Optimization Methods for Designing Sequences with Low Autocorrelation Sidelobes

Unimodular sequences with low autocorrelations are desired in many applications, especially in the area of radar and code-division multiple access (CDMA). In this paper, we propose a new algorithm to design unimodular sequences with low integrated sidelobe level (ISL), which is a widely used measure of the goodness of a sequence's correlation property. The algorithm falls into the general framework of majorization-minimization (MM) algorithms and thus shares the monotonic property of such algorithms. In addition, the algorithm can be implemented via fast Fourier transform (FFT) operations and thus is computationally efficient. Furthermore, after some modifications the algorithm can be adapted to incorporate spectral constraints, which makes the design more flexible. Numerical experiments show that the proposed algorithms outperform existing algorithms in terms of both the quality of designed sequences and the computational complexity

Performance Assessment of Polyphase Sequences Using Cyclic Algorithm

Polyphase Sequences (known as P1, P2, Px, Frank) exist for a square integer length with good auto correlation properties are helpful in the several applications. Unlike the Barker and Binary Sequences which exist for certain length and exhibits a maximum of two digit merit factor. The Integrated Sidelobe level (ISL) is often used to define excellence of the autocorrelation properties of given Polyphase sequence. In this paper, we present the application of Cyclic Algorithm named CA which minimizes the ISL (Integrated Sidelobe Level) related metric which in turn improve the Merit factor to a greater extent is main thing in applications like RADAR, SONAR and communications. To illustrate the performance of the P1, P2, Px, Frank sequences when cyclic Algorithm is applied. we presented a number of examples for integer lengths. CA(Px) sequence exhibits the good Merit Factor among all the Polyphase sequences that are considered

Convolutional compressed sensing using deterministic sequences

This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain

One- and two-level filter-bank convolvers

In a recent paper, it was shown in detail that in the case of orthonormal and biorthogonal filter banks we can convolve two signals by directly convolving the subband signals and combining the results. In this paper, we further generalize the result. We also derive the statistical coding gain for the generalized subband convolver. As an application, we derive a novel low sensitivity structure for FIR filters from the convolution theorem. We define and derive a deterministic coding gain of the subband convolver over direct convolution for a fixed wordlength implementation. This gain serves as a figure of merit for the low sensitivity structure. Several numerical examples are included to demonstrate the usefulness of these ideas. By using the generalized polyphase representation, we show that the subband convolvers, linear periodically time varying systems, and digital block filtering can be viewed in a unified manner. Furthermore, the scheme called IFIR filtering is shown to be a special case of the convolver

POLYPHASE SEQUENCES ANALYSIS WITH GOOD MERIT FACTOR AND CORRELATION PROPERTIES

Polyphase sequences such as Pn (n = 1, 2, 3, 4, x), Frank, Golomb, the Chu with large Merit factor and correlation properties are helpful in applications like RADAR, SONAR, channel estimation and communications. The Correlation function of a given sequence expressed by integrated sidelobe level (ISL). The ISL related metrics minimized by improving the performance parameters Merit Factor (MF) and Modified Merit Factor (MMF). In this paper, the merit factors are compared with all sequences for the usual case and considering the Weights (ones and zeros throughout the sequence length) from 102 to 103~4 . The observation is made for four consecutive even, and odd square integer lengths say 162 , 172 , 182 , and 192 . The Px sequence exhibits the best merit factor among all Polyphase sequences. P2 sequence existed only for even square integer length when no weights applied. P1, Px, Frank sequences shows the good MMFs among all Polyphase sequences. For the possible lengths, the Elapsed time is more for MF than MMF except at four consecutive even and odd square integer lengths

Golden Modulation: a New and Effective Waveform for Massive IoT

This paper considers massive Internet of Things systems, especially for LoW Power Wide Area Networks, that aim at connecting billions of low-cost devices with multi-year battery life requirements. Current systems for massive Internet of Things exhibit severe problems when trying to pursue the target of serving a very large number of users. In this paper, a novel asynchronous spread spectrum modulation, called Golden Modulation, is introduced. This modulation provides a vast family of equivalent waveforms with very low cross-interference even in asynchronous conditions, hence enabling natural multiuser operation without the need for inter-user synchronization or for interference cancellation receivers. Thanks to minimal interference between waveforms, coupled with the absence of coordination requirements, this modulation can accommodate very high system capacity. The basic modulation principles, relying on spectrum spreading via direct Zadoff-Chu sequences modulation, are presented and the corresponding theoretical bit error rate performance in an additive white Gaussian noise channel is derived and compared by simulation with realistic Golden Modulation receiver performance. The demodulation of the Golden Modulation is also described, and its performance in the presence of uncoordinated multiple users is characterized.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Ternary and quadriphase sequence diffusers

A room acoustic diffuser breaks up reflected wavefronts, and this can be achieved by presenting a spatially varying surface impedance. In hybrid surfaces, varying impedance is achieved by patches of absorption and reflection, giving reflection coefficients nominally of 0 and 1. These surfaces are hybrids, absorbing some of the incident sound while diffusing any reflected energy. A problem with planar hybrid surfaces is that specular energy is only removed by absorption. By exploiting interference, by reflecting waves out-of-phase with the specular energy, it is possible to diminish the specular energy further. This can be achieved by using a diffuser based on a ternary sequence that nominally has reflection coefficients of 0, -1, and +1. Ternary sequences are therefore a way of forming hybrid absorber-diffusers that achieve better scattering performance without additional absorption. This paper discusses methods for making ternary sequence diffusers, including giving sequence generation methods. It presents prediction results based on Fourier and boundary element method models to examine the performance. While ternary diffusers have better performance than unipolar binary diffusers at most frequencies, there are frequencies at which the performances are the same. This can be overcome by forming diffusers from four-level, quadriphase sequences

