Golay Complementary Sequences Research Articles

Frequency Multiplexed Scheme for Optical Pulse-Coding φ-OTDR Based on Golay Complementary Sequence

Frequency Multiplexed Scheme for Optical Pulse-Coding φ-OTDR Based on Golay Complementary Sequence

Mutually Orthogonal Golay Complementary Sequences in Medical Ultrasound Diagnostics. Experimental Study

Mutually Orthogonal Golay Complementary Sequences in Medical Ultrasound Diagnostics. Experimental Study

A novel design of multi-user sequence set for joint vehicular radar-communication based on Oppermann family

In this paper, a novel multi-user sequence set which are to be potentially used as communication preambles for joint vehicular radar and communication using Oppermann sequences is proposed. Herein, a set of Oppermann sequences with suitable auto-ambiguity functions (AF) and cross-ambiguity functions (AF) properties have been proposed. Moreover, a channel estimation algorithm using the designed Oppermann sequences is also proposed. The designed preamble, composed of optimized Oppermann sequences is an appropriate candidate for wireless standards, where both channel estimation and multi-user vehicular radar sensing are jointly pursued. The simulation results demonstrate that the designed sequences provide a significant performance improvement for vehicular radar sensing and don't degrade the channel estimation accuracy. The proposed optimized Oppermann sequences have better auto- and cross-AF compared existing Golay complementary sequences (used in IEEE 802.11ad as preamble), Zadoff-Chu sequences (used in 5G to generate preambles for the Physical Random Access Channel (PRACH)) and the non-optimized Oppermann sequences. Specifically, compared to the preamble composed of Golay complementary sequences in IEEE 802.11ad, the proposed sequences reduce the maximum sidelobe level of the auto-AF and maximum value level of cross-AF by at least 2 and 2.85 times, respectively. The target can still be accurately detected in mutual interference scenario caused by multiple radars in the vicinity. Both the sequences, when used for channel estimation achieve the CRLB limit. Both the proposed sequences and Golay complementary sequences, when used for channel estimation achieve the Cramer-Rao Lower Bound.

Evaluation of ACF, CCF, RAC, RCC and MF Properties of Different Spreading Sequences Used in DS-CDMA Systems

This paper investigates the different sequences that can be used in direct sequence divisionmultiple access (DS- CDMA) systems. The auto-correlation, cross correlation, the mean square correlationmeasurements ( RAC, RcC ) and merit factor (MF) are used for evaluating the performance of differentspreading sequences. The results obtained small set of Kasami sequences is the most effective of binarysequences families in terms of correlation measure, but this set suffers from the limited number ofsequences. Overall among orthogonal category, Orthogonal Gold sequences and Golay complementarysequences are a better candidate in synchronous CDMA applications.

A New Construction of 4q-QAM Golay Complementary Sequences.

Quadrature amplitude modulation (QAM) constellation and Golay complementary sequences (GCSs) are usually applied in orthogonal frequency division multiplexing (OFDM) systems to obtain a higher data rate and a lower peak-to-mean envelope power ratio (PMEPR). In this paper, after a sufficient search of the literature, it was found that increasing the family size is an effective way to improve the data rate, and the family size is mainly determined by the number of offsets in the general structure of QAM GCSs. Under the guidance of this idea, we propose a new construction for -QAM GCSs through generalized Boolean functions (GBFs) based on a new description of a -QAM constellation, which aims to enlarge the family size of GCSs and obtain a low PMEPR. Furthermore, a previous construction of -QAM GCSs presented by Li has been proved to be a special case of the new one, and the family size of new sequences is much larger than those previously mentioned, which means that there was a great improvement in the data rate. On the other hand, a previous construction of 16-QAM GCSs presented by Zeng is also a special case of the new one in this paper, when . In the meantime, the proposed sequences have the same PMEPR upper bound as the previously mentioned sequences presented by Li when applied in OFDM systems, which increase the data rate without degrading the PMEPR performance. The theoretical analysis and simulation results show that the proposed new sequences can achieve a higher data rate and a low PMEPR.

