Walsh-Hadamard Sequences Research Articles

Robust Imaging of Speed of Sound Using Virtual Source Transmission.

Speed of sound (SoS) is a novel imaging biomarker for assessing the biomechanical characteristics of soft tissues. SoS imaging in the pulse-echo mode using conventional ultrasound (US) systems with hand-held transducers has the potential to enable new clinical uses. Recent work demonstrated that diverging waves (DWs) from a single element (SE) transmit to outperform plane-wave sequences. However, SE transmits have severely limited power and hence produce a low signal-to-noise ratio (SNR) in echo data. We herein propose Walsh-Hadamard (WH) coded and virtual-source (VS) transmit sequences for the improved SNR in SoS imaging. We additionally present an iterative method of estimating beamforming (BF) SoS in the medium, which otherwise confounds SoS reconstructions due to beamforming inaccuracies in the images used for reconstruction. Through numerical simulations, phantom experiments, and in vivo imaging data, we show that WH is not robust against motion, which is often unavoidable in clinical imaging scenarios. Our proposed VS sequence is shown to provide the highest SoS reconstruction performance, especially robust to motion artifacts. In phantom experiments, despite having a comparable SoS root-mean-square error (RMSE) of 17.5-18.0 m/s at rest, with a minor axial probe motion of ≈ 0.67 mm/s the RMSE for SE, WH, and VS already deteriorate to 20.2, 105.4, and 19.0 m/s, respectively, showing that WH produces unacceptable results, not robust to motion. In the clinical data, the high SNR and motion resilience of VS sequences are seen to yield superior contrast compared to SE and WH sequences.

The frequency modulation transfer function provides supplemental measures for the objective evaluation of pitch extractors

We propose to apply the frequency modulation transfer function as a supplemental measure for evaluating pitch extractors' performance. We introduced a new family of time-stretched-pulse for acoustic system analysis (Kawahara and Yatabe, ICASSP2021, called CAPRICEP). Composing a test signal using the CAPRICEP units by Walsh-Hadamard sequence enables simultaneous measurement of the linear-time-invariant, non-linear-time-invariant, and random-time-varying attributes. We applied the proposed analysis method to eighteen pitch extractors and visualized their behavior (represented more than five thousand plots) as a movie. The proposed procedure will be available as open-source tools in our GitHub repository.

FPGA implementation of orthogonal hyperchaotic sequences generator based on the CNN: application in multi-user chaotic communications

In this article, we propose an efficient orthogonal hyperchaotic sequences generator for application in multi-user chaotic communication systems. The proposed generator consists of two blocks. The first block generates binary hyperchaotic sequences of varying lengths using a 6-Dimensional Cellular Neural Network (CNN) system, offering a wide range of sequence length choices. The second block uses an optimized selection method to generate multiple sets of orthogonal sequences with interesting correlation properties. The method is based on the balance and correlation properties, where zero cross-correlation between any two sequences is considered. A FPGA-based implementation of the proposed generator is presented. The hardware architecture is designed in VHDL and deployed on a Xilinx Virtex-6 FPGA ML605 evaluation kit. The generator is then analyzed and compared with the existing generator in terms of logic area consumption, throughput, latency, and randomness quality. The comparative analysis results show the effectiveness of the proposed generator, which can achieve a high throughput, low latency, and successfully pass all NIST statistical tests. Moreover, the generated orthogonal hyperchaotic sequences exhibit promising performance in a multi-user Differential Chaos Shift Keying (MU-DCSK) system, outperforming the Walsh-Hadamard sequences in terms of bit-error rate under various channel conditions.

Orthogonal Time Sequency Multiplexing Modulation: Analysis and Low-Complexity Receiver Design

This paper proposes orthogonal time sequency multiplexing (OTSM), a novel single carrier modulation scheme that places information symbols in the delay-sequency domain followed by a cascade of time-division multiplexing (TDM) and Walsh-Hadamard sequence multiplexing. Thanks to the Walsh Hadamard transform (WHT), the modulation and demodulation do not require complex domain multiplications. For the proposed OTSM, we first derive the input-output relation in the delay-sequency domain and present a low complexity detection method taking advantage of zero-padding. We demonstrate via simulations that OTSM offers high performance gains over orthogonal frequency division multiplexing (OFDM) and similar performance to orthogonal time frequency space (OTFS), but at lower complexity owing to WHT. Then we propose a low complexity time-domain channel estimation method. Finally, we show how to include an outer error control code and a turbo decoder to improve error performance of the coded system.

