It is well known that Boolean functions used in stream and block ciphers should have high algebraic immunity to resist algebraic attacks. Up to now, there have been many constructions of Boolean functions achieving the maximum algebraic immunity. In this paper, we present several constructions of rotation symmetric Boolean functions with maximum algebraic immunity on an odd number of variables which are not symmetric, via a study of invertible cyclic matrices over the binary field. In particular, we generalize the existing results and introduce a new method to construct all the rotation symmetric Boolean functions that differ from the majority function on two orbits. Moreover, we prove that their nonlinearities are upper bounded by .

Polar and Spherical Fourier analysis can be used to extract rotation invariant features for image retrieval and pattern recognition tasks. They are demonstrated to show superiorities comparing with other methods on describing rotation invariant features of two and three dimensional images. Based on mathematical properties of trigonometric functions and associated Legendre polynomials, fast algorithms are proposed for multimedia applications like real time systems and large multimedia databases in order to increase the computation speed. The symmetric points are computed simultaneously. Inspired by relative prime number theory, systematic analysis are given in this paper. Novel algorithm is deduced that provide even faster speed. Proposed method are 9–15% faster than previous work. The experimental results on two and three dimensional images are given to illustrate the effectiveness of the proposed method. Multimedia signal processing applications that need real time polar and spherical Fourier analysis can be benefit from this work.

Cognitive radios are intelligent communications, and are expected to more efficiently utilize the radio channel. Modulation identification is one of the key issues in the cognitive radios. Many works were devoted to the classification of symbol-by-symbol modulations, however, few papers on block modulations have been published. In this paper, an identification error analysis is presented for block orthogonal modulations using General Orthogonal Modulation~(GOM). A symbol error probability is derived for the identified block orthogonal modulation. Numerical results of 4-dimensional block orthogonal modulation are presented with simulation results.

Determining the rotation angle between two images is essential when comparing images that may include rotational variation. While there are three representative methods that utilize the phases of Zernike moments (ZMs) to estimate rotation angles, very little work has been done to compare the performances of these methods. In this paper, we compare the performances of these three methods and propose a new, angular radial transform (ART)-based method. Our method extends Revaud et al.'s method [1] and uses the phase of angular radial transform coefficients instead of ZMs. We show that our proposed method outperforms the ZM-based method using the MPEG-7 shape dataset when computation times are compared or in terms of the root mean square error vs. coverage.

To improve the quality of wireless communication, transmit/receive diversity techniques in multiple-input multiple-output (MIMO) system have been investigated vigorously. In this paper, we consider an asymmetric MIMO orthogonal frequency division multiplexing (MIMO-OFDM) system, in which the number of transmit antennas is larger than that of receive antennas. In this system, there is a need to achieve the high quality of communication in both low and high mobility scenarios by a single transmit diversity scheme. Recently, as for the advanced diversity schemes based on space time block coding (STBC)/space frequency block coding (SFBC), STBC/STBC-phase shift diversity (PSD) and SFBC-frequency switched transmit diversity (FSTD) have been proposed. However, in these schemes, it is possible that time diversity gain can not be sufficiently obtained especially in the low mobility scenario. Therefore, in this paper, the joint use of grouped phase rotation in time/frequency domain and STBC (GPR-STBC) is proposed to get the larger channel coding gains than other schemes. In this paper, we evaluate the average bit error rate (BER) performance by computer simulation in a comparison with the conventional transmit diversity schemes and discuss the relationship from the viewpoints of BER performance and computational complexity.

To characterize and predict the dynamics of the nonlinear polarization rotation in SOAs, an experimental method based on the frequency response technique and a model based on the density matrix and effective index formalisms are presented. Both determine the angular displacement, at the Poincare Sphere, that produces the evolution of the polarization of the output signal.

Fourier transform is a significant tool in image processing and pattern recognition. By introducing a hypercomplex number, hypercomplex Fourier transform treats a signal as a vector field and generalizes the conventional Fourier transform. Inspired from that, hypercomplex polar Fourier analysis that extends conventional polar Fourier analysis is proposed in this paper. The proposed method can handle signals represented by hypercomplex numbers as color images. The hypercomplex polar Fourier analysis is reversible that means it can be used to reconstruct image. The hypercomplex polar Fourier descriptor has rotation invariance property that can be used for feature extraction. Due to the noncommutative property of quaternion multiplication, both left-side and right-side hypercomplex polar Fourier analysis are discussed and their relationships are also established in this paper. The experimental results on image reconstruction, rotation invariance, color plate test and image retrieval are given to illustrate the usefulness of the proposed method as an image analysis tool.

