Golay Complementary Codes Research Articles

PAPR Reduction of CC-OFDM MIMO Radar Waveform using Golay Codes

The development of modern radar technology demands multi-functional features that lead to the importance of designing a flexible, software-controlled digital waveform generator. The CC-OFDM MIMO radar waveforms allow flexibility in subcarrier management; hence it is possible to generate multiple narrow beams which transmitted simultaneously for providing all time coverage of the area.However, the main issue of OFDM is the high level of its PAPR value. This will cause non-linear distortion that potentially ruin the orthogonality of the OFDM subcarriers and in the end gives error in the radar detection results. In this paper, PAPR reduction using phase coding is done, by comparing the performance of complementary Hadamard, complementary Golay codes and combining it with Selective Mapping (SLM). The PAPR results show that complementary Golay codes without SLM are superior to complementary Hadamard with or without SLM. The maximum PAPR value of 65 beams transmitted simultaneously are 4.9 dB and 11.1 dB for CC OFDM waveform using complementary Golay codes and Hadamard respectively.

Joint Radar Communication With Novel GCC Preamble and Point-Wise Minimum Fusion

In this paper, a new preamble waveform design and a corresponding minimum-point processing algorithm at receiver are proposed to perform radar sensing of communication signal echoes. In our design, we consider the millimeter wave (mmWave) 802.11ad/802.11ay communication frame format as a reference. Our proposed new preamble replaces the second pair of single-carrier (SC) Golay complementary code (GCC) used in the preamble of IEEE 802.11ad/802.11ay by orthogonal frequency-division multiplexing (OFDM) GCC waveform, resulting in a SC-OFDM GCC preamble waveform. At the receiver, a point-wise minimum operation is performed on the separate radar ambiguity functions (AF) of the SC-GCC and OFDM-GCC to improve the overall quality of the preamble AF. Furthermore, point-wise minimum processing is applied to fuse the communication data AF and the preamble AF, so as to further enhance the radar sensing quality of the entire communication frame. In addition, theoretical analysis of the performance gain of such radar AF fusion is provided. Both theoretical analysis and simulation results demonstrate that the newly proposed SC-OFDM GCC preamble design and the minimum-point fusion of data AF and preamble AF provide a significant performance improvement for automotive radar sensing. Specifically, the proposed SC-OFDM GCC preamble with minimum-point processing algorithm improves the peak-to-max-sidelobe ratio (PMSR) of radar AF over the conventional 802.11ad/802.11ay preamble. Moreover, the proposed preamble-data AF fusion technique further enhances the PMSR as well as the Doppler resolution over the existing joint radar communication systems (which process either the preamble echo or the data echo only). Finally, the proposed minimum-point processing and data AF fusion are extended from single-frame to multi-frame processing to further improve the Doppler resolution.

Nonlinear Harmonic Distortion of Complementary Golay Codes.

Recent advances in electronics miniaturization have led to the development of low-power, low-cost, point-of-care ultrasound scanners. Low-cost systems employing simple bi-level pulse generation devices need only utilize binary phase modulated coded excitations to significantly improve sensitivity; however the performance of complementary codes in the presence of nonlinear harmonic distortion has not been thoroughly investigated. Through simulation, it was found that nonlinear propagation media with little attenuative properties can significantly deteriorate the Peak Sidelobe Level (PSL) performance of complementary Golay coded pulse compression, resulting in PSL levels of -62 dB using nonlinear acoustics theory contrasted with -198 dB in the linear case. Simulations of 96 complementary pairs revealed that some pairs are more robust to sidelobe degradation from nonlinear harmonic distortion than others, up to a maximum PSL difference of 17 dB between the best and worst performing codes. It is recommended that users consider the effects of nonlinear harmonic distortion when implementing binary phase modulated complementary Golay coded excitations.

A Crack Size Quantification Method Using High-Resolution Lamb Waves.

