Carrier Modulation Research Articles

Improved CPS-PWM Approach for Over-Modulation Operations of Hybrid Modular Multilevel Converter

The over-modulation capability of the hybrid modular multilevel converter (MMC), mixed by half-bridge and full-bridge submodules (SMs), has acquired widespread attention recently, which can significantly increase the design freedom of the hybrid MMC. When the hybrid MMC is applied in the medium-voltage occasions, an improved carrier phase shift pulsewidth modulation (CPS-PWM) approach is put forward in this article for its over-modulation operation under the nominal and variable dc conditions. It is featured with high flexibility, adjustability, and simple implementation. A new standard voltage is introduced to normalize the modulation wave, by which there is always a sufficient margin between the peaks of the normalized modulation wave and carrier waves under any modulation indexes. Also, it can perform well when the nominal dc voltage of the hybrid MMC is not the integer multiple of SM voltage. Moreover, the carrier wave arrangements are decoupled with the number of SMs, dc voltage, and ac voltage, so the variable dc operation of the hybrid MMC can be achieved without rearranging the carrier waves. Finally, the simulations and experiments are carried out to confirm the effectiveness of the proposed CPS-PWM approach for over-modulation operations under the steady-state and variable dc conditions.

A Three-Level Output Modulation Strategy for Conventional 3 × N Direct Matrix Converters

To utilize the full potential of the direct matrix converter (DMC) and improve the output waveform quality, a three-level output strategy for conventional 3N (N3) DMCs is presented, where three-level output voltages are achieved without any changes in the topology. In this developed strategy, the DMC is treated as a two-stage converter that consists of a fictitious rectifier and a neutral-point clamped (NPC) three-level inverter. By applying a phase-shifted carrier modulation strategy to the rectifier and a modified carrier-based double-signal pulse width modulation strategy to the NPC inverter, sinusoidal input and output, reduced switching losses, and controllable input power factors are achieved in conventional 3N DMCs. The developed three-level output strategy improves output waveform quality while sacrificing input performance to some extent. Finally, the effectiveness of the developed strategy is verified by both simulations and experimental results.

Precise Mathematical Model of PSCM Class-D Amplifiers

A mathematical analysis of four-level (three-phase) phase-shifted carrier modulation class-D amplifiers with analog feedback is proposed. The nonlinear difference equations are extracted and solved using the perturbation theorem. In this way, a closed-form function describes the low-frequency part of the output for an arbitrary input signal. The results are generalized for an arbitrary number of levels by analogy, well matched with the previous model of two-, three-, and the proposed four-level ones. The analytical results confirm that, apart from switching frequency, the multilevel class-D amplifiers converge to linear amplifiers as the number of output levels increases. An analytical equation expresses the harmonic distortion of practically interesting five-level amplifiers with bridge-tied load. The model is verified by system-level simulations and circuit-level implementation. In this way, a prototype fully differential five-level circuit is implemented on the printed circuit board to confirm the model.

Photonic Sub-Terahertz IM Links: Comparison Between Double and Single Carrier Modulation

Two different modulation schemes have been employed in photonic sub-THz systems to transmit intensity modulated signals: the dual-carrier (D-C) and single-carrier (S-C) schemes. Although it has been stated in the literature that D-C modulation performs better than S-C modulation, no demonstration of such claim has been provided so far. In this letter, we show that the superiority of one scheme or the other depends on the normalization factor that is used for comparison. Through mathematical analysis we show that, when 2-pulse amplitude modulation (2-PAM) signals are considered and the average photocurrent is taken as the normalization factor, the D-C scheme exhibits a 3-dB gain over the S-C scheme in the peak voltage of the recovered signal. However, the analysis also reveals that equal performance should be obtained when these schemes are compared in terms of transmitted sub-THz energy and that the S-C scheme should achieve better results when the comparison is made in terms of the output power of the lasers. We also run simulations to examine the impact of the non-linear transfer curve of a Mach-Zehnder modulator (MZM) on higher-order IM formats such as 4- and 8-PAM. The results of these simulations show that the penalty of the S-C scheme under photocurrent normalization progressively vanishes as the modulation order increases, and for 8-PAM signals, the S-C achieve better results than the D-C scheme. We attribute the deterioration of the D-C scheme with higher modulation orders to the signal-signal beat interference (SSBI).

