Zadoff-Chu Sequences Research Articles

Phase coded waveforms for integrated sensing and communication systems

AbstractNowadays, especially with the developments in the automotive industry, it has become a highly popular topic for radar and communication systems to operate on the same platform and perform joint tasks to increase situational awareness. Sharing the hardware of the radar and communication systems and using a joint waveform for both functions eliminate interference problems between the systems, increasing the effectiveness of the joint task. In studies where radar signals are utilised for communication functions, continuous wave frequency modulation or intra‐pulse frequency modulation is generally employed to transmit communication signals. There are a few studies in the literature on joint radar and communication waveforms using phase modulation. In these studies, phase modulation is not employed directly for both functions. As a contribution to the literature, this study evaluates the usage of joint radar and communications waveforms, such as Barker sequences and Zadoff–Chu sequences as opposed to linear frequency modulation. We compare these waveforms terms of range‐speed detection and symbol error rate.

Zadoff–Chu Sequence Pilot for Time and Frequency Synchronization in UWA OFDM System

In underwater communications for 6G, Doppler effects cause the coherent time to become similar to or shorter than the orthogonal frequency division multiplexing (OFDM) symbol length. Conventional time and frequency synchronization methods require additional training symbols for synchronization, which reduces the traffic data rate. This paper proposes the Zadoff–Chu sequence (ZCS) pilot-based OFDM for time and frequency synchronization. The proposed method transmits ZCS as a pilot for OFDM symbols and simultaneously transmits traffic data to increase the traffic data rate while estimating the CFO at each coherence time. For time–frequency synchronization, the correlation of the ZCS pilot is used to perform coarse and fine time and frequency synchronization in two stages. Since the traffic data cause interference with the correlation of ZCS pilots, we theoretically analyzed the relationship between the amount of traffic data and interference and verified it through computer simulations. The synchronization and BER performance of the proposed ZCS pilot-based OFDM were evaluated by conduction computer simulations and a practical ocean experiment. Compared to the methods of Ren, Yang, and Avrashi, the proposed method demonstrated a 6.3% to 14.3% increase in traffic data rate with similar BER performance and a 2 dB to 3.8 dB SNR gain for a 14.3% to 23.8% decrease in traffic data rate.

Robust Symbol and Frequency Synchronization Method for Burst OFDM Systems in UAV Communication

This paper introduces a robust synchronization method for orthogonal frequency division multiplexing (OFDM) in multi-unmanned aerial vehicle (UAV) communication systems, focusing on minimizing overhead while achieving reliable synchronization. The proposed synchronization scheme enhances both frame efficiency and implementation simplicity. Initially, a high-efficiency frame structure is designed without a guard time interval, utilizing a preamble sequence to simultaneously achieve both symbol synchronization and automatic gain control (AGC) before demodulation. Subsequently, a novel 2-bit non-uniform quantization method for the Zadoff–Chu sequences is developed, enabling the correlation operations in the traditional symbol synchronization algorithm to be implemented via bitwise exclusive OR (XOR) and addition operations. The complexity of hardware implementation and the energy consumption for symbol synchronization can be reduced significantly. Furthermore, the impact of AGC on frequency synchronization performance is examined, and an improved frequency synchronization method based on AGC gain compensation is proposed. Finally, the performance of the proposed method is rigorously analyzed and compared with that of the traditional method through computer simulations, demonstrating the effectiveness and superiority of the proposed approach.

Permutation Polynomial Interleaved Zadoff-Chu Sequences

Permutation Polynomial Interleaved Zadoff-Chu Sequences

Enhanced resource allocation strategies to improve the spectral efficiency in massive MIMO systems

The accuracy of the channel state information is important for correct channel estimation. However, when conducting channel estimation, more resources are allocated to pilots for estimation compared to data transmission. Furthermore, when the number of users increases, the number of pilots for estimation increases. Subsequently, there is an increase in the transmission overhead and hence reduces the spectral efficiency. Therefore, the advantage of obtaining channel state information is significantly reduced. To improve the performance of massive MIMO systems, the study analyses the tradeoff between the number of resources required to correctly estimate the channel using pilots to avoid interference while maintaining optimum spectral efficiency in massive MIMO antennas. Therefore, this study proposes an algorithm to address the challenge of optimum resource allocation in a massive MIMO. Pilot Frequency reuse, max–min fairness algorithm, and Zadoff–Chu sequences were adopted to achieve optimal allocation of resources and reduce interference for users in different cells using the same frequencies. The results reveal improved performance in terms of spectral efficiency with the adoption of the resource optimization approach. The study contributes to the performance improvement of massive MIMO antennas for 5 G communications.