Traditional tone burst excitation cannot attain a high output resolution, due to the time duration. The received signal is much longer than that of excitation during the propagation, which can increase the difficulty of signal processing, and reduce the resolution. Therefore, it is of significant interest to develop a general methodology for crack quantification through the optimal design of the excitation waveform and signal-processing methods. This paper presents a new crack size quantification method based on high-resolution Lamb waves. The linear chirp (L-Chirp) signal and Golay complementary code (GCC) signal are used as Lamb wave excitation signals. After dispersion removal, these excitation waveforms, based on pulse compression, can effectively improve the inspection resolution in plate-like structures. A series of simulations of both healthy plates and plates with different crack sizes are performed by Abaqus CAE, using different excitation waveforms. The first wave package of the S0 mode after pulse compression is chosen to extract the damage features. A multivariate regression model is proposed to correlate the damage features to the crack size. The effectiveness of the proposed crack size quantification method is verified by a comparison with tone burst excitation, and the accuracy of the crack size quantification method is verified by validation experiments.

Range-Doppler Sidelobe Suppression for Pulsed Radar Based on Golay Complementary Codes

To relieve the interference caused by range-Doppler sidelobes in pulsed radars, we propose a new method to construct Doppler resilient complementary waveforms based on Golay codes. We design both the transmit pulse train and the receive pulse weights, so that the similarity between the pulse weights and a given window function is maximized and the constraints on Doppler null points and energy are met. That is summarized as a two-way partitioning problem, and then solved by semidefinite programming and randomization techniques. The novel waveform thus obtained has its range sidelobe outright suppressed in multiple and flexibly-adjustable Doppler zones, and performs well in Doppler sidelobe suppression, Doppler resolution and SNR. It shows great promise in detecting slightly-moving weak targets with the existence of dense interference.

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.

Improving the Signal-to-Noise Ratio of Time Domain Fiber Bragg Grating Sensor Based on Hybrid Simplex and Golay Coding Technique

We report on the experimental results of the combination of unique auto-correlation properties of Golay complementary code and Hadamard matrix properties of standard simplex code. The combination of the two coding techniques results in improvement of the signal-to-noise ratio (SNR) of time domain multiplexed fiber Bragg grating (TDM-FBG) sensor for temperature measurement. Previously, we have analyzed the properties of both coding techniques when deployed separately in the TDM-FBG sensor. In this case, both coding techniques result in the same amount of SNR improvement for code length longer than 31 bits. In this paper, we demonstrate the combination and simultaneous deployment of the two techniques to measure multiple FBGs under room condition (25 °C) and 50 °C temperature. The two schemes combination results in remarkable improvement of SNR and still retains the original spatial property of the decoded FBG signals, confirming the successful deployment of the hybrid codes. From the measurement of two FBG sensors located after 16 km of fiber, the combination of 31 bits of simplex- and 64 bits of Golay codes has resulted in a total of 10.5 dB improvement of SNR.

Beam Coding with Orthogonal Complementary Golay Codes for Signal to Noise Ratio Improvement in Ultrasound Mammography

Beam Coding with Orthogonal Complementary Golay Codes for Signal to Noise Ratio Improvement in Ultrasound Mammography

Beam coding with orthogonal complementary Golay codes for signal-to-noise ratio improvement in ultrasound mammography

In this paper, the experimental results of using Golay coded signals at 7.5 MHz to detect breast microcalcifications of 50 μm size is presented. For improving the success on detecting the microcalcifications, orthogonal Golay complementary sequences up to 40 chips having cross correlation for minimum interference are used as coded signals and they are compared to tone burst pulse of equal energy in terms of resolution under weak signal conditions. The measurements are conducted using an experimental ultrasound research scanner, DiPhAS having 256 channels, a phased array transducer with 7.5 MHz center frequency, and the results obtained through experiments are validated by Field-II simulation software. In addition, to investigate the superiority of coded signals in terms of resolution, multipurpose tissue equivalent phantom (Model 84-317) containing series of monofilament nylon targets, 240 μm in diameter, and cyst-like objects with attenuation of 0.5 dB/(MHz*cm) is used in the experiments. We obtained ultrasound images of monofilament nylon targets and cyst-like objects for the evaluation of resolution. Experimental results show that it is possible to differentiate closely positioned small targets with increased success by using coded excitation in very weak signal conditions.

