Showing papers on "Continuous phase modulation published in 2020"

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.

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.

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 and design the IRS training reflection matrix for channel estimation as well as the passive beamforming for data transmission, both subject to the new constraint of discrete phase shifts. We show that the training reflection matrix design with discrete phase shifts greatly differs from that with continuous phase shifts, and the corresponding passive beamforming design should take into account the correlated IRS channel estimation errors due to discrete phase shifts. Moreover, a novel hierarchical training reflection design is proposed to progressively estimate IRS elements’ channels over multiple time blocks by exploiting the 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. Extensive numerical results are presented, which demonstrate the significant performance improvement of proposed channel estimation and passive beamforming designs as compared to various benchmark schemes.

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 application in practical scenarios. Although it has been well known for decades that the classical communication capacity of 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 an entangled two-mode squeezed vacuum state saturates the entanglement-assisted classical communication capacity of a very noisy channel and overcomes the fundamental limit on covert communication that exists without the assistance of entanglement. We then construct receivers for optimum hypothesis-testing protocols with discrete phase modulation and for optimum noisy phase-estimation protocols with continuous phase modulation. Our results pave the way for entanglement-assisted communication and sensing in the radio-frequency and microwave spectral ranges.

Controlling Clutter Modulation in Frequency Hopping MIMO Dual-Function Radar Communication Systems

Abstract: We present a dual-function radar communication (DFRC) system applying signal embedding through a code shift keying (CSK) strategy. The information symbol is phase encoded into a sequence and then modulated by the continuous phase modulation (CPM) before embedding into frequency hopping (FH) radar sub-pulses. The CPM modulated communication symbol phase coded sequence is multiplied with the FH radar waveforms in fast-time and transmitted through multiple-input multiple-output (MIMO) radar platforms. We address the problem of range sidelobe modulation (RSM) and propose the design of the optimum CSK sequences to reduce the degree of change in the range sidelobe levels (RSLs) of the ambiguity function (AF). It is shown that the optimum CSK sequences yield significant reduction in the RSLs of the DFRC system. They also maintain the same degree of correlation between FH sub-pulses regardless of the communication symbol sequences embedded. Additionally, the proposed DFRC system with the optimized waveform design provides good spectrum containment and achieves high communication data rates.

A Novel Chip Pulse Employed by Ranging Code Based on Simultaneous Transmitting CPM Modulation and PN Ranging in Inter-Satellite Links of GNSS

Abstract: The construction of a navigation constellation with inter-satellite links (ISLs) has become one of the important development trends for new-generation global navigation satellite systems (GNSSs), and ISLs currently realize navigation and communication functions through separate low-rate omnidirectional telemetry, tracking, command and high-rate data service channels, respectively. If the above two functions are integrated into one channel, this will result in simplification of the onboard equipment, improvement of the electromagnetic compatibility, power consumption reduction and frequency resources savings, and we speculate that autonomous navigation will be achieved by ISLs with navigation and communication fusion. In this paper, a system capable of simultaneous high-data rate communication transmission and precision ranging is investigated, and a specific scheme is introduced by combining continuous phase modulation (CPM) and a pseudonoise (PN) ranging code denoted as CPM + PN. The chip pulse is one of the key factors to design the ranging code, which not only affects the ranging performance but also influences the properties of the CPM + PN scheme, such as its spectral characteristics, communication reliability, and acquisition time. To consider the above performance indexes, a new chip pulse based on a normally distributed wave is proposed. Theoretical analysis and simulation results show that compared to square-wave and half-sine wave cases, the normally distributed wave attains great advantages in the ranging accuracy and communication reliability, which become more notable with reasonable selection of the energy distribution index. Moreover, the proposed chip pulse achieves a similar acquisition time as the traditional wave. As a result, the normally distributed wave can be used as a better alternative to the ranging chip pulse for the CPM + PN waveform.

Cooperative Beamforming for Large Intelligent Surface Assisted Symbiotic Radios

Abstract: In this paper, we investigate a large intelligent surface (LIS) assisted symbiotic radio (SR) system, in which a LIS device, operating as an Internet-of-Things (IoT) device, exploits the signal from a primary transmitter (PT) as its communication carrier to achieve its own information transmission, and concurrently serves as a desirable additional link to aid the primary transmission from the PT to a primary receiver (PR). A cooperative beamforming scheme (i.e., active transmit beamforming at the PT and passive reflecting beamforming at the LIS device) is proposed to minimize PT's transmit power under quality-of-service (QoS) constraints of both the primary and LIS device transmissions. Both continuous and discrete phase shift setups of the LIS device are considered. For the continuous phase shift setup, a closed-form solution is derived, analytically showing that by smartly configuring the phase shifts, the signals from primary link and backscatter link can add coherently at the PR; while for the discrete phase shift setup, a near-optimal solution for the 1-bit phase shifter is obtained via the semi-definite relaxation (SDR) technique, and a general successive refinement algorithm (SRA) is developed for any-bit phase shifter. Simulation results demonstrate that cooperative beamforming design can adaptively adjust beamformers to strike a balance between the primary and LIS device transmissions.

