Showing papers on "Continuous phase modulation published in 2019"

Beamforming Optimization for Intelligent Reflecting Surface with Discrete Phase Shifts

Abstract: Intelligent reflecting surface (IRS) is a cost-effective solution for achieving high spectrum and energy efficiency in future wireless communication systems by leveraging massive low-cost passive elements that are able to reflect the signals with adjustable phase shifts. Prior works on IRS mostly consider continuous phase shifts at each reflecting element, which however, is practically difficult to realize due to the hardware limitation. In contrast, we study in this paper an IRS-aided wireless network, where an IRS with only a finite number of phase shifts at each element is deployed to assist in the communication from a multi-antenna access point (AP) to a single-antenna user. We aim to minimize the transmit power at the AP by jointly optimizing the continuous transmit beamforming at the AP and discrete reflect beamforming at the IRS, subject to a given signal-to-noise ratio (SNR) constraint at the user receiver. We first propose a suboptimal and low-complexity solution to the problem by applying the alternating optimization technique. Then, we analytically show that as compared to the ideal case with continuous phase shifts, the IRS with discrete phase shifts achieves the same squared power gain in terms of asymptotically large number of reflecting elements, while a constant performance loss is incurred that depends only on the number of phase-shift levels. Simulation results verify our analytical result as well as the effectiveness of our proposed design as compared to different benchmark schemes.

Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface with Discrete Phase Shifts

Abstract: Intelligent reflecting surface (IRS) is a cost-effective solution for achieving high spectrum and energy efficiency in future wireless networks by leveraging massive low-cost passive elements that are able to reflect the signals with adjustable phase shifts. Prior works on IRS mainly consider continuous phase shifts at reflecting elements, which are practically difficult to implement due to the hardware limitation. In contrast, we study in this paper an IRS-aided wireless network, where an IRS with only a finite number of phase shifts at each element is deployed to assist in the communication from a multi-antenna access point (AP) to multiple single-antenna users. We aim to minimize the transmit power at the AP by jointly optimizing the continuous transmit precoding at the AP and the discrete reflect phase shifts at the IRS, subject to a given set of minimum signal-to-interference-plus-noise ratio (SINR) constraints at the user receivers. The considered problem is shown to be a mixed-integer non-linear program (MINLP) and thus is difficult to solve in general. To tackle this problem, we first study the single-user case with one user assisted by the IRS and propose both optimal and suboptimal algorithms for solving it. Besides, we analytically show that as compared to the ideal case with continuous phase shifts, the IRS with discrete phase shifts achieves the same squared power gain in terms of asymptotically large number of reflecting elements, while a constant proportional power loss is incurred that depends only on the number of phase-shift levels. The proposed designs for the single-user case are also extended to the general setup with multiple users among which some are aided by the IRS. Simulation results verify our performance analysis as well as the effectiveness of our proposed designs as compared to various benchmark schemes.

Channel Estimation and Passive Beamforming for Intelligent Reflecting Surface: Discrete Phase Shift and Progressive Refinement

Abstract: Prior studies on Intelligent Reflecting Surface (IRS) have mostly assumed perfect channel state information (CSI) available for designing the IRS passive beamforming as well as the continuously adjustable phase shift at each of its reflecting elements, which, however, have simplified two challenging issues for implementing IRS in practice, namely, its channel estimation and passive beamforming designs both under the constraint of discrete phase shifts. To address them, we consider in this paper an IRS-aided single-user communication system with discrete phase shifts and design the IRS training reflection matrix for channel estimation as well as the passive beamforming for data transmission, both subject to the constraint of discrete phase shifts. We show that the training reflection matrix design for discrete phase shifts greatly differs from that for continuous phase shifts, and thus the corresponding passive beamforming should be optimized by taking into account the correlated channel estimation error due to discrete phase shifts. Specifically, we consider a practical block-based transmission, where each block has a finite (insufficient) number of training symbols for channel estimation. A novel hierarchical training reflection design is proposed to progressively estimate IRS elements' channels over multiple blocks by exploiting IRS-elements grouping and partition. Based on the resolved IRS channels in each block, we further design the progressive passive beamforming at the IRS with discrete phase shifts to improve the achievable rate for data transmission over the blocks.