Pulse Compressed Time Domain Multiplexed Fiber Bragg Grating Sensor: A Comparative Study

This paper experimentally demonstrates the feasibility of improving the sensing performance of fiber Bragg grating (FBG)-based point sensors by deploying two pulse coding techniques, simplex coding (SSC), and Golay complementary codes (GCC). The two techniques are separately combined with the conventional time-domain multiplexed FBG (TDM-FBG) interrogation sensor, and their results are compared with respect to the conventional single pulse interrogation technique. Consistently with the theory, for both the coding techniques, we have confirmed that the signal-to-noise ratio improved proportionally to the code length. In details, for both the techniques, the signal-to-noise improvement ratio of two FBGs located after around 16.35 km of fiber has significantly increased up to about 6 dB. Furthermore, the decoded signals from both techniques conserve their original spatial properties, confirming the successfulness of Hadamard transform and Golay auto-correlation calculations. Our experimental analysis confirms the simplex codes with their significant noise reduction ability, which is translated into well formed and accurate mean amplitude calculations. Moreover, the analysis of TDM-FBG-based GCCs have confirmed the unique properties of the auto-correlation process to increase the FBG signals up to around 128 times compared with the single pulse case.

Improvement of signal to noise ratio of time domain mutliplexing fiber Bragg grating sensor network with Golay complementary codes

Abstract This paper reports the employment of autocorrelation properties of Golay complementary codes (GCC) to enhance the performance of the time domain multiplexing fiber Bragg grating (TDM-FBG) sensing network. By encoding the light from laser with a stream of non-return-to-zero (NRZ) form of GCC and launching it into the sensing area that consists of the FBG sensors, we have found that the FBG signals can be decoded correctly with the autocorrelation calculations, confirming the successful demonstration of coded TDM-FBG sensor network. OptiGrating and OptiSystem simulators were used to design customized FBG sensors and perform the coded TDM-FBG sensor simulations, respectively. Results have substantiated the theoretical dependence of SNR enhancement on the code length of GCC, where the maximum SNR improvement of about 9 dB is achievable with the use of 256 bits of GCC compared to that of 4 bits case. Furthermore, the GCC has also extended the strain exposure up to 30% higher compared to the maximum of the conventional single pulse case. The employment of GCC in the TDM-FBG sensor system provides overall performance enhancement over the conventional single pulse case, under the same conditions.

Coded excitation for diverging wave cardiac imaging: a feasibility study

Diverging wave (DW) based cardiac imaging has gained increasing interest in recent years given its capacity to achieve ultrahigh frame rate. However, the signal-to-noise ratio (SNR), contrast, and penetration depth of the resulting B-mode images are typically low as DWs spread energy over a large region. Coded excitation is known to be capable of increasing the SNR and penetration for ultrasound imaging. The aim of this study was therefore to test the feasibility of applying coded excitation in DW imaging to improve the corresponding SNR, contrast and penetration depth. To this end, two types of codes, i.e. a linear frequency modulated chirp code and a set of complementary Golay codes were tested in three different DW imaging schemes, i.e. 1 angle DW transmit without compounding, 3 and 5 angles DW transmits with coherent compounding. The performances (SNR, contrast ratio (CR), contrast-to-noise ratio (CNR), and penetration) of different imaging schemes were investigated by means of simulations and in vitro experiments. As for benchmark, corresponding DW imaging schemes with regular pulsed excitation as well as the conventional focused imaging scheme were also included. The results showed that the SNR was improved by about 10 dB using coded excitation while the penetration depth was increased by 2.5 cm and 1.8 cm using chirp code and Golay codes, respectively. The CNR and CR gains varied with the depth for different DW schemes using coded excitations. Specifically, for non-compounded DW imaging schemes, the gain in the CR was about 5 dB and 3 dB while the gain in the CNR was about 4.5 dB and 3.5 dB at larger depths using chirp code and Golay codes, respectively. For compounded imaging schemes, using coded excitation, the gain in the penetration and contrast were relatively smaller compared to non-compounded ones. Overall, these findings indicated the feasibility of coded excitation in improving the image quality of DW imaging. Preliminary in vivo cardiac images of a healthy volunteer were presented finally, and higher SNR and deeper penetration depth can be achieved by coded schemes.