Signal-to-noise ratio analysis of computational distributed fiber-optic sensing.

In this work, we analyze the signal-to-noise ratio of the computational distributed fiber-optic sensing technique via differential ghost imaging in the time domain using the illumination pattern of Walsh-Hadamard sequences instead of random sequences. When only the white Gaussian noise is considered in the detection, both the theoretical and experimental results show that the computational method requires twice more number of averages compared to the conventional time-domain method in order to achieve the same level of signal-to-noise ratio. Since the computational approach is focusing on stationary measurement, doubling the measurement time can normally be acceptable in practice, but it can reduce the sampling rate requirement significantly compared to the conventional method, offering great advantage to simplify the data acquisition design in the distributed fiber-optic sensing system.

A Low Complexity Iterative SLM-OFDM for SHF band applications

The transmitted Orthogonal Frequency Division Multiplexing signal in systems such as Wireless LAN,Mobile WiMAX, Digital Video Broadcasting (DVB) operating in the Super High Frequency (SHF) band suffers from high Peak to A verage P ower R atio .This is reduced in S elective L evel M apping  (SLM)  approach  b ut  at  the  expense  of  increased complexity.  In this paper,w e propose a iterative selective level mapping algorithm for PAPR reduction with reduced computation complexity . The performance of Iterative SLM is investigated for a new phase sequence set based on mutually orthogonal Golay complementary pairs and results are compared with Walsh-Hadamard sequence set. The iterative threshold is varied between 4-8 dB and candidate signal values of 4,8,16 and 32 are considered for a 64 subcarrier system. Computer simulation results show lesser  computational complexity  in terms  of candidate signal requirement in comparison to conventional SLM, while maintaining an almost identical PAPR.  The new phase sequence set achieves a 1.2 dB and 2.4 dB PAPR improvement over conventional SLM and OFDM respectively for maximum of 16 candidate signals at iterative threshold of 6 dB. The computational complexity reduction achieved is 59%.  Â

MAI Mitigation Using V-BLAST and PIC Based Binary Orthogonal Code Spreaded Multi Antenna MC-CDMA System

In this paper, the reduction of Multiple Access Interference (MAI) in Multi Carrier-Code Division Multiple Access (MC-CDMA) uplink system is analyzed. Simultaneous access over channels by numerous users results in MAI which leads to high Bit Error Rate (BER). Therefore the data received at the receiver is intended to numerous users. As a result, it is necessary to separate the data corresponding to different users efficiently. So in this paper, the Vertical-BELL Laboratories Layered Space-Time (V-BLAST) algorithm with Parallel Interference Cancellation (PIC) technique based MC-CDMA system is proposed. Due to the combination of V-BLAST and PIC in MC-CDMA system the MAI is reduced to a certain extent, which is shown in simulation result. Further the system performance is analyzed using Binary Orthogonal Codes (BOC) as spreading sequence. The result shows that Binary Orthogonal Coded V-BLAST and PIC based System provide better performance than conventional spreading sequence like Walsh Hadamard and Pseudorandom Noise (PN) sequence.

Interference Mitigation in MC-CDMA System with CFO compensation based Modified MMSE-FDE Technique

carrier Code Division Multiple Access (MC-CDMA) has been an attractive technique for wireless communication because it offers high data rate, high spectral efficiency, large system capacity, less transmit power and less implementation complexity. But due to Carrier Frequency Offset (CFO), which comes into account due to asynchrony between transmitter and receiver local oscillators or by Doppler Effect due to high mobility, orthogonality among the subcarriers gets effected resulting in Inter Carrier Interference (ICI) which leads to rapid degradation in performance of MC-CDMA system. In this paper, the performance of Uplink MC-CDMA system with Zero forcing- frequency domain Equalization (ZF-FDE), conventional MMSE equalizer and Modified MMSE-FDE using Walsh-Hadamard spreading sequence in multipath fading channel has been analyzed. Simulation has been performed using 32 subcarriers and 64 subcarriers for these equalization techniques. Simulation results confirm excellent performance of the Modified MMSE-FDE which outperforms the conventional MMSE equalization and ZF- FDE. The further improvement in performance is achieved by employing 64 subcarriers instead of 32 subcarriers. Numerical equations and simulation results are given to support the analysis. Keywords-CDMA, CFO, MMSE-FDE, ZF, ICI, Walsh-Hadamard Sequence.

