Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

Stresses around reinforced curvilinear holes in spherical shells

A perturbation technique is used to determine the stress concentration around reinforced curvilinear holes in thin pressurized spherical shells. Starting from the governing differential equations for thin shallow spherical shells, a solution is first obtained for a circular hole. The solution for an arbitrary shaped curvilinear hole is then obtained as a first-order perturbation over the circular hole solution using the conformal mapping technique. The effects of a large number of parameters involved in the design of a reinforcement around cutouts in shells are studied. The problems of symmetric and eccentric reinforcements are also considered. The results obtained would be very helpful in the design of an efficient reinforcement for elliptical and square holes in thin shallow spherical shells.

Three-dimensional corner reflector of arbitrary apex angle

A method of analysing a 3-dimensional corner reflector antenna of arbitrary apex angle is given. Expressions have been obtained for the far field of the 3-dimensional corner reflector fed by a dipole. The radiation resistance and the directive gain of the antenna have been calculated. The method described is applicable even when the feed dipole is arbitrarily oriented. It is found that the radiation along a prescribed direction can be circularly polarised (right or left) by suitably orienting the feed dipole.

Microstrip square ring antenna for dual-band operation

This paper presents a generalized approach to design an electromagnetically coupled microstrip ring antenna for dual-band operation. By widening two opposite sides of a square ring antenna, its fractional bandwidth at the primary resonance mode can be increased significantly so that it may be used for practical applications. By attaching a stub to the inner edge of the side opposite to the feed arm, some of the losses in electrical length caused by widening can be regained. More importantly, this addition also alters the current distribution on the antenna and directs radiations at the second resonant frequency towards boresight. It has also been observed that for the dual frequency configurations studied, the ratio of the resonant frequencies (center dot r(2)center dot center dot r(1)) can range between 1.55 and 2.01. This shows flexibility in designing dual frequency antennas with a desired pair of resonant frequencies.

Robust THP Transceiver Designs for Multiuser MIMO Downlink with Imperfect CSIT

We present robust joint nonlinear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for interuser interference precancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of CSIT errors. The first model is a stochastic error (SE) model, where the CSIT error is Gaussian-distributed. This model is applicable when the CSIT error is dominated by channel estimation error. In this case, the proposed robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. The other model we consider is a norm-bounded error (NBE) model, where the CSIT error can be specified by an uncertainty set. This model is applicable when the CSIT error is dominated by quantization errors. In this case, we consider a worst-case design. For this model, we consider robust (i) minimum SMSE, (ii) MSE-constrained, and (iii) MSE-balancing transceiver designs. We propose iterative algorithms to solve these problems, wherein each iteration involves a pair of semidefinite programs (SDPs). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints. We evaluate the robustness of the proposed algorithms to imperfections in CSIT through simulation, and show that the proposed robust designs outperform nonrobust designs as well as robust linear transceiver designs reported in the recent literature.

Non-linear Transceiver Designs with Imperfect CSIT Using Convex Optimization

In this paper, we consider non-linear transceiver designs for multiuser multi-input multi-output (MIMO) down-link in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas and each user terminal is equipped with multiple receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for inter-user interference pre-cancellation at the transmitter. We investigate robust THP transceiver designs based on the minimization of BS transmit power with mean square error (MSE) constraints, and balancing of MSE among users with a constraint on the total BS transmit power. We show that these design problems can be solved by iterative algorithms, wherein each iteration involves a pair of convex optimization problems. The robustness of the proposed algorithms to imperfections in CSIT is illustrated through simulations.

High-Rate Space-Time Coded Large-MIMO Systems: Low-Complexity Detection and Channel Estimation

In this paper, we present a low-complexity algorithm for detection in high-rate, non-orthogonal space-time block coded (STBC) large-multiple-input multiple-output (MIMO) systems that achieve high spectral efficiencies of the order of tens of bps/Hz. We also present a training-based iterative detection/channel estimation scheme for such large STBC MIMO systems. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed multistage likelihood ascent search (M-LAS) detector in conjunction with the proposed iterative detection/channel estimation scheme at low complexities. The fact that we could show such good results for large STBCs like 16 X 16 and 32 X 32 STBCs from Cyclic Division Algebras (CDA) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding) establishes the effectiveness of the proposed detector and channel estimator. We decode perfect codes of large dimensions using the proposed detector. With the feasibility of such a low-complexity detection/channel estimation scheme, large-MIMO systems with tens of antennas operating at several tens of bps/Hz spectral efficiencies can become practical, enabling interesting high data rate wireless applications.

