A general construction of space-time trellis codes for PSK signal sets

The diversity order and coding gain are crucial for the performance of a multiple antenna communication system. It is known that space-time trellis codes (STTC) can be used to achieve these objectives. In particular, we can use STTCs to obtain large coding gains. Many attempts have been made to construct STTCs which achieve full-diversity and good coding gains, though a general method of construction does not exist. Delay diversity code (rate-1) is known to achieve full-diversity, for any number of transmit antennas and any signal set, but does not give a good coding gain. A product distance code based delay diversity scheme (Tarokh, V. et al., IEEE Trans. Inform. Theory, vol.44, p.744-65, 1998) enables one to improve the coding gain and construct STTCs for any given number of states using coding in conjunction with delay diversity; it was stated as an open problem. We achieve such a construction. We assume a shift register based model to construct an STTC for any state complexity. We derive a sufficient condition for this STTC to achieve full-diversity, based on the delay diversity scheme. This condition provides a framework to do coding in conjunction with delay diversity for any signal constellation. Using this condition, we provide a formal rate-1 STTC construction scheme for PSK signal sets, for any number of transmit antennas and any given number of states, which achieves full-diversity and gives a good coding gain.

The radiation resistance of off-set series slots in microstrip line

The radiation resistance of off-set series slots has been calculated for microstrip lines using the method proposed by Breithaupt for strip lines. A suitable transformation is made to allow for the difference in structure. Curves relating the slot resistance to the microstrip length, width and off-set distance have been obtained. Microstrip slot antenna arrays are becoming important in applications where size and weight are of significance. The radiation resistance is a very significant parameter is the design of such arrays. Oliner first calculated the radiation conductance of centered series slots in strip transmission lines and that analysis was extended by Breithaupt to the off-set series slots in stripline. The radiation resistance of off-set series slots in microstrip lines is calculated in this paper and data are obtained for different slot lengths, slot widths and off-set values. An example of the use of these data in array antenna design in shown.

Calculating the Effect of Uneven Terrain on Glide Path Signals

A method for calculating the bends in the glide slope due to uneven terrain is presented. A computer program written for the purpose enables the calculation of the difference in depth of modulation (DDM) at any point, taking into account the effect of uneven terrain. Results are presented for a hypothetical case of a hill in front of the runway. The program enables us to predict the glide slope bends due to irregular terrain, so that proper selection of glide slope antenna location can be made.

Interacting fermions in synthetic non-Abelian gauge fields

Generation and study of synthetic gauge fields has enhanced the possibility of using cold atom systems as quantum emulators of condensed matter Hamiltonians. In this article we describe the physics of interacting spin -1/2 fermions in synthetic non-Abelian gauge fields which induce a Rashba spin-orbit interaction on the motion of the fermions. We show that the fermion system can evolve to a Bose-Einstein condensate of a novel boson which we call rashbon. The rashbon-rashbon interaction is shown to be independent of the interaction between the constituent fermions. We also show that spin-orbit coupling can help enhancing superfluid transition temperature of weak superfluids to the order of Fermi temperature. A non-Abelian gauge field, when used in conjunction with another potential, can generate interesting Hamiltonians such as that of a magnetic monopole.

Multi-Port Network Approach for the Analysis of Dual Band Fractal Microstrip Antennas

The multiport network approach is extended to analyze the behavior of microstrip fractal antennas. The capacitively fedmicrostrip square ring antenna has the side opposite to the feed arm replaced with a fractal Minkowski geometry. Dual frequency operation is achieved by suitably choosing the indentation of this fractal geometry. The width of the two sides adjacent to this is increased to further control the resonant characteristics and the ratio of the two resonance frequencies of this antenna. The impedance matrix for the multiport network model of this antenna is simplified exploiting self-similarity of the geometry with greater accuracy and reduced analysis time. Experimentally validated results confirm utility of the approach in analyzing the input characteristics of similar multi-frequency fractal microstrip antennas with other fractal geometries.

Subdiffusion in hair bundle dynamics: The role of protein conformational fluctuations

The detection of sound signals in vertebrates involves a complex network of different mechano-sensory elements in the inner ear. An especially important element in this network is the hair bundle, an antenna-like array of stereocilia containing gated ion channels that operate under the control of one or more adaptation motors. Deflections of the hair bundle by sound vibrations or thermal fluctuations transiently open the ion channels, allowing the flow of ions through them, and producing an electrical signal in the process, eventually causing the sensation of hearing. Recent high frequency (0.1-10 kHz) measurements by Kozlov et al. Proc. Natl. Acad. Sci. U. S. A. 109, 2896 (2012)] of the power spectrum and the mean square displacement of the thermal fluctuations of the hair bundle suggest that in this regime the dynamics of the hair bundle are subdiffusive. This finding has been explained in terms of the simple Brownian motion of a filament connecting neighboring stereocilia (the tip link), which is modeled as a viscoelastic spring. In the present paper, the diffusive anomalies of the hair bundle are ascribed to tip link fluctuations that evolve by fractional Brownian motion, which originates in fractional Gaussian noise and is characterized by a power law memory. The predictions of this model for the power spectrum of the hair bundle and its mean square displacement are consistent with the experimental data and the known properties of the tip link. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4768902]