Photonic generation and application of dual-band phase-coded LFM signals

A novel photonic method is proposed to generate dual-band phase encoding linearly frequency modulation (LFM) waveforms. In this scheme, two binary sequences are sent into one dual-polarization Mach–Zehnder modulator (DPol-MZM) to perform phase modulation with the optical carrier, while driving LFM signal is sent into another DPol-MZM to generate second and fourth-order optical sidebands. Then, the generated sidebands and the phase modulated optical carrier are combined together to perform optical to electrical conversion. As a result, bandwidth doubled and quadrupled phase coded LFM signals can be produced. The proposed scheme is verified by simulation, dual-band signals of 6 ~ 10 GHz & 12 ~ 20 GHz, 6 ~ 13 GHz & 12 ~ 26 GHz and 8 ~ 10 GHz & 16 ~ 20 GHz are obtained by using 3 ~ 5 GHz, 3 ~ 6.5 GHz, and 4 ~ 5 GHz driving LFM signals, respectively. Furthermore, the applications of the generated dual-band signals on both radar and communication are demonstrated. For radar detection, optical de-chirping operation for the dual-band signals can be simultaneously realized by using a DPol-MZM, on the other hand, the time bandwidth product of the radar waveform can be improved by phase encoding the LFM signal with M sequence. For wireless communication, each band LFM signal can be modulated with a binary sequence, and the two phase-coded LFM signals can be coherently demodulated in the optical domain. The proposed method features multi-functional operation, which can be potentially employed in radar-communication integrated systems.

Simulating Spectral Kurtosis Mitigation against Realistic Radio Frequency Interference Signals

We investigate the effectiveness of the statistical radio frequency interference (RFI) mitigation technique spectral kurtosis () in the face of simulated realistic RFI signals. estimates the kurtosis of a collection of M power values in a single channel and provides a detection metric that is able to discern between human-made RFI and incoherent astronomical signals of interest. We test the ability of to flag signals with various representative modulation types, data rates, duty cycles, and carrier frequencies. We flag with various accumulation lengths M and implement multiscale , which combines information from adjacent time-frequency bins to mitigate weaknesses in single-scale . We find that signals with significant sidelobe emission from high data rates are harder to flag, as well as signals with a 50% effective duty cycle and weak signal-to-noise ratios. Multiscale with at least one extra channel can detect both the center channel and sideband interference, flagging greater than 90% as long as the bin channel width is wider in frequency than the RFI.

Kendali Kecepatan Switched Reluctance Motor Berbasis FPGA

-- Renewable drive technology is developing in the current era, one of which is electric transportation. The Switched Reluctance Motor (SRM) was chosen for the transportation development because it has many advantages, including not using permanent magnets and simple construction in the form of an iron core in the rotor and stator windings. SRM works based on the reluctance phenomenon, namely, if the stator is energized, the stator will attract the nearby rotor, this is based on the tendency of the rotor poles to align with the stator excitation poles. SRM requires high speed switching control to operate and requires correct rotor position to operate. Maximum switching and good accuracy can use Field-Programmable Gate Array (FPGA) and rotary encoder as input for rotor position information. To use SRM in electric transport, it is necessary to adjust the speed with ease and precision. With the Pulse Width Modulation (PWM) technique, the size of the excitation depends on the size of the current, the size of the current is determined by the input voltage to the SRM. In this control, the PWM width can be changed by setting the carrier set and modulation set in the FPGA program. In this study, it is proposed to control the SRM speed by adjusting the PWM of the rotary encoder to produce the desired RPM. To support the achievement of this research, hardware testing was carried out in the laboratory. Keywords-- Duty cycle, FPGA, PWM, Reluctance, Switched Reluctance Motor.