A Low-Complexity Near-ML Performance Achieving Algorithm for Large MIMO Detection

In this paper, we present a low-complexity, near maximum-likelihood (ML) performance achieving detector for large MIMO systems having tens of transmit and receive antennas. Such large MIMO systems are of interest because of the high spectral efficiencies possible in such systems. The proposed detection algorithm, termed as multistage likelihood-ascent search (M-LAS) algorithm, is rooted in Hopfield neural networks, and is shown to possess excellent performance as well as complexity attributes. In terms of performance, in a 64 x 64 V-BLAST system with 4-QAM, the proposed algorithm achieves an uncoded BER of 10(-3) at an SNR of just about 1 dB away from AWGN-only SISO performance given by Q(root SNR). In terms of coded BER, with a rate-3/4 turbo code at a spectral efficiency of 96 bps/Hz the algorithm performs close to within about 4.5 dB from theoretical capacity, which is remarkable in terms of both high spectral efficiency as well as nearness to theoretical capacity. Our simulation results show that the above performance is achieved with a complexity of just O(NtNt) per symbol, where N-t and N-tau denote the number of transmit and receive antennas.

Diversity and degrees of freedom of cooperative wireless networks

Two key parameters in the outage characterization of a wireless fading network are the diversity and the degrees of freedom (DOF). These two quantities represent the two endpoints of the diversity multiplexing gain tradeoff, In this paper, we present max-flow min-cut type theorems for computing both the diversity and the DOF of arbitrary single-source single-sink networks with nodes possessing multiple antennas. We also show that an amplify-and-forward protocol is sufficient to achieve the same. The DOF characterization is obtained using a conversion to a deterministic wireless network for which the capacity was recently found. This conversion is operational in the sense that a capacity-achieving scheme for the deterministic network can be converted into a DOF-achieving scheme for the fading network. We also show that the diversity result easily extends to multisource multi-sink networks whereas the DOF result extends to a single-source multi-cast network. Along the way, we prove that the zero error capacity of the deterministic network is the same as its c-error capacity.

Efficient computation of volume fractions for multi-material cell complexes in a grid by slicing

The paper presents a novel slicing based method for computation of volume fractions in multi-material solids given as a B-rep whose faces are triangulated and shared by either one or two materials. Such objects occur naturally in geoscience applications and the said computation is necessary for property estimation problems and iterative forward modeling. Each facet in the model is cut by the planes delineating the given grid structure or grid cells. The method, instead of classifying the points or cells with respect to the solid, exploits the convexity of triangles and the simple axis-oriented disposition of the cutting surfaces to construct a novel intermediate space enumeration representation called slice-representation, from which both the cell containment test and the volume-fraction computation are done easily. Cartesian and cylindrical grids with uniform and non-uniform spacings have been dealt with in this paper. After slicing, each triangle contributes polygonal facets, with potential elliptical edges, to the grid cells through which it passes. The volume fractions of different materials in a grid cell that is in interaction with the material interfaces are obtained by accumulating the volume contributions computed from each facet in the grid cell. The method is fast, accurate, robust and memory efficient. Examples illustrating the method and performance are included in the paper.

Low PAPR STBCs from Complex Partial-Orthogonal Designs (CPODs)

Space-time codes from complex orthogonal designs (CODs) with no zero entries offer low Peak to Average power ratio (PAPR) and avoid the problem of turning off antennas. But CODs for 2(a) antennas with a + 1 complex variables, with no zero entries are not known in the literature for a >= 4. In this paper, a method of obtaining no zero entry (NZE) codes, called Complex Partial-Orthogonal Designs (CPODs), for 2(a+1) antennas whenever a certain type of NZE code exists for 2(a) antennas is presented. This is achieved with slight increase in the ML decoding complexity for regular QAM constellations and no increase for other complex constellations. Since NZE CODs have been constructed recently for 8 antennas our method leads to NZE CPODs for 16 antennas. Moreover, starting from certain NZE CPODs for n antennas, a construction procedure is given to obtain NZE CPODs for 2n antennas. The class of CPODs do not offer full-diversity for all complex constellations. For the NZE CPODs presented in the paper, conditions on the signal sets which will guarantee full-diversity are identified. Simulations results show that bit error performance of our codes under average power constraint is same as that of the CODs and superior to CODs under peak power constraint.