Signal-to-noise ratio of diverging waves in multiscattering media: Effects of signal duration and divergence angle.

In this paper, SNR maximization in coded diverging waves is studied, and experimental verification of the results is presented. Complementary Golay sequences and binary phase shift keying modulation are used to code the transmitted signal. The SNR in speckle and pin targets is maximized with respect to chip signal length. The maximum SNR is obtained in diverging wave transmission when the chip signal is as short a duration as the array permits. We determined the optimum diverging wave profile to confine the transmitted ultrasound energy in the imaging sector. The optimized profile also contributes to the SNR maximization. The SNR performances of the optimized coded diverging wave and conventional single-focused phased array imaging are compared on a single frame basis. The SNR of the optimized coded diverging wave is higher than that of the conventional single-focused phased array imaging at all depths and regions.

Radar Imaging Based on IEEE 802.11ad Waveform in V2I Communications

Since most of vehicular radar systems are already exploiting millimeter-wave (mmWave) spectra, it would become much more feasible to implement a joint radar and communication system by extending communication frequencies into the mmWave band. In this paper, an IEEE 802.11ad waveform-based radar imaging technique is proposed for vehicular settings. A roadside unit (RSU) transmits the IEEE 802.11ad waveform to a vehicle for communications while the RSU also listens to the echoes of transmitted waveform to perform inverse synthetic aperture radar (ISAR) imaging. To obtain high-resolution images of the vehicle, the RSU needs to accurately estimate round-trip delays, Doppler shifts, and velocity of vehicle. The proposed ISAR imaging first estimates the round-trip delays using a good correlation property of Golay complementary sequences in the IEEE 802.11ad preamble. The Doppler shifts are then obtained using least square estimation from the echo signals and refined to compensate phase wrapping caused by phase rotation. The velocity of vehicle is determined using an equation of motion and the estimated Doppler shifts. Simulation results verify that the proposed technique is able to form high-resolution ISAR images from point scatterer models of realistic vehicular settings with different viewpoints. The proposed ISAR imaging technique can be used for various vehicular applications, e.g., traffic condition analyses or advanced collision warning systems.

Interference-Fading-Suppressed Pulse-Coding Φ-OTDR Using Spectrum Extraction and Rotated-Vector-Sum Method

With phase-sensitive optical time-domain reflectometry (Φ-OTDR), an optic fiber can be used as a distributed vibration sensor to perceive the external disturbance along the fiber through the phase variation of the Rayleigh backscatter light. However, due to the inevitable interference fading phenomenon, the signal-to-noise ratio (SNR) of Rayleigh backscatter light at certain points is insufficient, thus affecting the fidelity of vibration sensing. In this paper, we propose the spectrum extraction and the rotated-vector-sum (SERVS) method to suppress the interference fading in the pulse-intensity-coding Φ-OTDR, which applies Golay complementary sequence through acousto-optic modulator (AOM). Benefited from the easier implementation, the experimental results demonstrate that the percentage of fading points can be reduced from 2.98% to 0.33% significantly and the standard deviation of differential phase is also decreased from 0.6556 rad to 0.2901 rad. Also the minimum level of averaged power spectral density (PSD) of the differential phase at whole locations along the fiber is reduced about 6 dB/Hz effectively. For the demodulated disturbance signal, no influence on the SNR is observed thus it maintains a SNR improvement of 8.6 dB compared to the traditional single pulse Φ-OTDR system, achieving a noise floor of 2.38 pϵ/√Hz.

Design of QAM-OFDM Radar-Communication Integrated Signal Based on Golay Complementary sequences

The integration of radar and communication is conducive to improving the utilization rate of hardware resources and spectrum. To address the issue that the communication information in orthogonal frequency division multiplexing (OFDM) integrated signal for radar and communication affects detection performance, an OFDM integrated signal for radar and communication based on precoding was proposed. The communication information of the integrated signal was pre-coded by using the Gray Complementary Sequences (GCS) with better correlation performance to improve the performance of the ambiguity function of the integrated signal and its detection ability. Simulation results show that GCS have better correlation performance compared to M and Gold sequences, and the OFDM integrated signal pre-coded by GCS has lower Peak Sidelobes Ratio (PSLR) and comparable radar performance to LFM.