Circulating Current Control of Phase-Shifted Carrier-Based Modular Multilevel Converter Fed by Fuel Cell Employing Fuzzy Logic Control Technique

The contribution of the modular multilevel converter (MMC) in integrating non-conventional energy sources into the grid is significant; the integration of fuel cells with distributed energy sources is especially prominent as they provide a constant voltage and current for constant load applications. Still, there is a high demand for a high-quality power conditioning unit since there is an occurrence of frequent power spikes. Further, the circulating current (CC) in phase legs is an inherent phenomenon of MMC that must be mitigated. Hence, this article proposed an MMC incorporating a fuzzy logic controller (FLC)-based technique to control the circulating currents. The fuzzy controller effectively reduced the harmonics of the CC in the dc-link system. In addition, phase-shifted carrier (PSC) modulation was employed for the MMC to improve the capacitor voltage balancing to maintain the constant input voltage. Moreover, a mathematical analysis of PSC modulation for MMC was performed to identify the PWM harmonic characteristics of the output voltage and the CC. The performance analysis of the proposed system was tested using the hardware in loop (HIL) simulation with the help of the real-time simulator OP-5700 to verify the feasibility.

Behavioral remodeling of perovskite BiFeO3 by Ag-doping strategies for enhanced and ppb level acetone sensing performance: An advanced enlightenment for selectivity and sensing mechanism

Improvement of the catalytic reactions on the sensing surface or modulation of charge carriers of the sensing material are the most favorable ways to enhance sensing performance for a chemi-resistive sensor. Incorporation of noble metals can enhance the sensing features of chemi-resistive type sensors by synergistic effect of chemical (catalytic effect) or electronic (tuning of charge carrier concentration) sensitization. In this view, the present study performs a behavioral remodeling of sol-gel synthesized BiFeO3 (BFO) chemi-resistive sensor by low-cost Ag-doping strategies to enhance its acetone sensing performance with removal of irreversibility. The Ag-doped BFO (Bi0.9Ag0.1FeO3) sensor can selectively detect acetone vapor (Rcross = RAcetone/RXylene: 17; RAcetone/RHexane: 08; RAcetone/RToluene: 05; RAcetone/RMethanol: 2.5; RAcetone/REthanol: 2.2) operating at 350°C. Ag-BFO sample shows an enhancement (1.8-fold) in response (R∼22) value with 5-fold faster response time (τres∼8s) for 50 ppm acetone exposure compared to pristine BFO (R∼12, τres∼45s). Excellent repeatability over 09 loop character with high degree of long-term stability for 300 days and ppb level detection (500 ppb) favorable to biomarker recognition for critical diseases confirms the commercial viability of Ag-doped BFO sample. The ion-dipole (highest interaction energy, Ei-d = -1.02 × 10−19 J for acetone)/dipole-dipole coupling, the ferroelectric nature of BiFeO3 and sensitization effect (by metallic Ag-phase) has paved the path for revealing the selectivity and sensing mechanism for the prepared prototype in an innovative way.

Dual-Sideband Constant-Envelope Frequency-Hopping Binary Offset Carrier Multiplexing Modulation for Satellite Navigation

Frequency-hopping binary offset carrier modulation improves the anti-interference performance and mitigates the autocorrelation function (ACF) ambiguity problem of binary offset carrier modulation. To save payload resources and make high-power amplifiers on satellites operate at the nonlinear saturation region, there is further demand for finding an efficient constant-envelope frequency-hopping binary offset carrier multiplexing technique to combine several signal components. Thus, we propose a dual-sideband constant-envelope multiplexing modulation, named asymmetric constant-envelope frequency-hopping binary offset carrier multiplexing (ACE-FHBOC), which is also a multicarrier constant-envelope multiplexing modulation. ACE-FHBOC provides higher design flexibility in the number of subcarrier frequencies than ACE-BOC while maintaining the same flexibility of signal design as ACE-BOC in the number of signal components and power ratio among components. We first establish the theory and give implementation methods of ACE-FHBOC. Then, we develop a software-defined receiver to simulate and analyze the performance for several specific ACE-FHBOC and ACE-BOC signals. The results show that the recommended ACE-FHBOC signals have lower ACF ambiguity, better anti-narrowband interference, and multipath performance than ACE-BOC under the same conditions. With these advantages, ACE-FHBOC is a promising solution for the signal design of new generation global navigation satellite systems.

Stimulation Rate and Voice Pitch Perception in Cochlear Implants.