On the LoRa Modulation for IoT: Waveform Properties and Spectral Analysis

Abstract: An important modulation technique for Internet of Things (IoT) is the one proposed by the LoRa allianceTM. In this paper we analyze the M-ary LoRa modulation in the time and frequency domains. First, we provide the signal description in the time domain, and show that LoRa is a memoryless continuous phase modulation. The cross-correlation between the transmitted waveforms is determined, proving that LoRa can be considered approximately an orthogonal modulation only for large M. Then, we investigate the spectral characteristics of the signal modulated by random data, obtaining a closed-form expression of the spectrum in terms of Fresnel functions. Quite surprisingly, we found that LoRa has both continuous and discrete spectra, with the discrete spectrum containing exactly a fraction 1/M of the total signal power.

High-speed 3D shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system.

Abstract: In this paper, we propose a high-speed 3D shape measurement technique based on the optimized composite fringe patterns and stereo-assisted structured light system. Stereo phase unwrapping, as a new-fashioned method for absolute phase retrieval based on the multi-view geometric constraints, can eliminate the phase ambiguities and obtain a continuous phase map without projecting any additional patterns. However, in order to ensure the stability of phase unwrapping, the period of fringe is generally around 20, which limits the accuracy of 3D measurement. To solve this problem, we develop an optimized method for designing the composite pattern, in which the speckle pattern is embedded into the conventional 4-step phase-shifting fringe patterns without compromising the fringe modulation, and thus the phase measurement accuracy. We also present a simple and effective evaluation criterion for the correlation quality of the designed speckle pattern in order to improve the matching accuracy significantly. When the embedded speckle pattern is demodulated, the periodic ambiguities in the wrapped phase can be eliminated by combining the adaptive window image correlation with geometry constraint. Finally, some mismatched regions are further corrected based on the proposed regional diffusion compensation technique (RDC). These proposed techniques constitute a complete computational framework that allows to effectively recover an accurate, unambiguous, and distortion-free 3D point cloud with only 4 projected patterns. Experimental results verify that our method can achieve high-speed, high-accuracy, robust 3D shape measurement with dense (64-period) fringe patterns at 5000 frames per second.

Exploiting Intelligent Reflecting Surfaces in Multi-Antenna Aided NOMA Systems

Abstract: This paper investigates a downlink multiple-input single-output intelligent reflecting surface (IRS) aided non-orthogonal multiple access (NOMA) system, where a base station (BS) serves multiple users with the aid of IRSs. Our goal is to maximize the sum rate of all users by jointly optimizing the active beamforming at the BS and the passive beamforming at the IRS, subject to successive interference cancellation decoding rate conditions and IRS reflecting elements constraints. In term of the characteristics of reflection amplitudes and phase shifts, we consider ideal and non-ideal IRS assumptions. To tackle the formulated non-convex problems, we propose efficient algorithms by invoking alternating optimization, which design the active beamforming and passive beamforming alternately. For the ideal IRS scenario, the two subproblems are solved by invoking the successive convex approximation technique. For the non-ideal IRS scenario, constant modulus IRS elements are further divided into continuous phase shifts and discrete phase shifts. To tackle the passive beamforming problem with continuous phase shifts, a novel algorithm is developed by utilizing the sequential rank-one constraint relaxation approach, which is guaranteed to find a locally optimal rank-one solution. Then, a quantization-based scheme is proposed for discrete phase shifts. Finally, numerical results illustrate that: i) the system sum rate can be significantly improved by deploying the IRS with the proposed algorithms; ii) 3-bit phase shifters are capable of achieving almost the same performance as the ideal IRS; iii) the proposed IRS-aided NOMA systems achieve higher system sum rate than the IRS-aided orthogonal multiple access system.

