Constant Amplitude Zero Autocorrelation Sequence Research Articles

Performance Enhancement of W-Band RoF System Using 4D Trellis Coded Modulation OFDM With Precoding

In the paper, a four-dimensional trellis-coded modulation 16-quadrature amplitude modulation-orthogonal frequency division multiplexing (4D TCM 16QAM-OFDM) combined with precoding scheme is proposed and experimentally demonstrated in W-band radio-over-fiber (RoF) system. In W-band RoF system, frequency selective fading can cause unbalanced signal-to-noise ratio (SNR) distribution on the sub-carriers of the 4D TCM 16QAM-OFDM signals. Orthogonal circulant matrix transform (OCT) precoding, discrete Fourier transform (DFT) precoding, and constant amplitude zero autocorrelation sequence (CAZAC) precoding can be used to balance the SNR over the data subcarriers of 4D TCM 16QAM-OFDM signals. Moreover, DFT precoding and CAZAC precoding can reduce the peak-to-average power ratio (PAPR) of 4D TCM 16QAM-OFDM signals. After 50km single-mode fiber (SMF) and 5m free space transmission, the experimental results show that, at the bit error rate (BER) of 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> , compared with 4D TCM 16QAM-OFDM using OCT precoding and DFT precoding, 4D TCM 16QAM-OFDM using CAZAC precoding can achieve the receiver sensitivity improvement of 2.33 dB and 0.48 dB respectively. In addition, compared with 4D TCM 16QAM-OFDM without precoding, it can achieve the receiver sensitivity improvement of 3 dB by using CAZAC precoding. Furthermore, 4D TCM 16QAM-OFDM has higher spectral efficiency than 8QAM-OFDM at the same symbol rate. The receiver sensitivity for 4D TCM 16QAM-OFDM using CAZAC precoding is enhanced about 1.1 dB, compared with 8QAM-OFDM using CAZAC precoding.

Cubic metric reduction for repetitive CAZAC sequences in frequency domain

In NR-based Access to Unlicensed Spectrum (NR-U) of 5G system, to satisfy the rules of Occupied Channel Bandwidth (OCB) of unlicensed spectrum, the channels of PRACH and PUCCH have to use some sequence repetition mechanisms in frequency domain. These repetition mechanisms will cause serious cubic metric(CM) problems for these channels, although these two types of channels are composed of Constant Amplitude Zero Auto-correlation(CAZAC) sequences.. Based on the characteristics of CAZAC sequences, which are used for PRACH and PUCCH (refer to PUCCH format 0 and format 1) in 5G NR, in this paper, we propose some new mechanisms of CM reduction for these two types of channels considering the design principles to ensure the sequence performance of the auto-correlation and cross-correlation. Then the proposed CM schemes are evaluated and the optimized parameters are further provided considering CM performance and the complexity.

Enhanced performance of PS-256QAM-OFDM for optical access network

In this paper, to increase communication capacity and improve receiver sensitivity for optical access networks, probabilistically-shaped orthogonal frequency division multiplexing (PS-OFDM) assisted by constant amplitude zero autocorrelation sequence (CAZAC) is investigated in cost-effective intensity-modulation and direct-detection (IM-DD) system. Since 256-QAM is adopted in PS-OFDM, it can significantly improve spectral efficiency and shaping gain Moreover, we compared the probability shaping scheme with the traditional scheme in the terms of receiver sensitivity and achievable information rate (AIR). Experimental results demonstrate that the performance of probabilistically-shaped OFDM scheme outperforms the traditional OFDM scheme. At the same rate of 6.0 bits/QAM symbol, 2.0-dB performance improvement in both receiver sensitivity and AIR can be achieved employing probabilistic shaping assisted by CAZAC precoding. Meanwhile, a 2.45-Gbit/s/λ capacity increase can be achieved with the proposed scheme. In addition, a 30.61-Gbit/s/λ PS-256QAM-OFDM can achieve 20km single-mode fiber (SMF) transmission at BER below 10−6.

Efficient Channel Estimation for Aerial Wireless Communications

We present a technique to jointly estimate the channel taps and the frequency offset due to the Doppler effect of a special class of doubly dispersive aeronautical channels. The algorithm includes the use of pulse repetition techniques at the transmitter and the “power method” subspace iteration at the receiver. We show that transmitting constant-amplitude zero-autocorrelation sequences for channel sounding yields estimators with low computational complexity. Numerical simulations indicate performance comparable to the estimation-theoretic lower bound.