Constant Modulus Precoded MIMO Radar Based on Zadoff-Chu Sequences

Constant Modulus Precoded MIMO Radar Based on Zadoff-Chu Sequences

Design of Intelligent City Communication Network Based on Internet of Things

Abstract In response to the advancements in Internet of Things (IoT) technology and the growing demands for data transmission, there is a crucial need for further integration of communication network technology with IoT to enhance efficiency. This paper presents the design of a multi-node communication network model utilizing the Orthogonal Frequency-Division Multiplexing (OFDM) algorithm. In the realm of physical layer parameter design, uplink, and downlink carriers are allocated based on OFDM symbols, employing the Zadoff-Chu (ZC) sequence as the pilot frequency sequence. Additionally, the Cyclic Redundancy Check (CRC) error-checking code is implemented to ensure the accuracy of network transmissions. The model proposed in this study is applied to the operational dynamics of traffic systems within a smart city, focusing on the security and operational efficiency of the traffic communication network. Empirical testing and analysis demonstrate that the communication network, as designed, is susceptible to malware attacks by 25.68%, representing the least vulnerability among the three algorithms assessed. Moreover, in examining the bus trip time distribution with the implementation of this model, the average running time is predominantly around 11.76 minutes, which is a reduction of 0.74 minutes compared to previous configurations, thereby indicating an improvement in operational efficiency.

Generalized Zadoff-Chu Sequences With Low PMEPR Property

Generalized Zadoff-Chu Sequences With Low PMEPR Property

Orthogonal Circulant Multiplexing for Bandwidth- Limited Direct-Detected Optical Communication Systems

We propose and investigate a novel orthogonal circulant multiplexing (OCM) technology for bandwidth-limited direct detection (DD) optical systems. We analytically derive that any OCM, i.e. using any orthogonal circulant matrix for multiplexing, can redistribute the noise uniformly across the subcarriers. However, the distribution of inter-symbol interference (ISI) and inter-carrier interference (ICI) strongly depends on the design of OCM. The previously proposed orthogonal chirp division multiplexing (OCDM), although showing better ISI/ICI tolerance than discrete-Fourier-transform spread (DFT-S) orthogonal frequency division multiplexing (OFDM), is a kind of OCM with poorer performance. We propose and analytically reveal that OCM based on chirp-like polyphase sequence (CLPS), general chirp sequence (GCS), sparse CLPS (SCLPS), and sparse GCS (SGCS) can achieve flatter ISI/ICI distribution across subcarriers and so better performance than OCDM in bandwidth-limited DD systems. The optimal parameter vector of the E-parameter CLPS is a Zadoff-Chu sequence while the parameter α in GCS should be larger. The optimal performance can be achieved by either CLPS (or GCS) using a larger E (or α) or SCLPS (or SGCS) with optimized sparsity. ∼110Gbit/s experiments using Mach-Zehnder modulator or electro-absorption modulator and receiver of 10-GHz photodiode or 8-GHz avalanche photodiode are conducted. The results agree with the theory and show that the proposed OCM outperforms conventional OFDM, DFT-S OFDM, and OCDM.