OFDM-IM for Joint Communication and Radar-Sensing: A Promising Waveform for Dual Functionality

The demand for dual-functional wireless systems is on the rise as certain resources become more congested and scarce. Joint communication-radar (JCR) is a promising technology that is becoming very critical and growing in popularity, where communication and radar applications are serviced simultaneously sharing the same hardware/software and the frequency band resources. JCR and its alternatives need to be cleverly integrated into certain waveforms such as orthogonal frequency division multiplexing (OFDM) to function properly without degradation in the performance. With the aid of the promising concepts of index modulation (IM) and Golay complementary sequences, a novel JCR waveform is proposed to serve both communication and radar applications with the same resources. It has been shown by extensive computer simulations that the proposed OFDM with an index modulation (OFDM-IM) waveform outperforms the classical OFDM with fixed pilot design both in bit error rate (BER) performance and radar-based applications by introducing diversity among subcarriers and frequency agility over the whole frequency band.

Selection on Golay complementary sequences in binary pulse compression for microbubble detection

In medical ultrasound imaging using microbubbles (MBs), the nonlinear echoes from the MBs are used for contrast-specific image construction. Techniques such as pulse inversion, amplitude modulation, and the combined method (PIAM) are employed to increase nonlinear components in the echoes. In addition, employment of pulse compression using binary-coded ultrasound can potentially increase the components. In the case of the nonlinear echo, however, a nonlinear sidelobe occurs around the compressed pulse (correlation peak), and nonlinear components for PIAM in the correlation peak are reduced. The shape of the nonlinear sidelobe and the nonlinear-component reduction in the correlation peak can be estimated from the binary codes used. In this study, the optimal binary codes for PIAM are determined from all patterns of 10, 16, and 20 bit Golay codes. Then, the performance of PIAM with pulse compression using each code is evaluated via computer simulations and experiments using the SonoVue MBs.

Mutually orthogonal Golay complementary sequences in the simultaneous synthetic aperture method for medical ultrasound diagnostics. An experimental study

Complementary Golay coded sequences (CGCS) have several advantages over conventional short pulse transmitted signals. Specifically, CGCS allow the signal-to-noise ratio (SNR) to be increased. Moreover, due to matched filtering and compression, echoes resembling the short pulse waveform with substantially higher amplitude can be obtained. However, CGCS require two subsequent transmissions to obtain a single compressed signal. This decreases the data acquisition rate and the frame rate of ultrasound imaging by two-fold. To alleviate this problem, mutually orthogonal Golay complementary sequences (MOGCS) can be used. MOGCS allow the simultaneous transmission of two CGCS pairs to be implemented, yielding the acoustic data for two image frames in one data acquisition cycle.The main objective of this work was an experimental study of the most crucial parameters of the received acoustic signals, e.g. the signal-to-noise ratio (SNR), the side-lobes level (SLL) of the signal and the axial resolution, obtained from simultaneous transmission of two pairs of CGCS comprising a MOGCS set to demonstrate their feasibility of being used in ultrasonography. For this purpose, a simultaneous synthetic transmit aperture method (SSTA) was proposed. The SSTA is based on MOGCS transmission and simultaneous reconstruction of two image frames from a single data acquisition cycle. This doubles the image reconstruction rate in comparison with conventional CGCS signals.In this paper, the ultrasound data from a perfect reflector, commercial phantoms and in vivo measurements were analysed. Two 16-bit long CGCS pairs comprising the MOGCS set were programmed and transmitted using the Verasonics Vantage™ research ultrasound system equipped with a Philips ATL L7-4 linear array ultrasound probe. It was shown that the signal parameters and overall quality of reconstructed B-mode images did not deteriorate when using the MOGCS in comparison to the conventional CGCS and short pulse signals explored so far.