Good code sets from complementary pairs via symmetrical/antisymmetrical chips

Golay complementary code pairs have the advantage of being biphase codes, available at a variety of lengths, with exact sidelobe cancellation. However, they require transmission at two frequencies or channels. At the receiver, the two codes require reception in their own matched filters. The two matched filter outputs are then added, resulting in complete sidelobe cancellation. However, frequency- or channel-selective fading could result in inexact sidelobe cancellation. This paper introduces a new code constructed from the complementary code pair (A, B) by concatenating them with a gap in between, using one frequency band or one channel. The autocorrelation of this code contains a zero-sidelobe region on either side of the mainlobe and an adjacent region of small cross-correlation sidelobes. This is achieved by having the chips used for A and B satisfy the following two conditions: The two chips are symmetrical/antisymmetrical mirror images of each other and the cross-correlation between them is small-i.e., they are quasiorthogonal in the convolution sense. The symmetry/antisymmetry property results in the zero-sidelobe region, while the quasiorthogonality makes the adjacent region of cross-correlation sidelobes small. Linear frequency-modulated (LFM) and piecewise LFM chips satisfy both the symmetry/ antisymmetry and quasiorthogonality conditions. The symmetry/antisymmetry property is shown to be invariant under frequency-selective fading; therefore, sidelobe cancellation is also fading invariant. Any good code set that satisfies the symmetry/antisymmetry condition could be used as chips with the same Golay complementary code pair to generate a good code set with a zero-sidelobe region and an adjacent region of small cross-correlation sidelobes. Such sets are generated by varying the slope of the LFM and piecewise LFM chips.

Excitation Waveform Design for Lamb Wave Pulse Compression.

Most ultrasonic guided wave methods focus on tone burst excitation to reduce the effect of dispersion so as to facilitate signal interpretation. However, the resolution of the output cannot attain a very high value because time duration of the excitation waveform cannot be very small. To overcome this limitation, a pulse compression technique is introduced to Lamb wave propagation to achieve a δ-like correlation so as to obtain a high resolution for inspection. Ideal δ-like correlation is impossible as only a finite frequency bandwidth can propagate. The primary purpose of this paper is to design a proper excitation waveform for Lamb wave pulse compression, which shortens the correlation as close as possible to a δ function. To achieve this purpose, the performance of some typical signals is discussed in pulse compression, which include linear chirp (L-Chirp) signal, nonlinear chirp (NL-Chirp) signal, Barker code (BC), and Golay complementary code (GCC). In addition, how the excitation frequency range influences inspection resolution is investigated. A strategy for the frequency range determination is established subsequently. Finally, an experiment is carried out on an aluminum plate where these typical signals are used as excitations at different frequency ranges. The quantitative comparisons of the pulse compression responses validate the theoretical findings. By utilizing the experimental data, the improvement of pulse compression in resolution compared with tone burst excitation is also validated, and the robustness of the waveform design method to inaccuracies in the dispersion compensation is discussed as well.

Three-Stage Treatment of TX/RX IQ Imbalance and Channel with CFO for SC-FDE Systems

Direct-conversion transceiver obtains increasing attentions due to its low power consumption, but it confronts with serious IQ imbalance. In this paper, a three-stage treatment of transmitter/receiver (TX/RX) IQ imbalance and channel, in the presence of carrier frequency offset (CFO), is proposed for single-carrier-frequency-domain-equalization (SC-FDE) systems. First, RX IQ imbalance and CFO are handled with a repetitive preamble. Second, joint responses of TX IQ imbalance and channel are estimated by designing another preamble via complementary Golay codes. Third, joint compensation of TX IQ imbalance and time-varying channel is conducted using the minimal-mean-square-error criterion. Simulations are presented to verify the proposed method, in terms of normalized mean square error for the estimation and bit error rate for the overall system.

Implementation of Golay Complementary Code Sequences Generator Based on FPGA

Implementation of Golay Complementary Code Sequences Generator Based on FPGA

Design and performance of Huffman sequences in medical ultrasound coded excitation

This paper deals with coded-excitation techniques for ultrasound medical echography. Specifically, linear Huffman coding is proposed as an alternative approach to other widely established techniques, such as complementary Golay coding and linear frequency modulation. The code design is guided by an optimization procedure that boosts the signal-to-noise ratio gain (GSNR) and, interestingly, also makes the code robust in pulsed-Doppler applications. The paper capitalizes on a thorough analytical model that can be used to design any linear coded-excitation system. This model highlights that the performance in frequency-dependent attenuating media mostly depends on the pulse-shaping waveform when the codes are characterized by almost ideal (i.e., Kronecker delta) autocorrelation. In this framework, different pulse shapers and different code lengths are considered to identify coded signals that optimize the contrast resolution at the output of the receiver pulse compression. Computer simulations confirm that the proposed Huffman codes are particularly effective, and that there are scenarios in which they may be preferable to the other established approaches, both in attenuating and non-attenuating media. Specifically, for a single scatterer at 150 mm in a 0.7-dB/(MHz·cm) attenuating medium, the proposed Huffman design achieves a main-to-side lobe ratio (MSR) equal to 65 dB, whereas tapered linear frequency modulation and classical complementary Golay codes achieve 35 and 45 dB, respectively.