Continuous Voltage Vector Model-Free Predictive Current Control of Surface Mounted Permanent Magnet Synchronous Motor

Abstract: To reduce the current ripples of finite control set model predictive control, this paper proposes a continuous voltage vector model-free predictive current control method for the surface mounted permanent magnet synchronous motor (SMPMSM) In the proposed method, the continuous phase and the amplitude of the voltage vector are optimized in a sequence based on their uncoupling feature, and then the steady-state current fluctuation can be reduced Only six active voltage vectors are enumerated, and the optimal phase is obtained by establishing the Lagrange interpolation polynomial between the cost function and the phase of voltage vectors Then, the amplitude of the voltage vector with the optimal phase is optimized based on the principle of minimizing the cost function, and the optimal voltage vector is synthesized by a three-vector method In addition, the ultra-local model of the SMPMSM drive system from the previous study is used to improve the robustness of the proposed method The current dynamic and steady-state responses are demonstrated through the simulation and experimental results

On the LoRa Modulation for IoT: Waveform Properties and Spectral Analysis

Abstract: An important modulation technique for Internet of Things (IoT) is the one proposed by the low power long range (LoRa) alliance. In this paper, we analyze the $M$ -ary LoRa modulation in the time and frequency domains. First, we provide the signal description in the time domain, and show that LoRa is a memoryless continuous phase modulation. The cross-correlation between the transmitted waveforms is determined, proving that LoRa can be considered approximately an orthogonal modulation only for large $M$ . Then, we investigate the spectral characteristics of the signal modulated by random data, obtaining a closed-form expression of the spectrum in terms of Fresnel functions. Quite surprisingly, we found that LoRa has both continuous and discrete spectra, with the discrete spectrum containing exactly a fraction $1/M$ of the total signal power.

Robust 2D phase unwrapping algorithm based on the transport of intensity equation

Abstract: 2D phase-unwrapping algorithms (PUAs) are commonly used to obtain a continuous phase map from the sawtooth-shaped phase map. However, implementing PUAs can be time consuming, and the accuracy of those algorithms may be low if there is heavy noise. In this paper, we develop a simple and robust PUA based on the transport of intensity equation (TIE). In our method, the TIE was solved using the fast cosine transform, and a phase correction operation was introduced after the TIE was solved. Because of the phase correction operation, the proposed method can obtain a satisfactory unwrapping result even in a notably hash noise condition. The simulation and experimental results are presented to validate the effectiveness of the proposed method. The detailed software package can be found at https://ww2.mathworks.cn/matlabcentral/fileexchange/68493-robust-2d-phase-unwrapping-algorithm.

Discrete Phase Shift Design for Practical Large Intelligent Surface Communication

Abstract: In this paper, we investigate a downlink channel of a large intelligent surface (LIS) communication system. The LIS is equipped with B-bit discrete phase shifts while base station (BS) exploits low-resolution digital-to-analog converters (DACs). Without the knowledge of channel state information (CSI) related to the LIS, we propose a practical phase shift design method, whose computational complexity increases by 2B independent of the number of reflecting elements N. A tight lower bound for the asymptotic rate of the user is obtained in closed form. As N increases, we observe that the asymptotic rate becomes saturated because both the received signal power and the DAC quantization noise increase. Compared to the optimal continuous phase shift design with perfect CSI, our proposed method asymptotically approaches the ideal benchmark performance for moderate to high values of B. The derived results and observations are verified by simulation results.

Analysis of Communication Symbol Embedding in FH MIMO Radar Platforms

Abstract: Information embedding into the emission of multiple-input multiple-output (MIMO) frequency hopping (FH) radar is analyzed. It is assumed that the radar is primary under dual function radar communication system platforms. phase shift keying (PSK) communication symbols are embedded in each hop of the FH waveforms. The impact of embedding is a significant reduction in range sidelobe levels. We examine the impact of PSK symbol embedding on the power spectral density (PSD) of the MIMO radar. It is shown that there is spectral leakage due to the disruption of the continuous phase of the FH waveforms by the PSK symbol embedding. The trade-off between low sidelobe levels and low spectral leakage is analyzed. To maintain the phase continuity between the frequency hops, modulation of FH waveforms with frequency shift keying (FSK) symbols is considered and its performance is compared with that of the FH/PSK radar communication waveforms.

Integrated Waveform for a Joint Radar-Communication System With High-Speed Transmission

Abstract: Joint radar-communication systems based on integrated waveforms can simultaneously realize high-speed data transmission and target detection in one device, providing information sharing networks and information sources for decision-making of intelligent transportation systems. In this letter, based on a combination of linear frequency modulation (LFM) signals and continuous phase modulation (CPM) signals with an adjustment of communication symbols of length ${k}$ , an integrated waveform ${k}$ -LFM-CPM and a complete system framework cascaded with low-density parity-check (LDPC) codes is carried out. With a limited bandwidth, this system achieves a better bit-error rate than original LFM-CPM-LDPC systems, benefiting from an almost non-broadening power spectrum and additional information used in the cascaded decoding process. Finally, through the optimization of the mismatched filter, it is verified that the detection performance of the integrated waveform with accumulation is almost the same as that of the LFM signal.