Construction of Golay Complementary Matrices and Its Applications to MIMO Omnidirectional Transmission

Golay complementary sequences (GCS) have found wide applications in radar and communications thanks to their prominent property of complementary autocorrelation. This paper studies the extension of Golay complementary sequences to Golay complementary matrices (GCM), i.e, a pair of matrices whose two-dimensional autocorrelations add to be a two-dimensional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> -function. While the construction of (real) binary GCM are available in the literature, how to construct the quaternary GCM (and the more general unimodular GCM) remains unknown. We put together this missing piece, and show the feasible size that allows for binary and quaternary GCM. The feasible sizes can be further expanded if the phases of the matrices’ entries can be arbitrary. In addition, we consider the extension of the GCM to the set of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N\geq 2$</tex-math></inline-formula> ) matrices, whose two-dimensional autocorrelations add to be a two-dimensional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> -function, which we refer to as autocorrelation complementary matrices (ACM). For <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N=4$</tex-math></inline-formula> , the ACM allows for matrices of arbitrary size. The GCM/ACM can be applied to omnidirectional transmission for a multi-input multi-output (MIMO) communication system with a uniform rectangular array (URA), which is useful for broadcasting cell-wide common messages. We propose two schemes for omnidirectional transmission, one is based on space-time block code (STBC) and the other is based on the dual cross-polarization of the antenna array. Both schemes can be implemented in the radio frequency (RF) analog domain, generating (theoretically) perfect omnidirectional beampattern with low hardware cost.

Binary Golay Spreading Sequences and Reed-Muller Codes for Uplink Grant-Free NOMA

Non-orthogonal multiple access (NOMA) is an emerging technology for massive connectivity in machine-type communications (MTC). In code-domain NOMA, non-orthogonal spreading sequences are uniquely assigned to all devices, where active ones attempt a grant-free access to a system. In this paper, we study a set of user-specific, non-orthogonal, binary spreading sequences for uplink grant-free NOMA. Based on binary Golay complementary sequences, each spreading sequence provides the peak-to-average power ratio (PAPR) of at most 3 dB for multicarrier transmission. Exploiting the theoretical connection to Reed-Muller codes, we conduct a probabilistic analysis to search for a permutation set for Golay sequences, which presents theoretically bounded low coherence for the spreading matrix. Simulation results confirm that the maximum PAPR of transmitted multicarrier signals via the spreading sequences is significantly lower than those for random bipolar, Gaussian, and pseudo-random sequences. Thanks to the low coherence, the performance of compressed sensing (CS) based joint channel estimation and multiuser detection using the spreading sequences turns out to be superior or similar to those for random bipolar, Gaussian, pseudo-random, and Zadoff-Chu sequences. The binary Golay spreading sequences have only two phases regardless of the sequence length, which can make them suitable for low cost MTC devices.

Non-Orthogonal Golay-Based Spreading Sequences for Uplink Grant-Free Access

In this letter, new sets of non-orthogonal spreading sequences are constructed for uplink grant-free access of devices. Based on Golay complementary sequences and sets, the spreading sequences have theoretically bounded low peak-to-average power ratio (PAPR) for multicarrier transmission. Also, the corresponding spreading matrix has theoretically bounded low coherence, which guarantees the reliable performance of compressed sensing (CS) based joint channel estimation (CE) and multiuser detection (MUD). While the spreading sequence set accommodates up to 300% overloaded devices, a large number of distinct sequence sets can also be constructed for future applications. Simulation results demonstrate that the Golay-based sequences exhibit the PAPR of at most 4, which is lower than those for random bipolar, Gaussian, and Zadoff-Chu (ZC) sequences. We also observe that the Golay-based sequences provide the reliable performance for CS-based joint CE and MUD. Finally, the Golay-based sequences have fewer phases than ZC sequences, which can be more suitable for low cost devices in machine-type communications (MTC).