Design and Analysis of Low Power and High SFDR Direct Digital Frequency Synthesizer

Abstract: Due to the advantages of fast frequency shifting, continuous phase shifting, fine frequency resolution, large bandwidth, and excellent spectral purity, the direct digital frequency synthesis (DDFS) technique is attracting more attention than ever before. Although the DDFS suffer from high power consumption, recent researches on the development of the low power DDFS (LP-DDFS) increases the feasibility of applying the DDFS to portable devices. To further accelerate the use of LP-DDFS, a new LP-DDFS design to significantly improve power efficiency is proposed and analyzed in this paper. In the new design, the dominant spur by truncation errors causing performance degradation has been also thoroughly considered. Since the existing dithering techniques for the truncation error problems can cause the additional performance degradation due to the side effects such as frequency offset and SNDR deterioration, an enhanced dithering technique is also proposed in this paper. The proposed technique includes a frequency compensation circuit and thus minimizes the truncation errors in the LP-DDFS with the minimal additional power consumption and SNDR degradation. Both theoretical and experimental analysis are conducted to verify the proposed design, where a prototype chip is fabricated and measured.

Performance comparison of dual-function systems embedding phase-modulated signals in FH radar

Abstract: In this paper, we compare the performance of different phase modulated frequency hopping (FH) multiple-input multiple-output (MIMO) radar waveforms. The communication symbols are embedded into the FH waveforms under the auspices of dual-function (DF) radar and communications system. In the proposed scheme, each embedded symbol is represented by a sequence of phases. The phase modulated sequence is embedded through multiplication with the radar hops and is transmitted through a MIMO radar platform. Using this scheme, we consider information embedding in MIMO FH radar implementing different types of phase modulated sequence, including phase shift keying (PSK), differential phase shift keying (DPSK) and continuous phase modulation (CPM). We analyze the corresponding ambiguity functions (AFs) in terms of reducing or increasing range and Doppler sidelobes compared to the FH radar without any signal embedding. The spectral sidelobe levels and the complexity of the demodulator at the communication receiver are also examined. It is shown the proposed embedding scheme for DPSK and CPM minimizes the frequency leakage outside the radar signal bandwidth. To demonstrate the effectiveness of proposed scheme, we compare its performance with existing embedding schemes, all for FH radars. It is shown that our approach, in its significant reductions of range sidelobes, permits high data rate transmission. This is made possible because the FH radar can now afford using duplicate hopping code values without the penalty of incurring high correlations, or range sidelobe levels.

Noncoherent Symbol Detection of Short CPM Bursts in Frequency-Selective Fading Channels

Abstract: We consider the detection of short continuous phase modulation (CPM) bursts in a frequency-selective fading channel. The conventional solution comprises training-aided channel estimation followed by coherent detection. However, the performance of the coherent detector is optimal only when the channel is perfectly known, which is practically never the case. In practice, the performance is limited by the quality of the channel estimate. This poses a problem for short bursts, where the number of training symbols must be kept low. When the channel is unknown, the optimal receiver uses available a priori stochastic information to marginalize the channel out of the likelihood function and determine the transmit sequence that maximizes it. Due to the lack of a priori information and the high complexity associated with marginalizing out a multi-tap channel, we derive a suboptimal detector, which replaces the unknown channel by the conditional maximum likelihood (ML) estimate for each hypothesis transmit sequence. From that, we derive a noncoherent soft-input soft-output (SISO) symbol-by-symbol detector. Using Monte-Carlo simulations to estimate the bit error rate (BER), we show the superiority of the proposed approach over the conventional one, especially for extremely short bursts in a time-variant environment.

Off-Chip-Controlled Droplet-on-Demand Method for Precise Sample Handling

Abstract: We present a simple, stable, and highly reproducible off-chip-controlled method for generating droplets-on-demand. To induce the droplet generation, externally pre-programmed positive pressure pulses are applied to the dispersed phase input while the continuous phase channel remains at constant input pressure. By controlling solely one fluid phase, the method allows for connecting multiple independent dispersed-phase channels to a single continuous channel. Experimental results show that the method allows for a droplet generation frequency of 33 Hz and a high reproducibility of droplets with standard deviations less than 5% of the mean value. Moreover, utilization of the off-chip-controlled method results in the simplicity in chip design and allows rapid (∼5 min) and cost-efficient (0.5 USD) prototyping of the device.

