Optimal Joint Antenna Selection and Power Adaptation in Underlay Cognitive Radios

Transmit antenna selection (AS) is a popular, low hardware complexity technique that improves the performance of an underlay cognitive radio system, in which a secondary transmitter can transmit when the primary is on but under tight constraints on the interference it causes to the primary. The underlay interference constraint fundamentally changes the criterion used to select the antenna because the channel gains to the secondary and primary receivers must be both taken into account. We develop a novel and optimal joint AS and transmit power adaptation policy that minimizes a Chernoff upper bound on the symbol error probability (SEP) at the secondary receiver subject to an average transmit power constraint and an average primary interference constraint. Explicit expressions for the optimal antenna and power are provided in terms of the channel gains to the primary and secondary receivers. The SEP of the optimal policy is at least an order of magnitude lower than that achieved by several ad hoc selection rules proposed in the literature and even the optimal antenna selection rule for the case where the transmit power is either zero or a fixed value.

Fault-tolerant secret key generation

Mobile nodes observing correlated data communicate using an insecure bidirectional switch to generate a secret key, which must remain concealed from the switch. We are interested in fault-tolerant secret key rates, i.e., the rates of secret key generated even if a subset of nodes drop out before the completion of the communication protocol. We formulate a new notion of fault-tolerant secret key capacity, and present an upper bound on it. This upper bound is shown to be tight when the random variables corresponding to the observations of nodes are exchangeable. Further, it is shown that one round of interaction achieves the fault-tolerant secret key capacity in this case. The upper bound is also tight for the case of a pairwise independent network model consisting of a complete graph, and can be attained by a noninteractive protocol.

Stability of long unsupported twin circular tunnels in soils

The stability of two long unsupported circular parallel tunnels aligned horizontally in fully cohesive and cohesive-frictional soils has been determined. An upper bound limit analysis in combination with finite elements and linear programming is employed to perform the analysis. For different clear spacing (S) between the tunnels, the stability of tunnels is expressed in terms of a non-dimensional stability number (gamma H-max/c); where H is tunnel cover, c refers to soil cohesion, and gamma(max) is maximum unit weight of soil mass which the tunnels can bear without any collapse. The variation of the stability number with tunnels' spacing has been established for different combinations of H/D, m and phi; where D refers to diameter of each tunnel, phi is the internal friction angle of soil and m accounts for the rate at which the cohesion increases linearly with depth. The stability number reduces continuously with a decrease in the spacing between the tunnels. The optimum spacing (S-opt) between the two tunnels required to eliminate the interference effect increases with (i) an increase in H/D and (ii) a decrease in the values of both m and phi. The value of S-opt lies approximately in a range of 1.5D-3.5D with H/D = 1 and 7D-12D with H/D = 7. The results from the analysis compare reasonably well with the different solutions reported in literature. (C) 2013 Elsevier Ltd. All rights reserved.

SEP-Optimal Transmit Power Policy for Peak Power and Interference Outage Probability Constrained Underlay Cognitive Radios

In underlay cognitive radio (CR), a secondary user (SU) can transmit concurrently with a primary user (PU) provided that it does not cause excessive interference at the primary receiver (PRx). The interference constraint fundamentally changes how the SU transmits, and makes link adaptation in underlay CR systems different from that in conventional wireless systems. In this paper, we develop a novel, symbol error probability (SEP)-optimal transmit power adaptation policy for an underlay CR system that is subject to two practically motivated constraints, namely, a peak transmit power constraint and an interference outage probability constraint. For the optimal policy, we derive its SEP and a tight upper bound for MPSK and MQAM constellations when the links from the secondary transmitter (STx) to its receiver and to the PRx follow the versatile Nakagami-m fading model. We also characterize the impact of imperfectly estimating the STx-PRx link on the SEP and the interference. Extensive simulation results are presented to validate the analysis and evaluate the impact of the constraints, fading parameters, and imperfect estimates.

On t-designs and bounds relating query complexity to error resilience in locally correctable codes

An n-length block code C is said to be r-query locally correctable, if for any codeword x ∈ C, one can probabilistically recover any one of the n coordinates of the codeword x by querying at most r coordinates of a possibly corrupted version of x. It is known that linear codes whose duals contain 2-designs are locally correctable. In this article, we consider linear codes whose duals contain t-designs for larger t. It is shown here that for such codes, for a given number of queries r, under linear decoding, one can, in general, handle a larger number of corrupted bits. We exhibit to our knowledge, for the first time, a finite length code, whose dual contains 4-designs, which can tolerate a fraction of up to 0.567/r corrupted symbols as against a maximum of 0.5/r in prior constructions. We also present an upper bound that shows that 0.567 is the best possible for this code length and query complexity over this symbol alphabet thereby establishing optimality of this code in this respect. A second result in the article is a finite-length bound which relates the number of queries r and the fraction of errors that can be tolerated, for a locally correctable code that employs a randomized algorithm in which each instance of the algorithm involves t-error correction.