Sound Fields for Coded Excitations in Water and Tissue: Experimental Approach

Coded ultrasonography is intensively studied in many laboratories due to its remarkable properties, particularly increased penetration depth and signal-to-noise ratio (SNR). However, no data on the spatial behavior of the pressure field generated by coded bursts transmissions in the tissue were yet reported. This paper reports the results of investigations of the field structure in water, in degassed beef liver and in pork tissue using four different excitations signals, two and 16 periods sine bursts and sinusoidal sequences with phase modulation using 13-bits Barker code and 16-bits Golay complementary codes. The results of measured pressure field distributions before and after compression were compared with those recorded using short pulse excitation. (E-mail: jlitn@ippt.gov.pl)

A post-compression based ultrasound imaging technique for simultaneous transmit multi-zone focusing

The compression error of post-compression based coded excitation techniques increases with decreasing f-number, which causes the elevation of side-lobe levels. In this paper, a post-compression based coded excitation technique with reduced compression errors through dynamic aperture control is proposed. To improve the near-field resolution with no frame rate reduction, the proposed method performs simultaneous transmit multi-zone focusing using two mutually orthogonal complementary Golay codes. In the proposed method, the two mutually orthogonal sequences of length 16 are simultaneously transmitted toward two different focal depths, which are separately compressed into two short pulses on receive after dynamic focusing is performed. After carrying out the same transmit-receive operation for the same scan line with the complementary set of the orthogonal Golay codes, a single scan line with two transmit foci is obtained.The computer simulation results using a linear array with a center frequency of 7.5 MHz and 60% 6 dB bandwidth show that the range side-lobe level can be suppressed below −50 dB, when f-number is maintained not smaller than 3. The performance of the proposed scheme for a smaller f-number of 2 was also verified through actual experiments using a 3.85 MHz curved linear array with 60% 6 dB bandwidth. Both the simulation and experimental results show that the proposed method provides improved lateral resolution compared to the conventional pre-compressed and post-compression based coded excitation imaging using Golay codes.

Comparison of sound fields generated by different coded excitations—Experimental results

This work reports the results of measurements of spatial distributions of ultrasound fields obtained from five energizing schemes. Three different codes, namely, chirp signal and two sinusoidal sequences were investigated. The sequences were phase modulated with 13 bits Barker code and 16 bits Golay complementary codes. Moreover, two reference signals generated as two and sixteen cycle sine tone bursts were examined. Planar, 50% (fractional) bandwidth, 15 mm diameter source transducer operating at 2 MHz center frequency was used in all measurements. The experimental data were collected using computerized scanning system and recorded using wideband, PVDF membrane hydrophone (Sonora 804). The measured echoes were compressed, so the complete pressure field in the investigated location before and after compression could be compared. In addition to a priori anticipated increase in the signal to noise ratio (SNR) for the decoded pressure fields, the results indicated differences in the pressure amplitude levels, directivity patterns, and the axial distance at which the maximum pressure amplitude was recorded. It was found that the directivity patterns of non-compressed fields exhibited shapes similar to the patterns characteristic for sinusoidal excitation having relatively long time duration. In contrast, the patterns corresponding to compressed fields resembled those produced by brief, wideband pulses. This was particularly visible in the case of binary sequences. The location of the maximum pressure amplitude measured in the 2 MHz field shifted towards the source by 15 mm and 25 mm for Barker code and Golay code, respectively. The results of this work may be applicable in the development of new coded excitation schemes. They could also be helpful in optimizing the design of imaging transducers employed in ultrasound systems designed for coded excitation. Finally, they could shed additional light on the relationship between the spatial field distribution and achievable image quality and in this way facilitate optimization of the images obtained using coded systems.