The stimulation rate in cochlear implant (CI) sound coding, or the "carrier" rate in pulses per second (pps), is known to influence pitch perception, as well as loudness perception and sound quality. Our main objective was to investigate the effects of reduced carrier rate on the loudness and pitch of coded speech samples. We describe two experiments with 16 Nucleus® CI users, where we controlled modulation characteristics and carrier rate using Spectral and Temporal Enhanced Processing (STEP), a novel experimental multichannel sound coder. We used a fixed set of threshold and comfortable stimulation levels for each subject, obtained from clinical MAPs. In the first experiment, we determined equivalence for voice pitch ranking and voice gender categorization between the Advanced Combination Encoder (ACE), a widely used clinical strategy in Nucleus® recipients, and STEP for fundamental frequencies (F0) 120-250Hz. In the second experiment, loudness was determined as a function of the input amplitude of speech samples for carrier rates of 1000, 500, and 250 pps per channel. Then, using equally loud sound coder programs, we evaluated the effect of carrier rate on voice pitch perception. Although nearly all subjects could categorize voice gender significantly above chance, pitch ranking varied across subjects. Overall, carrier rate did not substantially affect voice pitch ranking or voice gender categorization: as long as the carrier rate was at least twice the fundamental frequency, or when stimulation pulses for the lowest, 250 pps carrier were aligned to F0 peaks. These results indicate that carrier rates as low as 250 pps per channel are sufficient to support functional voice pitch perception for those CI users sensitive to temporal pitch cues; at least when temporal modulations and pulse timings in the coder output are well controlled by novel strategies such as STEP.

Low complexity blind detection in OFDM systems with phase noise

Phase noise is one of the major impairments that degrade the performance of orthogonal frequency division multiplexing (OFDM) systems. When an OFDM system works at high-order modulation or high carrier frequency, phase noise's impairments cannot be ignored. Existing phase noise estimation algorithms either require a large number of pilots or have high computation complexity. In this paper, we propose a low complexity blind data detector based on the maximum a posteriori (MAP) criterion. With prior knowledge of slow time-varying property of phase noise, a simplified iterative phase noise estimation and data detection algorithm is developed. Compared to existing algorithms, the proposed algorithm does not require pilot data transmission, and achieves satisfactory performance with low computation complexity. Simulation results validate the effectiveness of proposed algorithm.

The Method of Evaluation of Radio Altimeter Methodological Error in Laboratory Environment.

The presented article is focused on the evaluation of aviation radio altimeter (ALT) methodological error in order to increase air traffic safety. It briefly explains the background of methodological error at the theoretical level and offers practical conclusions to understand the issue. A radio altimeter provides information on an aircraft or helicopter’s instantaneous (radar) altitude or UAV to the pilot and another assistance system, such as an autopilot or an anticollision system. The height measurement of the most common used ALTs is realized with an accuracy of from ±0.30 m to ±0.75 m. This error rate corresponds to and is caused by the radio altimeter’s methodological error (ΔH). The ALT operating parameters are defined by carrier frequency, modulation frequency, and frequency lift. The methodological error of ALT can be obtained in three ways—calculated on a theoretical level, simulated in a suitable simulation environment, or evaluated in laboratory conditions. The ambiguity of ALT methodological error measurement causes bias in its presentation. This often leads to an incorrect determination of measurement inaccuracy (too optimistic statement of error value). The article’s primary goal is to present a new method for determining the value of the methodological error and its effect on the resulting error of measurement of the radio altitude (radar altitude). It presents a new experimental laboratory method for measuring ΔH and the resulting accuracy of height measurement with a radio altimeter. Thanks to this method, it can be verified that the information obtained by measuring the height above the ground corresponds to the standard specified by the manufacturer.

Charge carrier modulation in graphene on ferroelectric single-crystal substrates

Charge carrier modulation of graphene using the ferroelectricity of a nearby dielectric can be useful for controlling the electronic properties of graphene. However, when graphene is located on ferroelectric oxides, their electrical coupling frequently shows abnormal behaviors, such as anti-hysteresis, in field-effect transistor operation. From the systematic examination of graphene on a ferroelectric oxide single-crystal [Pb(Mg1/3Nb2/3)O3]1-x–[PbTiO3]x (PMNPT) substrate, we observed that the ferroelectric modulation of graphene was significantly influenced by the ambipolar nature of graphene and ferroelectric-assisted charge trapping with carrier-type dependency. For graphene/hexagonal-BN on the PMNPT, the Coulomb interaction between charges in interfacial traps and ferroelectric polarization seems to decouple the graphene conductance from the polarization field and induce only the charge trap effect on device performance. Consequently, the asymmetric surface charge compensation of ferroelectric oxide by the ambipolar graphene channel determines the detailed coupling process between the charge carrier of graphene and ferroelectric polarization, resulting in direct ferroelectric coupling or indirect anti-hysteretic coupling.

