Continuous Phase Frequency Shift Keying Research Articles

Performance of Hybrid Concatenated Trellis Codes CPFSK with Iterative Decoding over Fading Channels

Concatenation is a method of building long codes out of shorter ones, it attempts to meet the problem of decoding complexity by breaking the required computation into manageable segments. Concatenated Continuous Phase Frequency Shift Keying (CPFSK) facilitates powerful error correction. CPFSK also has the advantage of being bandwidth efficient and compatible with non-linear amplifiers. Bandwidth efficient concatenated coded modulation schemes were designed for communication over Additive White Gaussian noise (AWGN), and Rayleigh fading channels. An analytical bounds on the performance of serial concatenated convolutional codes (SCCC), and parallel concatenated convolutionalcodes (PCCC), were derived as a base of comparison with the third category known as hybrid concatenated trellis codes scheme (HCTC). An upper bound to the average maximum-likelihood bit error probability of the three schemes were obtained. Design rules for the parallel, outer, and inner codes that maximize the interleaver's gain were discussed. Finally, a low complexity iterative decoding algorithm that yields a better performance is proposed.

Iterative Multisymbol Noncoherent Reception of Coded CPFSK

A system involving the multisymbol noncoherent reception of coded continuous-phase frequency-shift keying is developed, optimized, and analyzed. Unlike coherent systems, the modulation index of the waveform does not need to be rational with a small denominator, and the oscillator only needs to be stable for the duration of a small block of symbols. The achievable performance over AWGN and Rayleigh block-fading channels is determined by computing the average mutual information, which is the capacity of a channel using the given modulation format and receiver architecture under the constraint of uniformly distributed input symbols. The code rate and modulation index are jointly optimized with respect to average mutual information under a bandwidth constraint. For binary and quaternary signaling, the information-theoretic results are corroborated by bit-error-rate curves generated using a standardized turbo code in conjunction with iterative demodulation and decoding. It is shown that, while more robust than a system with coherent reception, the proposed system offers superior energy efficiency compared with conventional single-symbol noncoherent reception.

Space-time block codes for noncoherent CPFSK

In this paper the problem of space-time block coding for multiple-input multiple-output communication systems employing continuous phase frequency shift keying and one-shot noncoherent detection is investigated. First, the detection problem is analysed in a maximum likelihood perspective; then, design criteria for optimal space-time codes are proposed and some error bounds are derived. Finally, some numerical results are illustrated for a couple of novel space-time block codes designed on the basis of the above mentioned criteria. Such results evidence that the use of the proposed schemes can entail a limited energy loss respect to other solutions available in the technical literature for coherent systems, with the relevant advantage, however, of a simple detection algorithm.

Line coding to enhance the performance of 10-Gb/s CPFSK-ASK directly modulated signals

The major drawback of frequency modulation (FM)-based directly modulated laser (DML) is its non-uniform FM response at low frequency range which gives rise to a severe pattern-dependent performance degradation. In this paper, we investigate the use of line coding to deplete the low-frequency spectral contents of the signal and thus to alleviate the degradation. We examine various line codes (8B/10B, 5B/6B, 7B/8B, 9B/10B, and 64B/66B) with continuous-phase frequency-shift keying/ amplitude-shift keying (CPFSK/ASK) signals generated using a DML and a delay interferometer. Experimental demonstrations are performed with a long pseudorandom bit sequence length of 2(20)-1 and the bandwidth expansion by each code is taken into consideration. The results show that among the five codes we tested, 9B/10B code outperforms the other codes in terms of receiver sensitivity an dispersion tolerance. We demonstrate successful transmission of 10-Gb/s CPFSK-ASK signals over 65-km standard single-mode fiber with a bandwidth expansion of only 11.1%.

Accurate Signal-to-Noise Analysis of Derivative and Quadrature Differential FM Discriminators Based on Multi-Sinusoidal AWGN Representation

The noise performances under AWGN channel of the IF-derivative and the quadrature differential FM discriminators, which are widely utilized in modern low power wireless radios, are analyzed and compared. The analysis relies upon the time-domain multi-sinusoidal representation of the noise that facilitates accurate and closed-form analytical SNR characteristics. Derivation of the SNR equations is detailed and discussion based on the analysis results is given to provide insights into the discriminators' performance limitation where it is demonstrated that the differential scheme is considerably more advantageous. Simulated SNR characteristics of practical continuous-phase frequency shift keying (CPFSK) systems using both the FM discriminators are presented as analysis verification.

Uncertainty aspects of coherent and direct detection of amplitude shift keying and continuous phase frequency shift keying in optical fiber transmission

The impulse and step responses as well as the pulse responses of a quadratic phase medium, the single-mode optical fiber, are presented. Analytical expressions of the fiber impulse and step responses are obtained, indicating the change of the phase of the lightwave carrier. Both coherent and incoherent detection schemes under the amplitude shift keying and continuous phase frequency shift keying (CPFSK) incorporating the maximum likelihood sequence estimation are examined with respect to the uncertainty depending on the number of bits of the sequence. The detection uncertainty shows that the coherent detection offers a high degree of discrimination as compared to its incoherent counterpart, especially for the case of CPFSK. The frequency discrimination detection of the CP FSK is correlated with the bandwidth-bit period product, the product between filter bandwidth and the bit period. Resilience to dispersion of ±9520 ps/nm can be achieved due to this minute uncertainty of this detection scheme.