Blum BlumShub Pseudorandom Sequence based Peak Power Control in MC-CDMA System

This paperanalyses thePeak to Average Power Ratio (PAPR) for various sequences such as Walsh Hadamard (WH), Gold Sequence,Welch-Gong(WG)sequence and Blum BlumShub (BBS) sequence in Multicarrier Code Division Multiple Access(MC-CDMA)system. Inmultiuser MC-CDMA system, the Blum BlumShub(BBS) sequence provides reduced peak to mean envelope power ratio(PMEPR)when comparedto WH sequence. So,this BBS sequence can be considered as a good alternative for Walsh Hadamard (WH) sequence in reducing PAPR in MC-CDMA system.

Two Dimensional Signal Spreading in UMTS LTE: Exploiting Time-Frequency Diversity to Increase Throughput

This paper proposes a two-dimensional spreading method in UMTS Long Term Evolution (LTE). Such a method brings additional time-frequency diversity which is beneficial in terms of the ability to decode transmitted data at the receiver site under multipath fading. Additional diversity is provided due to the fact that chips of transmitted signals are spread using a Walsh-Hadamard spreading sequence over several subcarriers as well as over several time-slots simultaneously. A comparison with state-of-the-art LTE downlink transmission is provided. To enable reproducibility and to increase credibility of our results, an open source Vienna LTE simulator is utilized. LTE transmissions with the proposed 2D spreading are tested on several channel models. Simulations show that apart from an Additive White Gaussian Noise channel model, this 2D spreading based method outperforms the throughput performance of standard LTE. At high Signal to Noise Ratio (SNR), the throughput increase in most channel models is higher than 10 %.

Peak Power Reduction for Pilot-Aided OFDM Systems with Semi-Blind Detection

Orthogonal Walsh-Hadamard sequences have been adopted for peak-to-average power ratio (PAPR) reduction without sending side information in pilot-aided orthogonal frequency division multiplexing systems. The PAPR reduction performance is determined by the number of orthogonal sequences, which is equal to the sequence length. However, increasing the length of pilot sequences significantly degrades bandwidth efficiency. The current study presents a novel set of pilot sequences obtained by sub-sampling the Zadoff-Chu sequences. The sub-sampled sequences are then equally partitioned into several groups, where sequences in the same group are orthogonal to one another and can therefore be blindly detected at the receiver. The number of pilot sequences can be doubled whenever one extra bit of side information is sent for a given pilot length. Therefore, the proposed scheme has the advantage of enhancing PAPR reduction performance with only marginal cost.

On the effect of Multiple Access Interference in a Space Time Spreading Time Hopping PPM UWB system

This study investigates the effect of multiple sources using STS across a Time-Hopping-PPM Modulation that is over an UWB Saleh-Valenzuela channel with each source using two transmit antennas. We model and analyze this system, showing that the presence of such MAI results in a significant degradation in BER performance. Simulation results show that for strong signal strength of interfering MAI signals degradation in BER performance is observed for the cases where we have five and 10 distinct MAI sources present when using Walsh-Hadamard thirty two chip spreading sequences. Using simulation, we investigate the use of other sets of orthogonal spreading sequences with improved cross correlation properties and find that for some sequences a significant improvement is seen compared to Walsh-Hadamard sequences when they are similarly misaligned. We show that MAI degrades the BER performance of such systems and that selection of improved cross correlation spreading code sequence sets improves BER.

Quasi-Synchronous CDMA Using Properly Scrambled Walsh Codes as User-Spreading Sequences

An orthogonal spreading code family based on scrambled Walsh-Hadamard (WH) sequences is proposed for quasi-synchronous (QS) code-division multiple-access (CDMA) systems. With 1 chip offset, either the top or the bottom half rows of the WH matrix remain orthogonal if they are scrambled using the proposed scrambling patterns. With quadriphase scrambling applied on a quarter row of the WH matrix, the zero-correlation zone (ZCZ) is extended to 3 chips. The proposed spreading codes satisfy the theoretical limit of code size for a given code length and ZCZ. Compared with existing spreading codes for QS-CDMA, the proposed spreading codes have several advantages: 1) A special procedure for code family construction is not needed; it only requires a simple modification to the scrambling sequence of the conventional CDMA, which employs WH sequences as user signatures. 2) Flexible code family size; the size can easily be extended for multicell applications without having to consider existing codes used. Moreover, if synchronization is guaranteed to be within 1 chip, the code size can be doubled by allocating another quarter member of the WH sequence set. 3) The benefits of long code scrambling from the conventional cellular CDMA systems are inherited, such as robustness against interception and multiaccess interference randomization.