LTE Device Radio Frequency Fingerprints Blind Extraction Based on Temporal-Frequency Domain PRACH Signals

A frequency-domain cepstrum correlation and temporal transient filtered radio frequency fingerprints (RFF) blind extraction method is proposed for long term evolution uplink device authentication in this work. With the merits of the constant-modulus nature of the Zadoff-Chu (ZC) sequence and the cyclic prefix (CP) structure of the physical random access channel (PRACH) frame, the device RFF integrated in both the frequency-domain ZC sequence and the transient ramp-on/ramp-off sequences are extracted. For the frequency-domain RFF extraction, the cepstrum of the ZC sequence is calculated to enlarge the gap between the constant RFF and the random fading effects, and the correlation between two cepstrum fragments is then calculated to mitigate the random fading components. For the temporal RFF extraction, the ramp-on and ramp-off features induced by the device-specific power amplifier are extracted by exploiting the CP structure of the PRACH frame, where the CP part and the duplicate part are adaptively filtered and the final adapted weight of the least mean square filter is used as RFF. No prior PRACH parameter knowledge is required in RFF extraction and both the frequency-domain and the temporal RFF are combined as the input of the convolutional neural network to enhance the classification accuracy. With four-months sampling of PRACH signals emitted from universal software radio peripheral devices, the experimental results show that the authentication accuracy of the proposed combined RFF can reach as high as 99.9% in the line-of-sight (LOS) scenario and 99.6% in the non-LOS scenario.

Channel estimation with Zadoff–Chu sequences in the presence of phase errors

AbstractDue to their perfect periodic autocorrelation property, Zadoff–Chu sequences are often used as stimulus signals in the measurement of radio channel responses. In this letter, the cross‐correlation of a linear shift‐invariant system's response to a Zadoff–Chu sequence is derived for the case that a multiplicative perturbation such as phase noise is present at its output. The perturbation signal is shown to incur a spurious discrete Fourier transform, thus degrading the correlation's peak to sidelobe ratio. The implications for the performance limits of channel measurement systems are discussed.

Composite Preambles Based on Differential Phase Rotations for Grant-Free Random Access Systems

With the advantages of low signaling overhead and latency, grant-free random access (GFRA) becomes a promising technology for supporting massive machine-type communications (mMTC), but poses new challenges for active user detection (AUD) and channel estimation (CE), whose performance mainly depends on the preamble detection. In this paper, we design the composite preamble based on differential phase rotations by aggregating orthogonal Zadoff-Chu (ZC) sequences and multiple root ZC sequences with differential phase rotations to reduce the probability of preamble collisions, thereby improving the performance of AUD and CE. In particular, differential phase rotations extend the preamble set size so that users colliding in orthogonal sequences can be distinguished by phase rotations. In addition, it also reduces non-orthogonal interference and thus reduces CE errors. The preamble detection algorithm and CE scheme are proposed, along with the theoretical analysis of AUD and CE performance to verify the effectiveness of the designed preamble. In addition, the proposed preamble is extended to combine phase rotations with cyclic shifts to further enlarge the preamble set size with low non-orthogonality. Simulation results show that the proposed composite preamble outperforms existing preambles in terms of the probability of detection and CE accuracy.

Novel Access Methods in Cellular Networks Based on the Analog Bloom Filter

In cellular networks, the User Equipment (UE) often needs to send control information to the base station. For example, to initiate a connection, a UE transmits a Zadoff-Chu (ZC) sequence on a channel called PRACH, where the sequence is randomly selected from up to 64 sequences. Also, a connected UE may send the Scheduling Request (SR) bit on a channel called PUCCH to start an uplink data transmission. In this paper, novel access methods, namely, ABF PRACH and ABF SR, are proposed based on the Analog Bloom Filter (ABF). With ABF PRACH, a UE transmits a pattern, which consists of multiple ZC sequences. The performance is improved, because the number of patterns, currently 2304, is much larger than the number of sequences, resulting in a much lower collision probability. Similarly, with ABF SR, each connected UE is assigned a unique pattern. The system capacity is improved, because the resource is shared by many UEs, instead of dedicated to individual UEs. Both ABF PRACH and ABF SR have been demonstrated in real-world experiments. Simulations show that ABF PRACH significantly outperforms the existing PRACH. Also, ABR SR achieves a 2.52-fold increase of capacity, while maintaining very low error ratios.