Coherent Full-Duplex Double-Sided Two-Way Ranging and Velocity Measurement Between Separate Incoherent Radio Units

Abstract: This paper presents a novel coherent full-duplex (FD) double-sided two-way ranging (CFDDS-TWR) technique for wireless locating and velocity measurement between separate radio units. The idea presented here is a quantum leap in wireless locating since it enables coherent ranging, continuous phase tracking, and velocity measurement between wireless units that operate incoherently with separate low-cost crystal oscillator clock sources. Frequency modulated continuous wave chirp sequences are exchanged in a FD manner between two radio units. The signals transmitted from two radio units are received, respectively, by each of the two units and down-converted in a mixer with the receiver’s own transmit signal to generate a beat signal in each unit. The two beat signals are then processed together, after one beat signal is transmitted to the partner unit. Phase coherent range and Doppler phase measurements can be conducted between incoherent radio units. The presented CFDDS-TWR technique also offers options for reducing noise-like distortions caused by mixing the products of uncorrelated phase noise. We show both analytically and experimentally that the described compensation method reduces the noise level and enhances the dynamic range of the ranging signals tremendously—as evidenced by an improvement of around 24 dB in our results. These unique signal and synchronization properties show that the CFDDS-TWR method is a highly accurate measurement approach. Results acquired with a 24-GHz test system in a 7- to 17-m range demonstrate a standard deviation in range and velocity of 0.25 mm and 0.05 mm/s, respectively.

Single Carrier with Index Modulation for Low Power Terabit Systems

Abstract: Wireless terabit-per-second (Tb/s) links will become an urgent requirement within the next 10 years. However, current methodology for high data rate wireless communication that keep increasing the $M$ -ary modulation schemes and the order of MIMO spatial multiplexing cannot reach Tb/s with a low power consumption. Thus, a new methodology is required with a large bandwidth in the millimeter-wave (mm-Wave) and sub-Terahertz (sub-THz) bands above 90GHz. In addition, it must be able to provide an extremely high spectral efficiency with a low energy consumption. Note that this consumption can be reduced by using constant-envelope modulations such as continuous phase modulation (CPM). However, the CPM has a very low spectral efficiency that limits the desired data rate. This paper suggests a new methodology to reach 1 Tb/s with a low power consumption by using power efficient single carrier with Index Modulation (IM). Simulation results under various uncorrelated/correlated fading channels show that the systems with power efficient modulations as CPM or QPSK can achieve Tb/s with a good performance. Moreover, the link budget and power estimation prove that the constant and near-constant envelope modulations require less than 1–3 Watts for 1 Tb/s with 10−4un-coded BER. Finally, this paper shows that conveying most of the information bits using IM to reach an ultra-high data rate is more power efficient than high order MIMO spatial multiplexing with large $M$ -ary QAM as used in LTE.

Practical route to entanglement-assisted communication over noisy bosonic channels.

Abstract: Entanglement offers substantial advantages in quantum information processing, but loss and noise hinder its applications in practical scenarios. Although it has been well known for decades that the classical communication capacity over lossy and noisy bosonic channels can be significantly enhanced by entanglement, no practical encoding and decoding schemes are available to realize any entanglement-enabled advantage. Here, we report structured encoding and decoding schemes for such an entanglement-assisted communication scenario. Specifically, we show that phase encoding on the entangled two-mode squeezed vacuum state saturates the entanglement-assisted classical communication capacity over a very noisy channel and overcomes the fundamental limit of covert communication without entanglement assistance. We then construct receivers for optimum hypothesis testing protocols under discrete phase modulation and for optimum noisy phase estimation protocols under continuous phase modulation. Our results pave the way for entanglement-assisted communication and sensing in the radio-frequency and microwave spectral ranges.