Performance Evaluation of Band-Limited Baseband Synchronous CDMA Using Orthogonal ICA Sequences

Performance of band-limited baseband synchronous CDMA using orthogonal Independent Component Analysis (ICA) spreading sequences is investigated. The orthogonal ICA sequences have an orthogonality condition in a synchronous CDMA like the Walsh-Hadamard sequences. Furthermore, these have useful correlation properties like the Gold sequences. These sequences are obtained easily by using the ICA which is one of the brain-style signal processing algorithms. In this study, the ICA is used not as a separator for received signal but as a generator of spreading sequences. The performance of the band-limited synchronous CDMA using the orthogonal ICA sequences is compared with the one using the Walsh-Hadamard sequences. For limiting bandwidth, a Root Raised Cosine filter (RRC) is used. We investigate means and variances of correlation outputs after passing the RRC filter and the Bit Error Rates (BERs) of the system in additive white Gaussian noise channel by numerical simulations. It is found that the BER in the band-limited system using the orthogonal ICA sequences is much lower than the one using the Walsh-Hadamard sequences statistically.

PAPR 감소와 주파수 다이버시티 효과를 갖는 FD-CI-OFDM 시스템의 성능 평가

높은 데이터 전송 속도를 갖는 OFDM(Orthogonal Frequency Division Multiplexing) 통신 시스템은 시간 영역에서 높은 PAPR(Peak-to-Average Power Ratio)이 발생되는 중요한 단점이 있다. 이 때문에 송신 신호의 비선형 왜곡을 일으켜 통신 성능을 매우 나쁘게 된다. CI(Carrier Interferometry) - OFDM 시스템은 각각 병렬 데이터를 N개의 모든 부반송파와 서로 직교하는 위상 성분에 실어 전송함으로써 첨두값이 낮추는 효과를 얻는다. 또한, 한 데이터를 N개의 부반송파에 나누어 전송하기 때문에 주파수 다이버시티(FD: Frequency Diversity) 효과를 얻는다. 그러므로 CI-OFDM은 PAPR 저감과 BER 개선에 우수한 성능을 보인다. 그러나 CI-OFDM을 실제로 구현할 때, 송신기에서 모든 데이터마다 각각 다른 위상 성분들과 반송파에 실려 동시에 전송되기 때문에 수신기에서 독립적인 위상 성분들을 차례로 보상할 수 있는가가 매우 중요한 문제점이 된다. 이 논문에서는 Walsh Hadamard 시퀀스를 사용하여 각 병렬 데이터를 구분하고, 동시에 기존 CI-OFDM의 특성을 갖는 개선된 CI-OFDM, 즉 FD-CI-OFDM 시스템을 제안하고 성능을 평가한다 컴퓨터 시뮬레이션을 통하여 그 성능이 기존 OFDM이나 CI-OFDM보다 개선됨을 보인다. Orthogonal frequency division multiplexing(OFDM) that is very useful for the high-speed communication system has serious problem of high peak-to-average power ratio(PAPR) in time domain. Because of this, the non-linear distortion can be produced and system performance gets worse. CI-OFDM system can get the peak power lowered. In this CI-OFDM system, each parallel data is distributed into N all sub-carriers and conveyed by the orthogonal phase factor. Also, CI-OFDM shows frequency diversity effect. Therefore, CI-OFDM system is better than ordinary OFDM system in terms of BER performance and the PAPR reduction. When it is implemented, however, there is a serious problem whether it can separate and compensate the phase factor in order in the receiver. Because all bits are transmitted simultaneously over all subcarriers and each other phase factors in transmitter. In this paper, we propose and evaluate a FD-CI-OFDM system that is a version of improved CI-OFDM. This is designed by use of the Walsh Hadamard sequence. The FD-CI-OFDM shows better performance than ordinary OFDM and CI-OFDM system.