Differential evolution based 3-D guidance law for a realistic interceptor model

This paper presents a novel, soft computing based solution to a complex optimal control or dynamic optimization problem that requires the solution to be available in real-time. The complexities in this problem of optimal guidance of interceptors launched with high initial heading errors include the more involved physics of a three dimensional missile-target engagement, and those posed by the assumption of a realistic dynamic model such as time-varying missile speed, thrust, drag and mass, besides gravity, and upper bound on the lateral acceleration. The classic, pure proportional navigation law is augmented with a polynomial function of the heading error, and the values of the coefficients of the polynomial are determined using differential evolution (DE). The performance of the proposed DE enhanced guidance law is compared against the existing conventional laws in the literature, on the criteria of time and energy optimality, peak lateral acceleration demanded, terminal speed and robustness to unanticipated target maneuvers, to illustrate the superiority of the proposed law. (C) 2013 Elsevier B. V. All rights reserved.

On 2-D Non-Adjacent-Error Channel Models

In this work, we consider two-dimensional (2-D) binary channels in which the 2-D error patterns are constrained so that errors cannot occur in adjacent horizontal or vertical positions. We consider probabilistic and combinatorial models for such channels. A probabilistic model is obtained from a 2-D random field defined by Roth, Siegel and Wolf (2001). Based on the conjectured ergodicity of this random field, we obtain an expression for the capacity of the 2-D non-adjacent-errors channel. We also derive an upper bound for the asymptotic coding rate in the combinatorial model.

Vertical uplift resistance of two closely spaced horizontal strip anchors embedded in cohesive-frictional weightless medium

The vertical uplift resistance of two closely spaced horizontal strip plate anchors has been investigated by using lower and upper bound theorems of the limit analysis in combination with finite elements and linear optimization. The interference effect on uplift resistance of the two anchors is evaluated in terms of a nondimensional efficiency factor (eta(c)). The variation of eta(c) with changes in the clear spacing (S) between the two anchors has been established for different combinations of embedment ratio (H/B) and angle of internal friction of the soil (phi). An interference of the anchors leads to a continuous reduction in uplift resistance with a decrease in spacing between the anchors. The uplift resistance becomes a minimum when the two anchors are placed next to each other without any gap. The critical spacing (S-cr) between the two anchors required to eliminate the interference effect increases with an increase in the values of both H/B and phi. The value of S-cr was found to lie approximately in the range 0.65B-1.5B with H/B = 1 and 11B-14B with H/B = 7 for phi varying from 0 degrees to 30 degrees.

Vertical uplift resistance of two horizontal strip anchors with common vertical axis

With an application of the upper bound finite element limit analysis, the vertical pullout capacity of a group of two horizontal strip plate anchors, with the common vertical axis and placed in a cohesive-frictional soil, has been computed. The variation of the uplift factors Fc, Fq and Fy, due to the contributions of soil cohesion, surcharge pressure and unit weight, respectively, has been evaluated for different combinations of S/B and H/B. As compared to single isolated anchor, the group of two anchors generates significantly greater magnitude of Fc for Φ ≤ 20° especially with greater values of H/B and under fully bonded anchor-soil interface condition. The factor Fc attains almost the maximum value when the upper anchor plate is placed midway between ground surface and the lower anchor plate. The factors Fq and Fy, on the other hand, for a group of two anchors are found to remain almost equal to that of a single isolated anchor as long as the levels of the lower plate in the group and the single isolated anchor are kept the same.

Antenna Selection with Power Adaptation in Interference-Constrained Cognitive Radios

The performance of an underlay cognitive radio (CR) system, which can transmit when the primary is on, is curtailed by tight constraints on the interference it can cause to the primary receiver. Transmit antenna selection (AS) improves the performance of underlay CR by exploiting spatial diversity but with less hardware. However, the selected antenna and its transmit power now both depend on the channel gains to the secondary and primary receivers. We develop a novel Chernoffbound based optimal AS and power adaptation (CBBOASPA) policy that minimizes an upper bound on the symbol error probability (SEP) at the secondary receiver, subject to constraints on the average transmit power and the average interference to the primary. The optimal antenna and its power are presented in an insightful closed form in terms of the channel gains. We then analyze the SEP of CBBOASPA. Extensive benchmarking shows that the SEP of CBBOASPA for both MPSK and MQAM is one to two orders of magnitude lower than several ad hoc AS policies and even optimal AS with on-off power control.