Code design and analysis for multiple access communications

This thesis explores various coding aspects of multiple access communications, mainly for spread spectrum multiaccess(SSMA) communications and collaborative coding multiaccess(CCMA) communications. Both the SSMA and CCMA techniques permit efficient simultaneous transmission by several users sharing a common channel, without subdivision in time or frequency. The general principle behind these two multiaccess schemes is that one can find sets of signals (codes) which can be combined together to form a composite signal; on reception, the individual signals in the set can each be recovered from the composite signal. For the CCMA scheme, the isolation between users is based on the code structure; for the SSMA scheme, on the other hand, the isolation between users is based on the autocorrelation functions(ACFs) and crosscorrelation functions (CCFs) of the code sequences. It is clear that, in either case, the code design is the key to the system design.For the CCMA system with a multiaccess binary adder channel, a class of superimposed codes is analyzed. It is proved that every constant weight code of weight w and maximal correlation λ corresponds to a subclass of disjunctive codes of order T 3, the out-of-phase ACFs and CCFs of the codes are constant and equal to √L. In addition, all codes of the same length are mutually orthogonal.2. Maximal length sequences (m-sequences) over Gaussian integers, suitable for use with QAM modulation, are considered. Two sub-classes of m-sequences with quasi-perfect periodic autocorrelations are obtained. The CCFs between the decimated m-sequences are studied. By applying a simple operation, it is shown that some m-sequences over rational and Gaussian integers can be transformed into perfect sequences with impulsive ACFs.3. Frank codes and Chu codes have perfect periodic ACFs and optimum periodic CCFs. In addition, it is shown that they also have very favourable nonperiodic ACFs; some new results concerning the behaviour of the nonperiodic ACFs are derived. Further, it is proved that the sets of combinedFrank/Chu codes, which contain a larger number of codes than either of the two constituent sets, also have very good periodic CCFs. Based on Frank codes and Chu codes, two interesting classes of real-valued codes with good correlation properties are defined. It is shown that these codes have periodic complementary properties and good periodic and nonperiodic ACF/CCFs.Finally, a hybrid CCMA/SSMA coding scheme is proposed. This new hybrid coding scheme provides a very flexible and powerful multiple accessing capability and allows simple and efficient decoding. Given an SSMA system with K users and a CCMA system with N users, where at most T users are active at any time, then the hybrid system will have K . N users with at most T.K users active at any time. The hybrid CCMA/SSMA coding scheme is superior to the individual CCMA system or SSMA system in terms of information rate, number of users, decoding complexity and external interference rejection capability

Code design and analysis for multiple access communications

This thesis explores various coding aspects of multiple access communications, mainly for spread spectrum multiaccess(SSMA) communications and collaborative coding multiaccess(CCMA) communications. Both the SSMA and CCMA techniques permit efficient simultaneous transmission by several users sharing a common channel, without subdivision in time or frequency. The general principle behind these two multiaccess schemes is that one can find sets of signals (codes) which can be combined together to form a composite signal; on reception, the individual signals in the set can each be recovered from the composite signal. For the CCMA scheme, the isolation between users is based on the code structure; for the SSMA scheme, on the other hand, the isolation between users is based on the autocorrelation functions(ACFs) and crosscorrelation functions (CCFs) of the code sequences. It is clear that, in either case, the code design is the key to the system design.For the CCMA system with a multiaccess binary adder channel, a class of superimposed codes is analyzed. It is proved that every constant weight code of weight w and maximal correlation λ corresponds to a subclass of disjunctive codes of order T 3, the out-of-phase ACFs and CCFs of the codes are constant and equal to √L. In addition, all codes of the same length are mutually orthogonal.2. Maximal length sequences (m-sequences) over Gaussian integers, suitable for use with QAM modulation, are considered. Two sub-classes of m-sequences with quasi-perfect periodic autocorrelations are obtained. The CCFs between the decimated m-sequences are studied. By applying a simple operation, it is shown that some m-sequences over rational and Gaussian integers can be transformed into perfect sequences with impulsive ACFs.3. Frank codes and Chu codes have perfect periodic ACFs and optimum periodic CCFs. In addition, it is shown that they also have very favourable nonperiodic ACFs; some new results concerning the behaviour of the nonperiodic ACFs are derived. Further, it is proved that the sets of combinedFrank/Chu codes, which contain a larger number of codes than either of the two constituent sets, also have very good periodic CCFs. Based on Frank codes and Chu codes, two interesting classes of real-valued codes with good correlation properties are defined. It is shown that these codes have periodic complementary properties and good periodic and nonperiodic ACF/CCFs.Finally, a hybrid CCMA/SSMA coding scheme is proposed. This new hybrid coding scheme provides a very flexible and powerful multiple accessing capability and allows simple and efficient decoding. Given an SSMA system with K users and a CCMA system with N users, where at most T users are active at any time, then the hybrid system will have K . N users with at most T.K users active at any time. The hybrid CCMA/SSMA coding scheme is superior to the individual CCMA system or SSMA system in terms of information rate, number of users, decoding complexity and external interference rejection capability