Improved PGC demodulation algorithm to eliminate modulation depth and intensity disturbance.

In this paper, an improved phase generated carrier (PGC) demodulation algorithm based on frequency mixing and division difference is proposed. The effects of phase modulation depth variation and light intensity disturbance of the light source on the demodulated phase signal are investigated theoretically and experimentally. Compared to the traditional PGC differential-cross-multiplying (PGC-DCM) and PGC arctangent (PGC-Arctan) demodulation algorithms, the ameliorated demodulation algorithm eliminates the harmonic distortion of the demodulated signal by extracting the carrier modulation depth through frequency mixing. The demodulation error caused by the light intensity disturbance of the light source is suppressed by division difference. The stability of the demodulation system is improved. To verify the algorithm, a PGC demodulation system is built based on a Michelson interferometer. The experimental results show that when the frequency and amplitude of the sensed signal are set to 1 kHz and 0.4 rad, respectively, the signal-to-noise ratio with the proposed algorithm achieves a gain of 35.66 dB over the PGC-Arctan algorithm and 26.26 dB over the PGC-DCM algorithm.

Simulative Study to Reduce DC-Link Capacitor of Drive Train for Electric Vehicles

E-mobility is an emerging means of transportation, mainly due to the environmental impact of petroleum-based fuel vehicles and oil prices’ peak. However, electric vehicles face several challenges by the nature of technology. Consequently, electric vehicles have a limited travel range and are extremely heavy. In this research, an investigation is carried out on different measures to reduce the DC-link capacitor size in the drive train of an electric vehicle. The investigation is based on software simulations. The DC-link capacitor must be dimensioned with regards to relevant points of operation, which are defined by the rotation speed and torque of the motor as well as the available DC-link voltage. This also includes the field-oriented control (FOC). In order to optimally operate a three-phase inverter in the electric drive train, a suitable type and sizing of the capacitor was studied based on mathematical equations and simulations. Two measures were examined in this study: firstly, an auxiliary passive notch filter introduced in the electric drive train circuit is explored. Based on this measure, an advanced modulation scheme exploiting the control of individual currents within segmented windings of the PMSM is investigated in detail. It was seen that saw-tooth carrier modulation used in the parallel three-phase inverter is found to reduce DC-link capacitor size in the electric drive train circuit by 70%.

Coherent acoustic modulation and defect-sensitive ultrafast carrier dynamics of Pr0.5Ca0.5MnO3 thin films investigated by time-resolved terahertz spectroscopy

In transition metal oxides, the potential of competing energetics of interacting fundamental entities is best displayed in perovskite manganites via the formation of a variety of exotic phases; however, there are limitations of extreme sensitivity to extrinsic and intrinsic defects and the slightest of structural modulations. Here, we report the effect of oxygen annealing and epitaxial strain on the ultrafast carrier excitation and relaxation mechanism in charge-ordered (CO) manganite Pr0.5Ca0.5MnO3 (PCMO) thin films of 60 and 150 nm thicknesses, both as-grown and oxygen annealed, as investigated by optical pump–terahertz (THz) probe measurements. Transient THz transmittance is negative for both films. Bi-exponential relaxation behavior accompanied with acoustic modulations was observed that varies along with strain and oxygen content of the films. As fitted by the sum of exponentials, the fast relaxation time constant is found to be fluence independent, while the slow relaxation time constant decreases with pump fluence for both films and is less for the annealed film suggesting that the relaxation in PCMO strongly depends on strain and oxygen content. This study on non-equilibrium carrier dynamics depicting the sensitivity of defects and subtle structural modifications is unprecedented in demonstrating the ultrafast control of CO manganites.