Vertical Uplift Resistance of Two Interfering Horizontal Anchors in Clay

The vertical uplift resistance of two interfering rigid strip plate anchors embedded horizontally at the same level in clay has been examined. The lower and upper bound theorems of the limit analysis in combination with finite-elements and linear optimization have been employed to compute the failure load in a bound form. The analysis is meant for an undrained condition and it incorporates the increase of cohesion with depth. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (eta c gamma) resulting from the combined components of soil cohesion (c) and soil unit weight (gamma), has been computed for different values of embedment ratio (H/B), the rate of linear increase of cohesion with depth (m) and normalized unit weight (gamma H/c). The magnitude of eta c gamma has been found to reduce continuously with a decrease in the spacing between the anchors, and the uplift resistance becomes minimum for S/B=0. It has been noted that the critical spacing between the anchors required to eliminate the interference effect increases continuously with (1) an increase in H/B, and (2) a decrease in m.

Stability of a circular tunnel in presence of pseudostatic seismic body forces

The stability of a long circular tunnel in a cohesive frictional soil medium has been determined in the presence of horizontal pseudo-static seismic body forces. The tunnel is supported by means of lining and anchorage system which is assumed to exert uniform internal compressive normal pressure on its periphery. The upper bound finite element limit analysis has been performed to compute the magnitude of the internal compressive pressure required to support the tunnel. The results have been presented in terms of normalized compressive normal stress, defined in terms of sigma(i)/c; where sigma(i) is the magnitude of the compressive normal pressure on the periphery of the tunnel and c refers to soil cohesion. The variation of sigma(i)/c with horizontal earthquake acceleration coefficient (alpha(h)) has been established for different combinations of H/D, gamma D/c and phi where (i) H and D refers to tunnel cover and diameter, respectively, and (ii) gamma and phi correspond to unit weight and internal friction angle of soil mass, respectively. Nodal velocity patterns have also been plotted for assessing the zones of significant plastic deformation. The analysis clearly reveals that an increase in the magnitude of the earthquake acceleration leads to a significant increment in the magnitude of internal compressive pressure. (C) 2014 Elsevier Ltd. All rights reserved.

Stability of Unsupported Vertical Circular Excavations

A methodology has been presented for determining the stability of unsupported vertical cylindrical excavations by using an axisymmetric upper bound limit analysis approach in conjunction with finite elements and linear optimization. For the purpose of excavation design, stability numbers (S-n) have been generated for both (1) cohesive-frictional soils and (2) pure cohesive soils, with an additional provision accounting for linearly increasing cohesion with increasing depth by means of a nondimensional factor m. The variation of S-n with H/b has been established for different values of m and phi, where H and b refer to the height and radius of the cylindrical excavation. A number of useful observations have been gathered about the variation of the stability number and nodal velocity patterns as H/b, phi, and m change. The results of the analysis compare quite well with the different solutions reported in the literature. (C) 2014 American Society of Civil Engineers.

Codes With Local Regeneration and Erasure Correction

Regenerating codes and codes with locality are two coding schemes that have recently been proposed, which in addition to ensuring data collection and reliability, also enable efficient node repair. In a situation where one is attempting to repair a failed node, regenerating codes seek to minimize the amount of data downloaded for node repair, while codes with locality attempt to minimize the number of helper nodes accessed. This paper presents results in two directions. In one, this paper extends the notion of codes with locality so as to permit local recovery of an erased code symbol even in the presence of multiple erasures, by employing local codes having minimum distance >2. An upper bound on the minimum distance of such codes is presented and codes that are optimal with respect to this bound are constructed. The second direction seeks to build codes that combine the advantages of both codes with locality as well as regenerating codes. These codes, termed here as codes with local regeneration, are codes with locality over a vector alphabet, in which the local codes themselves are regenerating codes. We derive an upper bound on the minimum distance of vector-alphabet codes with locality for the case when their constituent local codes have a certain uniform rank accumulation property. This property is possessed by both minimum storage regeneration (MSR) and minimum bandwidth regeneration (MBR) codes. We provide several constructions of codes with local regeneration which achieve this bound, where the local codes are either MSR or MBR codes. Also included in this paper, is an upper bound on the minimum distance of a general vector code with locality as well as the performance comparison of various code constructions of fixed block length and minimum distance.

From Selective-ID to Full-ID IBS without Random Oracles

Since its induction, the selective-identity (sID) model for identity-based cryptosystems and its relationship with various other notions of security has been extensively studied. As a result, it is a general consensus that the sID model is much weaker than the full-identity (ID) model. In this paper, we study the sID model for the particular case of identity-based signatures (IBS). The main focus is on the problem of constructing an ID-secure IBS given an sID-secure IBS without using random oracles-the so-called standard model-and with reasonable security degradation. We accomplish this by devising a generic construction which uses as black-box: i) a chameleon hash function and ii) a weakly-secure public-key signature. We argue that the resulting IBS is ID-secure but with a tightness gap of O(q(s)), where q(s) is the upper bound on the number of signature queries that the adversary is allowed to make. To the best of our knowledge, this is the first attempt at such a generic construction.