Zero Crossing Modulation for Communication with Temporally Oversampled 1-Bit Quantization

Abstract: Today’s communication systems typically use high resolution analog-to-digital converters (ADCs). However, considering future communication systems with data rates in the order of 100Gbit/s the ADC power consumption becomes a major factor due to the high sampling rates. A promising alternative are receivers based on 1-bit quantization and oversampling w.r.t. the signal bandwidth. Such an approach requires a redesign of modulation, receiver synchronization, and demapping. A zero crossing modulation is a natural choice as the information needs to be carried in the zero crossing time instants. The present paper provides an overview on zero crossing modulation, achievable rates, sequence mapping and demapping, 1-bit based channel parameter estimation, and continuous phase modulation as an alternative zero crossing modulation scheme.

Efficient phase unwrapping algorithm based on cubature information particle filter applied to unwrap noisy continuous phase maps.

Abstract: This paper presents a new phase unwrapping algorithm for wrapped phase fringes through combining a cubature information particle filter with an efficient local phase gradient estimator and an efficient quality-guided strategy based on heap-sort. The cubature information particle filter that not only is independent from noise statistics but also is not constrained by the nonlinearity of the model constructed is applied to retrieve unambiguous phase from modulus 2π wrapped fringe patterns through constructing a recursive cubature information particle filtering phase unwrapping procedure to perform simultaneously phase unwrapping and noise filtering for the first time to our knowledge, which can be expected to obtain more robust solutions from wrapped phase fringes. Phase gradient estimate is one of the key steps in almost all phase unwrapping algorithms and is directly related to the precision and the efficiency of phase unwrapping procedure. Accordingly, an efficient local phase gradient estimator that is more efficient than ones published previously is deduced to obtain phase gradient information required by the proposed algorithm, which can drastically decrease time consumption of unwrapping procedure and drastically improve the efficiency of the algorithm. The efficient quality-guided strategy based on heap-sort guarantees that the proposed algorithm efficiently unwraps wrapped pixels along the path from the high-reliance regions to the low-reliance regions of wrapped phase images. In addition, the accelerated version of the proposed algorithm is further developed through combing with reversible modulo wavelet operators to solve phase unwrapping problem of wrapped phase images in wavelet transform domain, which can reduce the amount of wrapped pixels that need to be unwrapped, and can further decrease time consumption of unwrapping procedure performing on wrapped phase images. This algorithm and its accelerated version under the frame of wavelet transform are demonstrated with various types of wrapped phase images, showing acceptable solutions.

Under-Sampled Phase Retrieval of Single Interference Fringe Based on Hilbert Transform

Abstract: Phase retrieval from single interference fringe is important and effective method in obtaining the real phase distribution. The original phase can be retrieved by the line integral of its gradient expressed as sine and cosine components, which were gained by the Hilbert transform twice from a single interference fringe pattern. However, this method fails when the phase transformation of the interference fringe is too fast. In this paper, a novel method to recover the continuous phase of the whole field is proposed to solve the above problems. The shear interference technique is introduced into the phase retrieval method to build an exponential 2-D complex light field of natural base for the phase slope obtained by the Hilbert transform. Then, the expressions of phase slopes in x- and y-directions are constructed as a discrete Poisson equation. Therefore, the calculation of phase retrieval is equivalent to solve the discrete Poisson equation mathematically. Finally, the real phase is gotten by the weighted discrete cosine transform (WDCT) of the discrete Poisson equation. The simulation results verify the validity of this method and show that the proposed method can achieve the phase retrieval of the phase discontinuity in x- and y-directions, which leads to the under-sampled problem. It can restore the whole field phase distribution rapidly and accurately. Moreover, this method is applied to phase retrieval of interferometric synthetic aperture radar (InSAR) with the under-sampled problem in this paper. The experimental results show that this method can recover the phase of InSAR with the under-sampled problems caused by terrain abrupt change and so on. Compared with other commonly used methods, it achieved satisfactory results. This method provides a new idea for solving the under-sampled problem in the phase retrieval from a single-frame interference fringe.