Chaotic logistic map sequences with good auto-correlation properties

In this work, chaotic sequences with good auto-correlation properties are presented. The studied sequences are synthesized by means of the logistic map function and, been chaotic but fully deterministic, become a good alternative for well-known sequences, for example the Zadoff-Chu sequences, especially for small size sequences commonly used for frame synchronization purposes in digital communications systems. A new auto-correlation goodness metric is proposed, and it is employed as objective function in order to maximize the correlation goodness for short synchronization sequences synthesized by means the logistic map function.

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.

A Four-cell Division Method for Pilot Sequence Design to Reduce Pilot Pollution in Massive MIMO systems

A method for pilot sequence design with the Zadoff-Chu (ZC) sequence as a base sequence is proposed to address the problem of pilot pollution in massive multi-input multi-output (MIMO) systems. Instead of the odd-length ZC sequence currently in use, the ZC sequence of even length serves as the basis of the pilot. It has the advantage of a very small cross-correlation coefficient under the premise that the sum of cyclic displacement is odd. The results of the four-cell division method are compared between the even-length and odd-length ZC pilot sequences. The MATLAB simulation shows that the signal-to-noise ratio and the channel estimation mean square error of the designed even-length ZC pilot sequence are better than those of the existing odd-length ZC pilot sequence in the case of four-cell division.

A TDMA approach for OFDM-based multiuser RadCom systems

This paper is focused on the multiuser implementation of fusion of radar and communication (RadCom) in internet-of-vehicles (IoV) scenarios. Traditional time-division multiple access (TDMA) technology degrades the velocity detection performance of orthogonal frequency-division multiplexing (OFDM)-based RadCom systems. We propose a new TDMA approach for OFDM-based RadCom systems, where multiuser communication and radar detection are completed synchronously. We consider a continuous-wave TDMA OFDM structure in which random user data or Zadoff-Chu (ZC) sequences are transmitted in one symbol duration to ensure detection performance. As an application of interference cancellation method, user data demodulation and environment sensing can be simultaneously accomplished by our proposed approach. We carry out numerical evaluation and show wireless communication and radar detection performance over the continuous-wave TDMA OFDM-based RadCom approach.

Beam-Tracking Technique for IRS-Assisted mmWave Cellular Systems With Uniform Planar Array

In this paper, a beam-tracking technique is proposed for millimeter-wave (mmWave) cellular systems with an intelligent reflective surface (IRS). A preamble design technique for IRS-assisted cellular systems is proposed using the complex conjugate property of the Zadoff-Chu sequence and reflecting nature of IRS. Moreover, a beam-tracking technique for mmWave cellular systems with a uniform planar array (UPA) is also proposed to track the variation in the angle of departure (AoD) using subpanel structures of the UPA. Through simulation, it is demonstrated that the beam tracking technique with the proposed preamble can successfully track 2-D AoD trajectories of the base station and IRS.

Unimodular Perfect and Nearly Perfect Sequences: a Variation of Björck’s Scheme

Constant Amplitude (CA), Zero Auto Correlation (ZAC) sequences (or CAZAC sequences, aka perfect sequences) have numerous applications. We generalize the CAZAC notion to what we term as CASAC by permitting small autocorrelations (SAC). We extend Björck’s classification result of two-valued CAZAC sequences by providing a complete classification of all almost 2-valued (i.e., two-valued except for the first position which uses a third value) CASAC sequences. While Björck’s original work dealt only with primes p, we extend his ideas to any abelian group of order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v\equiv 1\pmod {4}$ </tex-math></inline-formula> , as opposed to restricting just to the prime fields GF(p). Björck sequences have better ambiguity function than Zadoff-Chu sequences, making them suitable for radar and communications applications in the presence of high Doppler shifts. In fact, the discrete narrow band ambiguity function has an optimal bound in case of Björck sequences (as opposed to Gauss sequences). A one-parameter infinite family of CASAC we construct would have applications in Multiple-Input Multiple-Output (MIMO) areas. Toward MIMO applications, we introduce a performance measure we term as cross merit factor to study cross correlation behavior, generalizing the well-known notion of Golay Merit Factor (GMF).

New supersets of Zadoff-Chu sequences via the Weil bound

New supersets of Zadoff-Chu sequences via the Weil bound