Performance Enhancement of Probabilistically Shaped OFDM Enabled by Precoding Technique in an IM-DD System

Probabilistically shaped orthogonal frequency-division multiplexing (PS-OFDM) signal is proposed and experimentally demonstrated in a low-cost intensity-modulation and direct-detection (IM-DD) system for optical access networks. The concatenation of constant composition distribution matcher (CCDM) and low-density parity-check (LDPC) code sequentially implements probabilistic amplitude shaping (PAS) and channel coding. Thanks to the precoding scheme, all data subcarriers can be treated equally by one optimized probabilistic distribution. Experimental results demonstrate that constant amplitude zero autocorrelation sequence (CAZAC) precoding can offer optimal performance compared to orthogonal circulant transform (OCT) precoding and discrete Fourier transform spread (DFT-spread) in terms of increasing generalized mutual information (GMI) and reducing PAPR. Moreover, probabilistically-shaped 64-QAM OFDM signal can provide shaping gains of 1.04/0.94/0.64 dB at 4.0/3.6/3.0 bits/QAM symbol compared to traditional 64-QAM OFDM signal. Meanwhile, compared to traditional 16-QAM OFDM, it can offer shaping gains of 1.64/0.64 dB at 3.6/3.0 bits/QAM symbol. In addition, net data rate ranging from 32.66 to 43.55-Gb/s over 20-km single mode fiber (SMF) can be achieved by only adjusting the probabilistic distribution.

Chromatic Dispersion Estimation Based on CAZAC Sequence for Optical Fiber Communication Systems

We propose a chromatic dispersion (CD) estimation method based on constant amplitude zero-autocorrelation (CAZAC) sequence and fractional Fourier transform (FrFT) algorithm for optical fiber communication systems, which extends the application of CAZAC sequence. By applying FrFT on the CAZAC sequence signal, the optimal order is searched and employed to estimate the accumulated CD because that the CAZAC sequence shares similar properties with chirp signal. We demonstrate the feasibility of the proposed method by the simulation of a 28 GBaud polarization-division-multiplexed (PDM) quadrature phase-shift keying (QPSK) optical fiber communication system. The error of CD estimation is less than 70 ps/nm for the standard single mode fiber (SSMF) link of 2000 km with OSNR in the range of 10–20 dB and the launch power in the range of 0–4 dBm per channel in a five channel system. It shows that the method is robust to ASE noise and optical fiber nonlinearity. Furthermore, the proposed method has been experimentally verified with the error of CD estimation less than 50 ps/nm after 100–900 km fiber link transmission.

A novel timing synchronization for CO-OFDM systems using CAZAC sequences

A novel symbol timing synchronization algorithm based on constant amplitude zero auto correlation (CAZAC) sequences is proposed for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The training symbol of the proposed algorithm is comprised of four different parts, utilizing even symmetry property of each part to accomplish timing synchronization. The performance of the proposed algorithm is demonstrated by means of simulations in OFDM and CO-OFDM systems. The proposed algorithm is shown to eliminate the timing sidelobes of Park’s algorithm and has a more accurate timing estimation. In the condition of chromatic dispersion (CD), the timing metric of the proposed method still maintains its peak value at the correct timing point, while the values are almost 0 at all the other positions. Meanwhile, the timing mean square error (MSE) of the proposed algorithm remains around 10-6.

Constructing Tight Gabor Frames Using CAZAC Sequences

The construction of finite tight Gabor frames plays an important role in many applications. These applications include significant ones in signal and image processing. We explore when constant amplitude zero autocorrelation (CAZAC) sequences can be used to generate tight Gabor frames. The main theorem uses Janssen’s representation and the zeros of the discrete periodic ambiguity function to give necessary and sufficient conditions for determining whether any Gabor frame is tight. The relevance of the theorem depends significantly on the construction of examples. These examples are necessarily intricate, and to a large extent, depend on CAZAC sequences. Finally, we present an alternative method for determining whether a Gabor system yields a tight frame. This alternative method does not prove tightness using the main theorem, but instead uses the Gram matrix of the Gabor system.