Zero Crossing Modulation for Communication with Temporally Oversampled 1-Bit Quantization

Abstract: Today's communication systems typically use high resolution analog-to-digital converters (ADCs). However, considering future communication systems with data rates in the order of 100Gbit/s the ADC power consumption becomes a major factor due to the high sampling rates. A promising alternative are receivers based on 1-bit quantization and oversampling w.r.t. the signal bandwidth. Such an approach requires a redesign of modulation, receiver synchronization, and demapping. A zero crossing modulation is a natural choice as the information needs to be carried in the zero crossing time instants. The present paper provides an overview on zero crossing modulation, achievable rates, sequence mapping and demapping, 1-bit based channel parameter estimation, and continuous phase modulation as an alternative zero crossing modulation scheme.

Exploiting Intelligent Reflecting Surfaces in NOMA Networks: Joint Beamforming Optimization

Abstract: This paper investigates a downlink multiple-input single-output intelligent reflecting surface (IRS) aided non-orthogonal multiple access (NOMA) system, where a base station (BS) serves multiple users with the aid of IRSs Our goal is to maximize the sum rate of all users by jointly optimizing the active beamforming at the BS and the passive beamforming at the IRS, subject to successive interference cancellation decoding rate conditions and IRS reflecting elements constraints In term of the characteristics of reflection amplitudes and phase shifts, we consider ideal and non-ideal IRS assumptions To tackle the formulated non-convex problems, we propose efficient algorithms by invoking alternating optimization, which design the active beamforming and passive beamforming alternately For the ideal IRS scenario, the two subproblems are solved by invoking the successive convex approximation technique For the non-ideal IRS scenario, constant modulus IRS elements are further divided into continuous phase shifts and discrete phase shifts To tackle the passive beamforming problem with continuous phase shifts, a novel algorithm is developed by utilizing the sequential rank-one constraint relaxation approach, which is guaranteed to find a locally optimal rank-one solution Then, a quantization-based scheme is proposed for discrete phase shifts Finally, numerical results illustrate that: i) the system sum rate can be significantly improved by deploying the IRS with the proposed algorithms; ii) 3-bit phase shifters are capable of achieving almost the same performance as the ideal IRS; iii) the proposed IRS-aided NOMA systems achieve higher system sum rate than the IRS-aided orthogonal multiple access system

Impedance-matched dielectric metasurfaces for non-discrete wavefront engineering

Abstract: Metasurfaces can manipulate optical wavefronts by locally shifting the phase of incident light with metallic or dielectric optical nanoresonators that are generally arranged on a lattice with subwavelength spacing. However, such conventional metasurfaces inevitably generate a spatially discrete multi-level phase profile due to the spacing of their building blocks. This directly leads to an efficiency reduction and thus limits their capability. Here, we propose and demonstrate highly efficient transmissive metasurfaces with the ability to form a continuous phase profile. The proposed strategy relies on the fact that high-index dielectric nanobeams with gradually modulated widths can be interpreted to be a virtually impedance-matched material with spatial variations of its refractive index. By highly utilizing such features, one-dimensionally continuous, arbitrary phase profiles can be created in a simple manner with the width profile design. Since spatial transmittance variations can be minimized due to the impedance matching feature, this approach provides a nearly ideal phase profile for spatial light modulation with phase-only filtering operations. We demonstrate that this approach has the capability to improve the performance in various metasurface-based optical components, including polarization-dependent, large-angle beam deflectors and versatile multi-beam splitters. Considering that designing optical phases even in deep-subwavelength regimes is critical for free-space optics, the proposed approach will enable new classes of optical components with complex wavefront engineering.

The Potential of Continuous Phase Modulation for Oversampled 1-Bit Quantized Channels

Abstract: We study the achievable rate of a 1-bit quantized temporally oversampled AWGN channel using continuous phase modulation schemes. Given a requirement for very high data rate, 1-bit quantization could become a key component to increase the energy efficiency in future communication systems since it greatly relieves the hardware requirements at the receiver. Due to its constant envelope, phase modulation furthermore relaxes the requirements on the transmitter architecture. We investigate the potential of continuous phase modulation and show that in order to approach the full potential of continuous phase modulation under 1-bit quantization, a tailored waveform design is required.

Two-Dimensional Phase Unwrapping via Balanced Spanning Forests

Abstract: Phase unwrapping is the process of recovering a continuous phase signal from an original signal wrapped in the (−π,π] interval. It is a critical step of coherent signal processing, with application...