Complex near-orthogonal designs with no zero entry

Zero entries in complex orthogonal designs (CODs) impede their practical implementation. In this paper, a method of obtaining a no zero entry (NZE) code for 2(k+1) antennas whenever a NZE code exists for 2(k) antennas is presented. This is achieved with slight increase in the ML decoding complexity for regular QAM constellations and no increase for other complex constellations. Since NZE CODs have been constructed recently for 8 antennas our method leads to NZE codes for 16 antennas. Simulation results show good performance of our new codes compared to the well known constructions for 16 and 32 antennas under peak power constraints.

Four group decodable differential scaled unitary linear space-time codes

Differential Unitary Space-Time Block codes (STBCs) offer a means to communicate on the Multiple Input Multiple Output (MIMO) channel without the need for channel knowledge at both the transmitter and the receiver. Recently Yuen-Guan-Tjhung have proposed Single-Symbol-Decodable Differential Space-Time Modulation based on Quasi-Orthogonal Designs (QODs) by replacing the original unitary criterion by a scaled unitary criterion. These codes were also shown to perform better than differential unitary STBCs from Orthogonal Designs (ODs). However the rate (as measured in complex symbols per channel use) of the codes of Yuen-Guan-Tjhung decay as the number of transmit antennas increase. In this paper, a new class of differential scaled unitary STBCs for all even number of transmit antennas is proposed. These codes have a rate of 1 complex symbols per channel use, achieve full diversity and moreover they are four-group decodable, i.e., the set of real symbols can be partitioned into four groups and decoding can be done for the symbols in each group separately. Explicit construction of multidimensional signal sets that yield full diversity for this new class of codes is also given.

Low-delay, high-rate, non-square STBCs from scaled complex orthogonal designs

Space-time block codes (STBCs) obtained from non-square complex orthogonal designs are bandwidth efficient compared to those from square real/complex orthogonal designs for colocated coherent MIMO systems and has other applications in (i) non-coherent MIMO systems with non-differential detection, (ii) Space-Time-Frequency codes for MIMO-OFDM systems and (iii) distributed space-time coding for relay channels. Liang (IEEE Trans. Inform. Theory, 2003) has constructed maximal rate non-square designs for any number of antennas, with rates given by [(a+1)/(2a)] when number of transmit antennas is 2a-1 or 2a. However, these designs have large delays. When large number of antennas are considered this rate is close to 1/2. Tarokh et al (IEEE Trans. Inform. Theory, 1999) have constructed rate 1/2 non-square CODs using the rate-1 real orthogonal designs for any number of antennas, where the decoding delay of these codes is less compared to the codes constructed by Liang for number of transmit antennas more than 5. In this paper, we construct a class of rate-1/2 codes for arbitrary number of antennas where the decoding delay is reduced by 50% when compared with the rate-1/2 codes given by Tarokh et al. It is also shown that even though scaling the variables helps to lower the delay it can not be used to increase the rate.

Robust joint precoder/receive filter designs for multiuser MIMO downlink

In this paper, we consider robust joint linear precoder/receive filter designs for multiuser multi-input multi-output (MIMO) downlink that minimize the sum mean square error (SMSE) in the presence of imperfect channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. We consider a stochastic error (SE) model and a norm-bounded error (NBE) model for the CSIT error. In the case of CSIT error following SE model, we compute the desired downlink precoder/receive filter matrices by solving the simpler uplink problem by exploiting the uplink-downlink duality for the MSE region. In the case of the CSIT error following the NBE model, we consider the worst-case SMSE as the objective function, and propose an iterative algorithm for the robust transceiver design. The robustness of the proposed algorithms to imperfections in CSIT is illustrated through simulations.