Adaptive Single Carrier Modulation scheme based MLI supported TDVC for Voltage Quality enhancement

Abstract In this article, An Adaptive Single Carrier Modulation (ASCM) scheme based Multilevel Inverter (MLI) is proposed for the Transformerless Dynamic Voltage Compensator (ASCM-MLITDVC) to enhance the load Voltage Quality (VQ). The enhancement of VQ includes voltage sag, swell, unbalance and reducing Total Harmonic Distortion (THD). The Pulse Generation Unit (PGU) require more Carrier Waves (CW) for higher levels of MLI with respect to the number of switches used. This made the PGU complex, hence a carrier wave modulation scheme is proposed which can use it for n number of levels. The Position of CW is altered automatically with respect to the amplitude of Reference Staircase Waveform (RSW). The RSW is created by utilizing the Half Height Method and optimized NLM scheme which makes the least possible output THD is achieved. This scheme is implemented utilizing a real-time simulator OP4500. The results are obtained by conducting Power Hardware in Loop (P-HIL) test method to prove ASCM-MLITDVC can enhance load VQ with reduced THD.

Single Sideband Suppressed Carrier Modulation With Spatiotemporal Metasurfaces at Near-Infrared Spectral Regime

Single sideband suppressed carrier (SSB-SC) modulation enables high efficiency and dispersion-tolerant shifting of light that is of great interest for many optical systems and applications. Herein, the design procedure of a spatiotemporal reflective metasurface is proposed to realize SSB-SC modulation in near-infrared spectral regime. The metasurface consists of a periodic array of plasmonic nanostrips integrated with indium-tin-oxide (ITO) in metal-insulator-metal configuration, wherein two sets of time-varying biasing signals are independently applied to the metasurface for modulating the permittivity of ITO in space and time. The spatiotemporal metasurface features a sawtooth phase profile with linear span over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\pi$</tex-math></inline-formula> and a constant amplitude in time domain, that can be obtained by judicious adjustment of the biasing waveforms. It is established that such spatiotemporal metasurface allows for spurious-free frequency conversion by transforming the incident signal into the first-order up-modulated sideband and suppressing all the undesired mixing products. The normalized conversion efficiency of more than 99% is achieved for the metasurface, while the peak levels of the largest undesired mixing product and the fundamental frequency are reduced down to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-39$</tex-math></inline-formula> dB and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-44$</tex-math></inline-formula> dB, respectively. The proposed spatiotemporal metasurface is exploited for multi-channel and multi-beam scanning via pixelated control over the modulation phase delays assigned to the constituent elements of the spatially-interleaved sub-arrays, rendering a shared-aperture metasurface in space-time. In this case, the crosstalk between the channels with identical operating frequencies is substantially reduced. In addition, spatiotemporal redirection of light based on frequency gradient metasurface is demonstrated, which enables ultrafast, all-angle, and continuous beam-scanning as progressing in time.

Spectral Efficiency Evaluation of an NR-Based 5G Terrestrial Broadcast System for Fixed Reception

LTE-based 5G terrestrial broadcasting, standardized in 3GPP Release 16, allows broadcasters to reach cellular devices. In this paper, toward the development of a future terrestrial broadcast system in Release 18 or later called 5G-Advanced, a specification for New Radio (NR) based 5G terrestrial broadcasting is presented for a 6 MHz-channel raster, which is used in current digital terrestrial television broadcasting. The transmission performance is evaluated in physical layer simulations. In particular, the spectral efficiency is evaluated and compared with a second-generation DTTB system at a required carrier-to-noise ratio (CNR) of 20 dB in a fixed-reception scenario with a rooftop receiving antenna. The evaluation in an additive white Gaussian noise channel indicates that the spectral efficiency of NR-based 5G terrestrial broadcasting can be improved by 0.83 (bps/Hz) by enhancing the code length of low density parity check code, the carrier modulation scheme, guard band ratio, and cyclic prefix ratio from what available so far in Release 16. Furthermore, when frequency interleaving is incorporated, the spectral efficiency is increased by 0.75 (bps/Hz) in a short echo channel with a desired-to-undesired signal power ratio of 0 dB. The introduction of time interleaving increases spectral efficiency by 0.97 (bps/Hz) in an impulsive interference channel with a carrier-to-interference signal power ratio of -20 dB. For each interleaving, the increase in spectral efficiency tends to be higher as the required CNR increases.