Research on an Optimization Method for a Partially Responsive Continuous Phase Modulated (CPM) Signal Based on an Optimal Generic Function

Abstract: This paper establishes an optimal generic function model in order to obtain a continuous phase modulated (CPM) signal with a smoother phase modulation function. This is achieved by finding the solution to the symbol signals at different lengths of the CPM function. In the solution process, the unknown amount that needs to be solved is reduced by using the even function symmetry characteristic of the signal to be solved. For each different form of the signal, the time domain form of the CPM function and the corresponding normalized energy spectral density are compared under the influence of the phase modulation signal length and the generic function parameter n. The data transmission rate is improved by introducing inter-symbol interference, and the modulation process is realized using six-way parallel transmission when the CPM function is 6T. The simulation results show that the CPM function obtained by establishing an optimal generic function model has high-quality time-frequency characteristics. The real-time phase trajectory and the high-order derivative are both continuous, and the modulated signal has constant envelope characteristics. The CPM function has a fast rolling-off in the frequency domain and small out-of-band radiation, which greatly improves the characteristics of the frequency band utilization.

Performance trade-off analysis of co-design of radar and phase modulated communication signals in frequency hopping MIMO systems

Abstract: We present a dual-function radar communication (DFRC) system in which phase modulated information symbols are embedded in the multiple-input multiple-output (MIMO) frequency hopping (FH) radar sub-pulses in fast-time. The communications are considered as the secondary function of the proposed dual-function radar communication (DFRC) systems. We use differential phase shift keying (DPSK) and continuous phase modulation (CPM). These modulations preserve the continuous phase between the FH sub-pulses, unlike phase shift keying (PSK) modulated symbols. The performance of FH/DPSK and FH/CPM systems is compared with that of the FH/PSK system in terms of range sidelobe levels (RSL) and power spectral density (PSD). It is shown that the proposed DFRC systems exhibit better spectral containment and lower spectral sidelobe levels. The communication data rates for the proposed system are derived, and to assume relatively high values.

Autocorrelation Function of Full-Response CPM Signals and Its Application to Synchronization

Abstract: Two types of the autocorrelation functions of the full-response continuous phase modulation (CPM) signal are investigated in the paper, the autocorrelation functions are proven to be periodic functions when the modulation index of the CPM signal is h=1. Then the autocorrelation functions are expanded in the form of Fourier series, and two synchronization schemes are proposed to estimate the synchronization parameters from the coefficients of the Fourier series, including the carrier frequency offset, the carrier phase and the timing offset. The performances of the synchronization algorithms are shown by simulations and compared with the modified Cramer-Rao bounds (MCRB) and other synchronization schemes. The simulation results show that the first type of the proposed scheme has better synchronization performances than the available schemes.

On Sparse Channel Estimation in Aeronautical Telemetry

Abstract: This paper examines the application of sparse estimation techniques for the estimation of a discrete-time equivalent multipath channel in the aeronautical telemetry context. The sensing matrix comprises samples of shaped offset QPSK-TG (a continuous phase modulation) based on the pilot bit sequence currently defined in the aeronautical telemetry standard. Representative algorithms from the three broad classes of sparse estimators were examined side by side using computer simulations to estimate the postequalizer bit error rate (BER). Ideal and nonideal frequency offset synchronization were assumed in the simulations. The results show that the performance of the matching pursuit (MP) algorithms seemed to be better suited to this application in the sense that no additional steps were required and the postequalizer BER of the best MP algorithm was slightly better than that of the other sparse estimation techniques. In the case of both ideal and nonideal frequency offset synchronization, the postequalizer BER achieved by the generalized orthogonal MP algorithm was approximately 1.5 dB better than that obtained using the nonsparse-constrained maximum likelihood channel estimate.

A Simplified Direct-Decision Synchronization Algorithm for Coherent CPM Receiver Using Linear Phase Approximation

Abstract: We propose a simplified decision-directed synchronization algorithm for continuous phase modulation (CPM) based on the linear approximation to the phase of the CPM signal. It yields simple and practical synchronization algorithm with closed-loop architecture, in which the derivative matched filters are not required. Numerical results demonstrate that this novel synchronizer achieves improved timing estimation performance while requiring lower complexity when compared with the well-known method based on pulse amplitude modulation approximation. The demodulation architecture with the proposed algorithm is presented, and its bit-error-rate approaches the theoretical bound.