Twin-field quantum key distribution with fully discrete phase randomization.

Abstract: Twin-field (TF) quantum key distribution (QKD) can overcome fundamental secret-key-rate bounds on point-to-point QKD links, allowing us to reach longer distances than ever before. Since its introduction, several TF-QKD variants have been proposed, and some of them have already been implemented experimentally. Most of them assume that the users can emit weak coherent pulses with a continuous random phase. In practice, this assumption is often not satisfied, which could open up security loopholes in their implementations. To close this loophole, we propose and prove the security of a TF-QKD variant that relies exclusively on discrete phase randomisation. Remarkably, our results show that it can also provide higher secret-key rates than counterpart protocols that rely on continuous phase randomisation.

Absolute phase recovery based on two-wavelength fringes using a defocusing technique in fringe projection profilometry

Abstract: We present an approach that combines binary structured patterns generated by tripolar pulse width modulation technique with a two-wavelength phase-shifting unwrapping method to realize absolute phase recovery at the same defocusing level. Optimized binary fringe patterns projected by a small defocusing degree projector can significantly alleviate the phase error based on fringe projection profilometry, providing the binary patterns with a similar performance to standard sinusoidal fringe patterns. With this method, a set of images using only two-wavelength fringe patterns is captured by the camera, and it is not obliged to obtain the equivalent wavelengths and their corresponding phase maps. In consequence, the error propagation is avoided, which leads to improved accuracy in the continuous phase map retrieval. Furthermore, The effectiveness of the presented phase recovery technique that can be utilized to measure discontinuous and multiple objects was also verified by experiments. And it can reach high-precision and fast three-dimensional shape measurement.

Turbo-Estimation for CPM Over Frequency-Selective Fast Fading Channels

Abstract: The benefits of continuous phase modulation (CPM), namely high power and spectral efficiencies, are often overshadowed by the high complexity that comes along with the nonlinearity of the modulation format. We tackle the problem of detection of a quaternary CPM signal in a frequency-selective fast fading channel. In particular, we derive a joint detector-equalizer using the Laurent principal pulse approximation. To handle time-selectivity, we adopt the well-known turbo-estimation approach. However, it turns out that classical turbo-estimation cannot be directly applied, but has to be modified beforehand. With the help of Monte Carlo bit error rate (BER) simulations, we show that using the modified turbo-estimation approach, the receiver is able to track channel variations within a transmit burst under fast fading conditions. This allows for a larger payload-to-overhead ratio. Since joint detection-equalization is practically feasible only for channels with short memory, we also consider a suboptimal approach which decouples detection from equalization.

Low-Complexity LMMSE–SIC Turbo Receiver for Continuous Phase Modulation, Based on a Multiaccess–Multipath Analogy

Abstract: Low-complexity iterative reception of Continuous Phase Modulation (CPM) is addressed using Linear Minimum Mean-Square Error (LMMSE) filtering empowered by Soft Interference Cancellation (SIC). The transmitter emits a convolutionally encoded, true CPM signal with a constant envelope. The receiver exploits Laurent–Mengali–Morelli’s (LMM) decomposition to reduce the detection complexity, where the transmitted true CPM signal is approximated as a superposition of a small number of parallel Pulse Amplitude Modulated (PAM) and phase–encoded terms. Pulses and phase–encoded pseudo-symbols arising from the LMM decomposition are treated, respectively, as parallel Inter–Symbol Interference (ISI) channels and Multiple Access Interference (MAI) components. Hence the transmitted signal is regarded to inherently contain controlled ISI and MAI, which are equalized for at the receiver front-end using LMMSE–SIC filters. The receiver back-end comprises a serially concatenated turbo scheme encompassing a Soft Input–Soft Output (SISO) CPM detector and a SISO channel decoder. Simulations conducted on various CPM schemes show that the proposed receiver provides significant complexity reduction for a small performance penalty. Consequently, CPM waveforms with long pulses, which have traditionally been deemed infeasible due to the prohibitive complexity, can now be implemented employing the proposed receiver. Hence substantial spectral side-lobe compaction offered by long CPM pulses can be harnessed.