We provide a BER analysis of the well-known rotation code, which has been applied to various transmission schemes, such as coordinate-interleaved design (CID) for space-time block codes and trans-modulation or constellation rearrangement for a cooperative relay system. An upper bound on the BER of the rotation code under a fading channel is derived. It turns out to be much tighter than the existing one, which relies on the Chernoff bound. More specifically, the proposed bound is virtually identical to simulation result when Eb/No is larger than 4 dB.

A BICM-ID system with 3-dimensional rotated BPSK constellation and signal space diversity (SSD) is proposed to combat the effect of Rayleigh fading. A new criterion based on mutual information is proposed to find the optimal rotation matrix, and the labeling that fits well with the outer code is presented. Simulation results show that at BER of 10-5 over a Rayleigh fading channel, with the code length of 192,000 bits and the iteration number of 100, the performance of the proposed system is only about 0.8 dB from the Gaussian-input Shannon limit and exceeds the limit constrained by the traditional QPSK input without rotation or SSD, at the spectrum efficiency of 1 bit/s/Hz.

Advanced Evolved Universal Terrestrial Radio Access (Advanced E-UTRA), called LTE-Advanced, has been standardized in the 3rd Generation Partnership Project (3GPP) as a candidate for IMT-Advanced. LTE-Advanced supports spatial orthogonal-resource transmit diversity (SORTD) [1],[2] for ACK/NACK signals and scheduling requests (SRs), which are used to control downlink hybrid automatic repeat requests (HARQs) and manage uplink radio resources based on uplink data traffic, respectively. Both ACK/NACK signals and SRs are carried via a physical uplink control channel (PUCCH) [3], and a common PUCCH format is used for both ACK/NACK signals and SRs. If SORTD is used, the base station assigns mutually orthogonal resources to each antenna included in the user equipment (UE) for ACK/NACK signals and SRs; hence, the number of required resources increases with the number of transmitting antennas in the UE. In this paper, we study the resource reduction method for ACK/NACK signal and SR in case of SORTD using the concept of common resource. In addition, we investigate a phase rotation scheme for common resources to improve the SR detection performance.

Hybrid automatic repeat request (HARQ) is employed for the Evolved Universal Terrestrial Radio Access (E-UTRA) downlink. The base station not only decodes the ACK/NACK signals from the user equipment (UE), but also detects a termination of the transmission (DTX) of the ACK/NACK signals caused by the mis-detection of the downlink control information (DCI) at the UE side. Since ACK/NACK signals from UEs are multiplexed by CDMA, there are sometimes severe inter-code interference (ICI) effects, which significantly degrade the performance of ACK/NACK signals. In order to mitigate such ICI effects, in [1],[2], we proposed a novel phase rotation scheme on the constellations of the uplink ACK/NACK signals, and confirmed the effects on the ACK/NACK bit error rate performance; however, the previous paper did not analyze the effects of the phase rotation on the DTX detection performance. Hence, in this paper, we further analyze the effects of the phase rotation for the ACK/NACK signals in conjunction with a new DTX detection scheme which utilizes equalizer outputs, and investigate the performance of the proposed scheme by means of computer simulations.

In this paper, a scheme for constructing the flat frequency spectrum of interleaved frequency division multiple access (IFDMA) is proposed. Since IFDMA is one of the single carrier modulation schemes, the frequency spectrum components are fluctuated and depend on the information data sequence. Even if IFDMA modulation scheme makes frequency spectrum dispersive for obtaining frequency diversity gain, frequency diversity gain is reduced by the fluctuation of frequency spectrum. In addition, in decision directed channel estimation (DDCE), which achieves good channel estimation accuracy in fast fading environment, the accuracy of channel transfer function estimated at the significant attenuated frequency component is much degraded. In the proposed technique, a random phase sequence is multiplied to the information data sequence for constructing the flat frequency spectrum. As a result, the frequency diversity gain is enlarged and the accuracy of channel estimation by DDCE is improved. Furthermore, we consider the blind estimation technique for the random phase sequence selected by transmitter. We show the effects of the proposed scheme by computer simulation.

Polar Fourier Descriptor(PFD) and Spherical Fourier Descriptor(SFD) are rotation invariant feature descriptors for two dimensional(2D) and three dimensional(3D) image retrieval and pattern recognition tasks. They are demonstrated to show superiorities compared with other methods on describing rotation invariant features of 2D and 3D images. However in order to increase the computation speed, fast computation method is needed especially for machine vision applications like realtime systems, limited computing environments and large image databases. This paper presents fast computation method for PFD and SFD that are deduced based on mathematical properties of trigonometric functions and associated Legendre polynomials. Proposed fast PFD and SFD are 8 and 16 times faster than direct calculation that significantly boost computation process. Furthermore, the proposed methods are also compact for memory requirements for storing PFD and SFD basis in lookup tables. The experimental results on both synthetic and real data are given to illustrate the efficiency of the proposed method.