A PAPR Joint Optimization Algorithm in AF Cooperative Multicarrier System

In this paper, to reduce PAPR (Peak-to-Average Power Ratio) in AF (Amplify and Forward) cooperative multicarrier system, an SLM-TR (Selective Mapping-Tone Reservation) joint optimization algorithm based on CAZAC (Constant Amplitude Zero Auto-Correlation) sequence is proposed. In our proposed method, several carriers are reserved for tone candidates, and then SLM (Selective Mapping) algorithm is utilized for the remaining data carriers. In SLM procedure, CAZAC sequences are utilized as the initial phase vector candidates and phase vector optimization is further processed by using feedback phase rotation algorithm for data carriers. After that, in continued TR (Tone Reservation) operation, random sequence is considered as the initial tone sequence and further optimized and subtracted from the modified data signal for peak cancelling using cyclic transposition searching algorithm to further reduce PAPR. Finally, the signal with the lowest PAPR is transmitted. By doing so, not only exhausting searching for optimal phase vectors is avoided efficiently, but also additional PAPR reduction is achieved by tone sequence modification. Simulation results show that the proposed method can reduce PAPR considerably and improve BER (Bit Error Rate) performance effectively, with insurance of high spectrum efficiency, low complexity and low loss in power efficiency. The influences of several conditions such as HPA (High power Amplifier) type, initial phase vector number, tone carrier number and sequence type are discussed to improve system QoS(Quality of Service).

Joint timing and frequency synchronization based on weighted CAZAC sequences for reduced-guard-interval CO-OFDM systems.

A novel joint symbol timing and carrier frequency offset (CFO) estimation algorithm is proposed for reduced-guard-interval coherent optical orthogonal frequency-division multiplexing (RGI-CO-OFDM) systems. The proposed algorithm is based on a constant amplitude zero autocorrelation (CAZAC) sequence weighted by a pseudo-random noise (PN) sequence. The symbol timing is accomplished by using only one training symbol of two identical halves, with the weighting applied to the second half. The special structure of the training symbol is also utilized in estimating the CFO. The performance of the proposed algorithm is demonstrated by means of numerical simulations in a 115.8-Gb/s 16-QAM RGI-CO-OFDM system.

Digital Signal Processing for Training-Aided Coherent Optical Single-Carrier Frequency-Domain Equalization Systems

In this paper, we present the design of digital signal processing (DSP) algorithms for training-aided coherent optical single-carrier frequency-domain equalization (SC-FDE) systems. Based on two training-aided channel estimation (TA-CE) schemes, the requirements for training sequence to achieve the minimum mean square error performance of channel estimation (CE) are outlined. Moreover, the practical implementation issues of constant-amplitude zero-autocorrelation sequence and Golay sequences are discussed. We propose to perform time-domain windowing to the CE taps for further noise suppression to improve the CE and achieve large overhead saving with the optimized CE. Furthermore, frame timing synchronization and frequency offset compensation algorithms based on Golay sequences are developed, which provide bandwidth-efficient solution with robust performance for long-haul transmission. Finally, a low-complexity fractionally spaced frequency-domain equalizer is reported to effectively reduce the computational complexity of the whole system. A total of 28-Gbaud coherent polarization division multiplexing (PDM) system simulations and 10-Gbaud coherent PDM system experiments are conducted to verify that the proposed DSP solutions provide robust performance and are suitable for implementation in high-speed long-haul digital coherent receivers.

Chirp Signal Transform and Its Properties

The chirp signalexp(iπ(x-y)2)is a typical example of CAZAC (constant amplitude zero autocorrelation) sequence. Using the chirp signals, the chirp z transform and the chirp-Fourier transform were defined in order to calculate the discrete Fourier transform. We define a transform directly from the chirp signals for an even or odd numberNand the continuous version. We study the fundamental properties of the transform and how it can be applied to recursion problems and differential equations. Furthermore, whenNis not prime and N=ML, we define a transform skippedLand develop the theory for it.