Codebook-based Phase Adjustment for IRS-aided Communication Via Time-Coding Modulation

Abstract: Intelligent reflecting surface (IRS) has been considered as a potential solution to enhance the performance of wireless communication systems. So far, the relevant works are mainly under the assumption of continuous phase shift, which is impractical due to the complexity and hardware cost. Finite discrete phase shifts, on the other hand, will cause significant performance deterioration. To solve this problem, we propose a codebook-based phase adjustment scheme via time-coding modulation with finite resolution. Specifically, by leveraging proper time-coding sequence, almost-full phase coverage with low-bit resolution can be achieved. Then, considering the scenario of IRS assisted wireless power transfer system, we propose a phase matching algorithm to achieve accurate energy-beam alignment. It is shown by simulation results that the performance of our proposed scheme is very close to that of the optimal one which is obtained assuming the continuous phase shift.

Continuous phase modulation with 1-bit quantization and oversampling using iterative detection and decoding

Abstract: A channel with continuous phase modulation and 1-bit ADC with oversampling is considered. Due to oversampling, higher-order modulations yield a higher achievable rate and this study presents methods to approach this with sophisticated channel coding. Iterative detection and decoding is considered, which exploits the soft information extracted from oversampled CPM sequences. Besides the strategy based on conventional channel coding techniques, a tailored bit mapping is proposed where two bits can be detected reliably at high SNR and only the third bit is affected by the uncertainties from the coarse quantization. With this, a convolutional code is only applied to the third bit. Our experiments with a turbo receiver show that the iterative detection and decoding is a promising approach for exploiting the additional information brought by oversampling. Moreover, it is shown that the proposed method based on the tailored bit mapping corresponds to a lower bit error rate in comparison with the case of conventional channel coding.

Performance vs. Spectral Properties For Single-Sideband Continuous Phase Modulation

Abstract: This study reports on a single side band spectrum directly generated by a continuous phase modulation (CPM) signal. This signal is analyzed in terms of modulation indices, pulse lengths, and pulse widths, all of which affect error probabilities, bandwidths, and SSB property. The error probability performance is based on an approximation of the minimum Euclidean distance. A numerical power spectral density calculation for this particular SSB modulation in terms of modulation index is presented. Reasonable tradeoffs in designing modulation schemes have been defined using multi-objective optimization to ensure sizable improvements in bit error rate (BER) and spectral efficiencies, without losing the property of being a SSB signal. Performance comparisons are made with known CPM schemes, e.g., Gaussian Minimum Shift Keying (GMSK) and Raised Cosine based CPM (RC).

Multi-Antenna Diversity Set for Transmission and Reception in Car-to-Car and Car-to-X Communication

Abstract: A microwave circuit for scan-phase antenna diversity for Car-to-Car and Car-to-X communication at 6 GHz is presented. Up to four independent antenna signals are selected and combined after a continuous phase alignment by 3-stage variable phase shifters. These phase shifters allow for continuous phase tuning between 0° and 360° with a nearly constant transmission factor within the complete frequency band of the IEEE 802.11p standard. Measurement results of the phase shift circuits are presented. The complete diversity circuit is evaluated by example of four monopole antennas which are mounted underneath the roof of a car. In a comparison with a single antenna, the improvement of signal-to-noise ratio can be shown. An avoidance of fades by more than 10 dB and an additional gain of around 5 dB is obtained for all azimuth directions around the car.

Multiband Multi-rate Narrowband Software Defined Radio waveform based on CPM

Abstract: Future Software Defined Radio (SDR) waveforms require increasing throughputs to support a wide variety of applications for military, commercial, and civilian applications. It requires a combination of spectral efficiency and better ber performance. To meet the heterogeneous requirement of future wireless networks, a multi-band multi-rate narrowband waveform for software-defined radio based on Continuous Phase Modulation (CPM) presented in this paper. The proposed waveform has ten modes of operation with the maximum achievable throughput of 176.2 kbps. Due to higher spectral efficiency provided by CPM, we show that the proposed waveform attains higher throughput by shifting towards multiple bandwidths and for the appropriate choice of alphabet size M, pulse length L and modulation index, h.In the end, the BER performance of proposed multiband modes for CPM is analyzed.

An Efficient Hardware Generator for Massive Non-Stationary Fading Channels

Abstract: In this paper, a discrete non-stationary multiple-input multiple output (MIMO) channel model based on the sum of linear frequency modulation (SoLFM) method is proposed. The new model is suitable for generating non-stationary fading with continuous phase and accurate Doppler frequency. In order to implement the proposed model with large-scale antennas by field-programmable gate array (FPGA) platform, an efficient coordinate rotation digital computer (CORDIC) method is proposed. By introducing a full parallel pipeline architecture, rotation factor state, and domain folding technique, the new generator can significantly reduce the hardware resource usage and meet the requirement of large-scale channel emulation. The measurement and analyze results show that the statistical properties, i.e., the probability density function (PDF) and autocorrelation function (ACF) of generated channels provide a good agreement to the theoretical ones.