Symmetry-Embedded Spreading Sequences for Multicarrier CDMA

It was shown by Slimane that the bit error rate (BER) performance of the downlink of multicarrier code-division multiple-access (MC-CDMA) systems can be improved significantly by employing quadrature spreading sequences instead of binary Walsh-Hadamard sequences. Inspired by Slimane's work, we propose a class of complex-valued spreading sequences, which are mathematically derivable from the Kronecker product of some basic matrices. The good algebraic structure in the proposed spreading sequences, when applied in a BPSK based MC-CDMA system, can be exploited for multiple access interference (MAI) suppression, for order-2 diversity combining, and for the reduction of peak-to-average power ratio. The new spreading sequences outperform the Slimane's quadrature sequences, as evidenced by various numerical results.

On the Peak Factors of BPSK and QPSK Modulated MC-CDMA Signals Employing WH Sequences and WH-Based Complementary Sequences

In this paper, the inverse discrete Fourier transform (IDFT) results of oversampled Walsh Hadamard (WH) sequences and WH-based complementary (CP) sequences are derived, based on which, the peak factors (PF) of MC-CDMA signals are investigated for both the two sequence sets. The upper bounds of PF for both BPSK and QPSK modulation are presented in this paper and the PF bounds presented in B.J. Choi and L. Hanzo (2003) can be regarded as special cases of the bounds derived here. Compared with accurate computing which requires prohibitive computations, the upper bounds obtained provide a more effective way to estimate the PF of BPSK and QPSK modulated MC-CDMA signals employing WH or WH-based CP sequences. In addition, based on the IDFT properties of WH sequences, a simplified search for optimum WH subset in the context of BPSK modulation is derived.

Performance of DS-CDMA Downlink Systems With Orthogonal UCHT Complex Sequences

This letter investigates a transmitted signaling technique using orthogonal unified complex Hadamard transform (UCHT) spreading sequences and the coherent RAKE receiver in direct-sequence code-division multiple-access (DS-CDMA) downlinks to maintain the orthogonality between users and reduce the effect of multipath fading and interference from other users. A general multipath-fading channel model is assumed. System performance is evaluated by means of signal-to-interference-plus-noise ratio (SINR) at the RAKE receiver. It is shown that the SINR of the system employing UCHT complex sequences is independent of the phase offsets between different paths, while the SINR of the system using Walsh-Hadamard (WH) sequences is related to the squared cosine of path phase offsets. As a result, the bit-error ratio performance of the DS-CDMA downlink system employing UCHT complex sequences is better than that of the system with WH sequences at high SINRs

Capacity of space–time block-coded CDMA systems: comparison of unitary and complementary codes

Two major categories of CDMA signature codes, namely unitary codes and complementary codes, are of interest. All currently available 2–3G CDMA systems make use of the unitary codes, such as Gold codes, m-sequences, Walsh–Hadamard sequences and OVSF codes, all of which work on a one-code-per-channel basis. On the other hand, a CDMA system based on complementary codes works on a flock-of-codes basis. Each user in such a CDMA system is assigned a flock of codes which should be sent to a receiver via different carriers to reconstruct perfect autocorrelation and crosscorrelation functions. A comprehensive analytical study of a STBC-CDMA system using different spreading codes is given and their bit error rate performance is evaluated and compared with both analysis and simulation under Rayleigh fading and multiple-access interference. The results reveal that a STBC-CDMA system based on complementary codes offers a capacity similar to that achievable in a noise-limited system, while a STBC-CDMA system based on traditional unitary codes suffers serious interference-limited problems even with full STBC diversity gain.

Williamson–Hadamard spreading sequences for DS‐CDMA applications

AbstractOrthogonal bipolar spreading sequences are used in direct sequence code division multiple access (DS‐CDMA) systems for both spectrum spreading and channel separation. The most commonly used sequences are Walsh–Hadamard sequences of lengths being an integer power of 2. A construction based on Williamson's arrays leading to sequences of lengths N≡4 (mod 8) is presented in the paper. Aperiodic correlation characteristics, for example sequence sets of lengths 12–252 are presented. The correlation properties of the sequence sets are later improved using a diagonal modification technique. Copyright © 2003 John Wiley & Sons, Ltd.