D2D 통신 시스템을 위한 CAZAC 시퀀스 기반 링크 스케줄링 기법

대표적인 D2D (Device-to-Device) 통신 시스템 중 하나인 Qualcomm사의 FlashLinQ 시스템에서는 링크 스케줄링 과정을 낮은 복잡도로 실현할 수 있도록 하기 위해 단일-톤 (single-tone) 신호를 이용한 우선순위 및 SIR (Signal-to-Interference power Ratio) 기반의 링크 스케줄링 기법을 수행한다. 하지만 다중 경로 채널 환경에서는 주파수 선택적 페이딩의 영향으로 단일-톤 위치에서와 실제 데이터가 전송되는 전체 대역에서의 수신 전력 간 오차가 발생할 수 있으며, 이는 공평성 측면에서 문제가 될 뿐만 아니라 셀 전체 전송률 상의 손실을 일으킬 수 있다. 따라서, 본 논문에서는 이러한 문제를 해결하기 위해 CAZAC (Constant Amplitude Zero Auto-Correlation) 시퀀스의 상관 특성을 이용해 전체 대역에 대한 SIR 에 가까운 값을 획득할 수 있는 링크 스케줄링 기법을 제안한다. 제안 기법은 전체 대역을 다수의 sub-block 으로 구분하고 각 sub-block 마다 링크의 우선순위에 해당하는 순환 오프셋 (cyclic offset) 을 적용한 CAZAC 시퀀스를 전 대역에 걸쳐 전송하여, 수신 신호와 참조 신호간의 순환 상호 상관 연산 (cyclic cross-correlation)을 통해 전체 대역에 대한 SIR 에 근접한 값을 획득할 수 있다. FlashLinQ, one of the typical D2D communication systems developed by Qualcomm, considers a single-tone communication based distributed channel-aware link scheduling method to realize the link scheduling process with low control overheads. However, considering the frequency selective fading effect of practical multi-path channel, the single-tone based SIR estimation causes a critical scheduling error problem because the received single-tone signal has quite different channel gain at each sub-carrier location. In order to overcome this problem, we propose a novel link scheduling method based on CAZAC (Constant Amplitude Zero Auto-Correlation) sequence for D2D communication system. In the proposed method, each link has a unique offset value set for the generation of CAZAC sequences. CAZAC sequences with the cyclic offsets are transmitted using multiple sub-blocks in the entire bandwidth, and then each device can obtain nearly full-band SIR using a good cyclic cross-correlation property of CAZAC sequence.

Adaptive highly localized waveform design for multiple target tracking

When tracking multiple targets, radar measurements from weak targets are often masked by the ambiguity function (AF) sidelobes of the measurements from stronger targets. This results in deteriorated tracking performance and lost tracks. In this study, we consider the design of configurable waveforms whose AF sidelobes can be positioned to unmask weak targets. Specifically, we construct multicarrier phase-coded (MCPC) waveforms based on Björck constant amplitude zero-autocorrelation (CAZAC) sequences. The MCPC CAZAC waveforms exhibit wide regions in their AF surface without sidelobes and allow for selective positioning of sidelobes. We apply these waveforms in the context of a target tracker by selecting waveform parameters that minimize the expected tracking error. We show that this is accomplished by selecting the position of AF sidelobes to unmask weak targets. The target tracker is based on an independent partitions likelihood particle filter that is capable of processing the high-resolution measurements resulting from the Björck CAZAC sequences and tracks a fixed and known number of targets. Using simulations, we demonstrate the improvement in tracking performance when we adaptively select the MCPC CAZAC waveforms over tracking using non-adaptive waveform configurations or single-carrier phase-coded CAZAC waveforms.

Carrier Frequency Offset Estimation for Multiuser MIMO OFDM Uplink Using CAZAC Sequences: Performance and Sequence Optimization

This paper studies carrier frequency offset (CFO) estimation in the uplink of multi-user multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. Conventional maximum likelihood estimator requires computational complexity that increases exponentially with the number of users. To reduce the complexity, we propose a sub-optimal estimation algorithm using constant amplitude zero autocorrelation (CAZAC) training sequences. The complexity of the proposed algorithm increases only linearly with the number of users. In this algorithm, the different CFOs from different users destroy the orthogonality among training sequences and introduce multiple access interference (MAI), which causes an irreducible error floor in the CFO estimation. To reduce the effect of the MAI, we find the CAZAC sequence that maximizes the signal to interference ratio (SIR). The optimal training sequence is dependent on the CFOs of all users, which are unknown. To solve this problem, we propose a new cost function which closely approximates the SIR-based cost function for small CFO values and is independent of the actual CFOs. Computer simulations show that the error floor in the CFO estimation can be significantly reduced by using the optimal sequences found with the new cost function compared to a randomly chosen CAZAC sequence.

Transmit Diversity for TDS-OFDM Broadcasting System Over Doubly Selective Fading Channels

The state-of-the-art time domain synchronous OFDM (TDS-OFDM) transmit diversity schemes are only suitable either for fast time-varying but weakly frequency-selective channels, or deeply frequency-selective but slowly time-varying channels. In this paper, a novel TDS-OFDM transmit diversity scheme based on the space-time shifted constant amplitude zero autocorrelation (CAZAC) sequence is proposed over doubly selective broadcasting channels. The space-shifted CAZAC sequence is used for the unbiased maximum likelihood (ML) channel estimation. The time-shifted sequence is utilized for the low-complexity cyclicity reconstruction of the received inverse discrete Fourier trans form (IDFT) block. Compared with the existing solutions, the signal-to-noise ratio (SNR) gain of about 2.5 dB can be achieved by the proposed scheme at the uncoded bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> over the deeply frequency-selective single frequency network (SFN) broadcasting channel when the receiver velocity is 140 km/h, at the cost of the spectral efficiency penalty of about 2.88%.