In this letter, a novel method is proposed for carrier-frequency offset (CFO) estimation for multiple users in orthogonal frequency division multiple access (OFDMA) uplink with the generalized carrier assignment scheme (GCAS). The base station (BS) is equipped with multiple antennas, and each user's CFO can be estimated by the ESPRIT-like method that utilizes the rotation invariance of the space-domain snapshot matrix. The method is still effective even in fully loaded system with all subcarriers allocated to users. Simulation results illustrate the high performance of the proposed algorithm.

Two novel frequency rotation techniques that suppress multipath interference and increase the frequency diversity gain are proposed for uplink IFDMA systems. These benefits are especially important as the performance of traditional IFDMA falls significantly when the number of simultaneous accessing users becomes large. Frequency rotation was originally proposed to suppress the multipath interference and enlarge the frequency diversity gain of downlink access. Unfortunately, it cannot be applied to the uplink due to the loss of orthogonality among users in the frequency domain. In the proposed frequency rotation techniques, users do not share the multiple frequency orthogonal channels and thus orthogonality among users is maintained. The proposed technique is verified by computer simulations.

This paper proposes an optimized phase rotation sequence method for side lobe suppression by complementing and regulating the side lobe suppression sequence set. The sequence set is efficiently enhanced through the quadratically constrained least square model. The theoretical suppression performance of our method is discussed. Furthermore, our scheme is also suitable for cognitive radio, which is analyzed in the simulation part. The simulation results confirm the effectiveness of our schemes.

Hybrid automatic repeat request (HARQ) is employed for the Evolved Universal Terrestrial Radio Access (E-UTRA) downlink. The ACK/NACK signals from each user equipment (UE) are multiplexed by code division multiple access (CDMA) and transmitted via a physical uplink control channel (PUCCH). The ACK/NACK signals are code spread by the cyclic shift (CS) sequences made from zero auto-correlation (ZAC) sequences; however, the orthogonality of these sequences is not guaranteed depending on the propagation channels; moreover, the amount of inter-code interference (ICI) depends on the delay spread of the channel and the transmitting timing control error of each UE. In the conventional PUCCH structure, ICI between two ACK signals does not degrade their detection performance, whereas ICI between an ACK signal and a NACK signal degrades the detection performance. This causes a serious gap between the detection performances of ACK and NACK signals, because generally in a PUCCH, there are more ACK signals than NACK signals. In this paper, we propose a novel phase rotation scheme on the constellations of ACK/NACK signals that can resolve this issue, and the simulation evaluation results confirm the benefits of the proposed phase rotation scheme.

In this paper, we propose a new approach to rotation invariant texture analysis. This method uses the Radon transform with some considerations in direction estimation of textural images. Furthermore, it utilizes the information obtained from the number of peaks in the variance array of the Radon transform as a realty feature. The textural features are then generated after rotation of texture along principle direction. Also, to eliminating the introduced error due to rotation of texture, a simple technique is presented. Experimental results on a set of images from the Brodatz album show a good performance achieved by the proposed method in comparison with some recent texture analysis methods.

This paper presents a technique for high-accuracy estimation of image rotation using 1D Phase-Only Correlation (POC). The rotation angle between two images is estimated as follows: (i) compute the amplitude spectra of the given images, (ii) transform the coordinate system of amplitude spectra from Cartesian coordinates to polar coordinates, and (iii) estimate the translational displacement between the polar-mapped amplitude spectra to obtain the rotation angle. While the conventional approach is to employ 2D POC for high-accuracy displacement estimation in (iii), this paper proposes the use of 1D POC with an adaptive line selection scheme. The proposed technique makes possible to improve the accuracy of rotation estimation for low contrast images of artificial objects with regular geometric shapes and to reduce the total computation cost by 50%.

A rotation invariant texture analysis technique is proposed with a novel combination of Radon Transform (RT) and Hidden Markov Models (HMM). Features of any texture are extracted during RT which due to its inherent property captures all the directional properties of a certain texture. HMMs are used for classification purpose. One HMM is trained for each texture on its feature vector which preserves the rotational invariance of feature vector in a more compact and useful form. Once all the HMMs have been trained, testing is done by picking any of these textures at any arbitrary orientation. The best percentage of correct classification (PCC) is above 98 % carried out on sixty texture of Brodatz album.