Time-variance of 60 GHz vehicular infrastructure-to-infrastructure (I2I) channel

In this paper, we study the time-variance of a roadside infrastructure to infrastructure (I2I) channel operating at 60 GHz millimetre wave (mmWave) band, where the time-variance is caused by moving vehicles acting as scatterers. At first, measurement data is obtained by placing the transmitter (TX) and the receiver (RX) at different heights to emulate a link between two nonidentical roadside units (RSUs), and time-domain channel sounding is performed by sending complementary Golay sequences from the TX to the RX. A linear piece-wise interpolation of the corresponding temporal auto-correlation function (ACF) is used to find the Doppler spread of the I2I channel, where our interpolation method compensates for a slower sampling rate. Next, a framework is presented for time-variant channel impulse response (CIR) simulation which focuses on moving scatterers only and validates the linear piece-wise ACF model. The framework is useful for time-variant vehicular I2I channel simulation and in speed estimation related vehicular applications. Finally, a double-slope curve-fitted analytical model for ACF is proposed as a generalisation to the linear piece-wise model. The proposed model and its Doppler spectrum are found to be in agreement with the analytical results for fixed-to-fixed (F2F) channels with moving scatterers and matches perfectly with the measured data.

A Family of New 16-QAM Golay Complementary Sequences without Higher PEP Upper Bounds

A Family of New 16-QAM Golay Complementary Sequences without Higher PEP Upper Bounds

A High Signal–Noise Ratio UWB Radar for Buried Pipe Location Using Golay Complementary Sequences

A Golay-based ultra wideband ground penetrating for underground pipes location is proposed and experimentally demonstrated. Golay complementary codes with the code length of 1024 and frequency of 1 GHz are used as the probe signals. The two-dimensional image of the buried pipes is achieved by a correlation method and a back-projection algorithm. The experimental results show that both the plastic pipe and metallic pipe can be located with a range resolution of 10 cm. Furthermore, as the Golay complementary sequences are a pair of complementary sequences, the sum of their correlation function yields twice the value of the peak at the target position and zero elsewhere. Thus, compared with the stepped frequency signal radar or chaotic signal radar, the Golay-based radar can significantly improve the signal–noise ratio and has the capability of deep detection.

A Sufficient Condition for General QAM Complementary Sequence Pairs

This paper investigates the construction of QAM Golay complementary sequence pairs (CSPs) based on standard binary Golay-Davis-Jedwab (GDJ) CSPs. In order to guarantee that the proposed construction produces QAM Golay CSPs, a sufficient condition that the coefficients of offsets should satisfy is developed, which is fit for finding all the coefficients by a computer. In particular, all the coefficients of offsets over the 64- and 256-QAM constellations are given. The proposed construction includes Zeng's and Ma et al.'s ones as special cases. The inputs of resultant sequence pairs are binary signals rather than quaternary ones, which means that the resulting sequences are fit for such QAM systems that merely depend on binary inputs. The obtained QAM Golay CSPs can be applied to orthogonal frequency division multiplexing systems so as to reduce peak envelope power of their signals.

Rudin-Shapiro-Like Sequences With Maximum Asymptotic Merit Factor

Borwein and Mossinghoff investigated the Rudin-Shapiro-like sequences, which are infinite families of binary sequences, usually represented as polynomials. Each family of Rudin-Shapiro-like sequences is obtained from a starting sequence (which we call the seed) by a recursive construction that doubles the length of the sequence at each step, and many sequences produced in this manner have exceptionally low aperiodic autocorrelation. Borwein and Mossinghoff showed that the asymptotic autocorrelation merit factor for any such family is at most 3, and found the seeds of length 40 or less that produce the maximum asymptotic merit factor of 3. The definition of Rudin-Shapiro-like sequences was generalized by Katz, Lee, and Trunov to include sequences with arbitrary complex coefficients, among which are families of low autocorrelation polyphase sequences. Katz, Lee, and Trunov proved that the maximum asymptotic merit factor is also 3 for this larger class. Here we show that a family of such Rudin-Shapiro-like sequences achieves asymptotic merit factor 3 if and only if the seed is either of length 1 or is the interleaving of a pair of Golay complementary sequences. For small seed lengths where this is not possible, the optimal seeds are interleavings of pairs that are as close as possible to being complementary pairs, and the idea of an almost-complementary pair makes sense of remarkable patterns in previously unexplained data on optimal seeds for binary Rudin-Shapiro-like sequences.