Björck sequence sets

Constant amplitude zero autocorrelation (CAZAC) sequences are increasingly used in new communication systems (e.g. LTE, WiMax). The (unique) Björck sequence whose length P is an odd prime is a less known CAZAC sequence. By modifying the Björck sequence through CAZAC transformations, a Björck set of P orthogonal sequences is introduced. The maximum absolute set cross-correlation is near 2/√P and the root-meansquare (RMS) of the cross-correlation function is 1/√P. A Björck set is contrasted with the widely used Zadoff-Chu set, which contains P−1 non-orthogonal sequences. The introduction of Björck sets gives a system designer more flexibility in sequence selection.

Adaptive High-Resolution Sensor Waveform Design for Tracking

Recent innovations in modern radar for designing transmitted waveforms, coupled with new algorithms for adaptively selecting the waveform parameters at each time step, have resulted in improvements in tracking performance. Of particular interest are waveforms that can be mathematically designed to have reduced ambiguity function sidelobes, as their use can lead to an increase in the target state estimation accuracy. Moreover, adaptively positioning the sidelobes can reveal weak target returns by reducing interference from stronger targets. The manuscript provides an overview of recent advances in the design of multicarrier phase-coded waveforms based on Bjorck constant-amplitude zero-autocorrelation (CAZAC) sequences for use in an adaptive waveform selection scheme for mutliple target tracking. The adaptive waveform design is formulated using sequential Monte Carlo techniques that need to be matched to the high resolution measurements. The work will be of interest to both practitioners and researchers in radar as well as to researchers in other applications where high resolution measurements can have significant benefits. Table of Contents: Introduction / Radar Waveform Design / Target Tracking with a Particle Filter / Single Target tracking with LFM and CAZAC Sequences / Multiple Target Tracking / Conclusions

Orthogonal Pilot Channel Using Combination of FDMA and CDMA in Single-Carrier FDMA-Based Evolved UTRA Uplink

In the Evolved UTRA (UMTS Terrestrial Radio Access) uplink, single-carrier frequency division multiple access (SC-FDMA) radio access was adopted owing to its advantageous low peak-to-average power ratio (PAPR) feature, which leads to wide coverage area provisioning with limited peak transmission power of user equipments. This paper proposes orthogonal pilot channel generation using the combination of FDMA and CDMA in the SC-FDMA-based Evolved UTRA uplink. In the proposed method, we employ distributed FDMA transmission for simultaneous accessing users with different transmission bandwidths, and employ CDMA transmission for simultaneous accessing users with identical transmission bandwidth. Moreover, we apply a code sequence with a good auto-correlation property such as a Constant Amplitude Zero Auto-Correlation (CAZAC) sequence employing a cyclic shift to increase the number of sequences. Simulation results show that the average packet error rate performance using an orthogonal pilot channel with the combination of FDMA and CDMA in a six-user environment, i. e., four users each with a 1.25-MHz transmission bandwidth and two users each with a 5-MHz transmission bandwidth, employing turbo coding with the coding r of R=1/2 and QPSK and 16QAM data modulation coincides well with that in a single-user environment with the same transmission bandwidth. We show that the proposed orthogonal pilot channel structure using the combination of distributed FDMA and CDMA transmissions and the application of the CAZAC sequence is effective in the SC-FDMA-based Evolved UTRA uplink.

MSE Performance Evaluation of Zero-Padded CAZAC Sequence for Reasonable Utilization

The classical 4-phase constant-amplitude zero-autocorrelation (CAZAC) sequence with the length of 16 has been used for multifarious purposes such as channel estimation and frequency/timing synchronizations since it presents good performance even in low signal to noise ratio (SNR) conditions. However, as multiple transmit antennas are employed, its properties are easily destroyed by the effect of multipath. In this letter, we propose a technique which ensures that the conventional CAZAC sequence is reliable in a multi-antenna system by inserting nulls. The performance of the modified sequence is verified through the mean s quare error (MSE) performance with the least squares (LS) method.