Non-coherent multi-symbol detection of PR-CPM for deep space relay satellites with physical-layer network coding

Abstract: The demand for wireless spectrum and data transmission has increased dramatically with the rapid growth of deep-space exploration and communication. The satellite relay communication is an essential technique to solve the issues above. The method of combining Physical-layer Network Coding (PNC) with Continuous Phase Modulation (CPM) on relay satellites can improve communication efficiency and perform the collection and transmission of space data effectively. Partial-Response CPM (PR-CPM) signals possess excellent spectrum and power characteristics and are suitable for deep-space communications with limited bandwidth and massive data transmission. In this paper, a partial response non-coherent multi-symbol detection algorithm is proposed based on the Maximum-Likelihood principle. The proposed algorithm fully utilizes the memory properties of PR-CPM signals and makes decisions on specified symbols by observing a number of symbols each time. Simulation results indicate that the performance gain under the Bit Error Rate of 10−4 is about 2 dB when 5 symbols are inspected, compared with the case where the observation length is 3.

Simultaneous Wireless Information and Power Transfer by Continuous-Phase Modulation

Abstract: A new concept of simultaneous wireless information and power transfer (SWIPT) is proposed, based on multiplexing a continuous-phase modulated (CPM) information transfer signal and a multitone power transfer (PT) signal. The tones of the PT signal have frequencies falling into low-power sub-bands and/or spectral null frequencies of the CPM signal. Therefore, the interference of the PT signal to the CPM signal is minimized and, simultaneously, the CPM and PT signals can be separated by the corresponding complementary filters in the receiver. Numerical evaluations show that the proposed PT signal design practically entails a negligible loss of CPM detection performance.

A novel high-power waveguide phase shifter with continuous linear phase adjustment.

Abstract: A novel all-metal phase shifter with continuous linear phase adjustment for high-power microwave applications is presented and tested in this paper. The phase adjustment is achieved through the rotation of a phase reverser for a circularly polarized wave, and the output phase accomplishes a phase adjustment range of 360° by rotating the phase reverser for 180°. Due to the symmetrical characteristics, its position after rotating 180° is the same as the initial position, which can achieve continuous phase adjustment and avoid phase mutation. Simulation results indicate that the phase shifter achieves the transmission efficiency greater than 99.90% at a center frequency of 8.4 GHz, and the bandwidth of transmission efficiency greater than 98.00% is up to 50 MHz. Experiments are carried out and the measured results are in good agreement with simulation. To sum up, the power capacity of this phase shifter is estimated to be more than 80 MW under vacuum conditions (<10−3 Pa), and it can be applied to fast continuous high-power beam-steerable antenna arrays or mode conversion systems.

Finite-Length Performance Analysis of LDPC Coded Continuous Phase Modulation

Abstract: Serial concatenation of LDPC codes and continuous phase modulation (CPM) has recently gained significant attention due to its capacity-approaching performance, efficient detection as well as owing to its constant-envelope nature. Most of the previous contributions on LDPC coded CPM were devoted to the design of LDPC codes and their asymptotic performance analysis. However, there is a paucity of work on the finite-length performance estimation of LDPC coded CPM, primarily because existing performance estimation techniques cannot be readily applied to the LDPC coded CPM. To fill this gap, we conceive an analytical bit error probability estimation technique for finite-length LDPC coded CPM in the waterfall region. Numerical results are provided both for regular and irregular LDPC codes having different codeword lengths, demonstrating that the estimated performances are closely matched by the simulated ones.

Carrier Frequency Offset Estimation in Burst-Type CPM via the EM Algorithm

Abstract: In this work, the continuous phase modulation (CPM) with short block lengths (up to 128 symbols) is considered as a waveform, which is used e.g. in tactical networks. In order to deploy an optimal coherent detector, among other parameters as e.g. carrier phase or symbol timing, the carrier frequency has to be estimated. It is proposed to use the expectation maximization algorithm (EM) for a maximum likelihood estimation. It is pointed out why finding a suitable starting value, so that the EM does not converge to a local maximum of the likelihood function, is non-trivial in this case. Based on the insights given on the likelihood function in this case, an algorithm to tackle that issue and to ensure convergence to the global maximum is formulated. The algorithm’s performance is evaluated in terms of estimation error variance, including a comparison to the theoretical limit, and in terms of bit error rate, where it is compared to the perfectly synchronized receiver. The algorithm’s robustness against unknown carrier phase is investigated and its computational complexity is reflected.