High Rate CPFSK Space-Time Trellis Codes

Space-time trellis coding is an established diversity technique that reduces the effects of multipath fading over wireless communication channels. Here, we consider high rate space-time trellis codes (STTC) with continuous phase frequency shift keying (CPFSK). We present optimized rate-2/3 STTC implemented with 3 transmit antennas. These codes provide system throughputs of 4 and 6 bits per channel use with 4-ary and 8-ary CPFSK respectively. Simulated error rate performance of the optimized codes with receive diversity is presented. We show that although the schemes do not achieve full transmit diversity, they provide excellent coding gains compared to full rank schemes that have equivalent throughput, but higher order modulations and greater complexity.

Coherent continuous-phase frequency-shift keying: Parameter optimization and code design

The symmetric information rate of a modulation-constrained transmission system is the information-theoretic limit on performance under the assumption that the inputs are independent and uniformly distributed. The symmetric information rate for continuous-phase frequency-shift keying (CPFSK) over an AWGN channel may be estimated by considering the system to be a finite-state Markov channel and executing a BCJR-like algorithm. In this paper, the estimated symmetric information rate is used along with the exact expression for the 99% power bandwidth to determine the information-theoretic tradeoff between energy and spectral efficiency for CPFSK modulation. Using this tradeoff, the code rate and modulation index are jointly optimized for a particular spectral efficiency and alphabet size. Codes are then designed for the optimized system. The codes are comprised of variable nodes (which represent irregular repetition codes), check nodes (which represent single parity-check codes), and an interleaver connecting the variable and check nodes. The degree distributions of the code are optimized from the system's EXIT chart by using linear programming. Additional details of the code design, including labeling and interleaver design, are also discussed. Simulation results show that the optimized coded systems achieve bit error rates within 0.4 dB of the information-theoretic limits at BER = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> .

Mitigation of Polarization Mode Dispersion in an Optical Heterodyne CPFSK Transmission System using Line Codes

A theoretical analysis for evaluating the performance of line codes in the polarization mode dispersion (PMD) mitigation of an optical heterodyne continuous phase frequency shift keying (CPFSK) transmission system with delay demodulation receiver is presented. It accounts for the combined effects of signal phase distortion due to PMD and chromatic dispersion in a single mode fiber. The analysis is carried out for three different linecoding schemes, i. e., alternate mark inversion, order-1 and delay modulation coding, to investigate the efficacy of the linecoding in counteracting the effect of PMD in CPFSK optical transmission system. Performance results are evaluated in terms of average bit error rate (BER) with line codes and compared with NRZ-CPFSK system at a bit rate of 10 Gbit/s considering Maxwellian probability distribution for the mean differential group delay (DGD) due to PMD. The results show that the penalty improvement of line coded systems is within 0.5 dB to 1.95 dB with respect to NRZ data for mean DGD 30 ps and at a BER of 10 -9 . .

Improved mapping policy for reducing error coefficient in CPFSK signals

An improved mapping policy is introduced that alternates between standard and inverted bit mapping functions at selected phase states to reduce the error coefficient of continuous phase frequency shift keying (CPFSK) signals. The proposed policy can be applied to many different forms of CPFSK signals. It is demonstrated that the mapping policy can significantly improve performance, particularly at lower to moderate SNR values.

Multilevel turbo coded–continuous phase frequency shift keying (MLTC–CPFSK)

In this paper, we introduce a Turbo coded modulation scheme, called multilevel turbo coded–continuous phase frequency shift keying (MLTC–CPFSK). The underlying basis of multilevel coding is to partition a signal set into several levels and to encode separately each level through the respective layer of the encoder. In MLTC–CPFSK, to provide phase continuity of the signals, turbo encoder and continuous phase encoder (CPE) are serially concatenated at the last level, while all other levels consist of only a turbo encoder. Therefore, the proposed system contains multiple turbo encoder/decoder blocks in its architecture. The parallel input data sequences are encoded by our multilevel scheme and mapped to CPFSK signals. Then, for the purpose of performance analysis, these modulated signals are passed through AWGN and fading channels. At the receiver side, the input sequence of the first level is estimated by the first turbo decoder block. Subsequently, the other input sequences of other levels are computed using the estimated input bit streams of the respective previous levels. Simulation results are drawn for 4-ary CPFSK two level and 8-ary CPFSK three level turbo codes over AWGN, Rician, and Rayleigh channels for three iterations while frame sizes are chosen as 100 and 1024. It is concluded that satisfactory performance is achieved in MLTC–CPFSK systems for all SNR values in various fading environments.

Constellation labeling maps for low error floors

A constellation labeling map is the assignment of a bit pattern to each symbol in a signal-set constellation. In a system with iterative decoding and demodulation, the error floor of the bit error rate is highly dependent on the labeling map. A simple class of labeling maps that significantly lower the error floors is presented. Examples show the applications of the proposed mapping to multiple phase-shift keying (MPSK), quadrature amplitude modulation (QAM), and continuous-phase frequency-shift keying (CPFSK). Simulation results indicate that the proposed labeling maps are comparable to or better than other labeling maps in providing a low error floor. A major advantage of the proposed labeling maps is that they are easily generated even when the alphabet size is large.

Performance of line codes in optical direct detection continuous phase frequency shift keying transmission system impaired by polarization mode dispersion

Small deviations from perfect circular symmetry in the core region of single mode fiber (SMF) cause optical pulses to become broadened as they propagate. This phenomenon is referred to as polarization mode dispersion (PMD), which leads to intersymbol interference and becomes a major impediment for the high speed long-haul fiber-optic links. We present here the theoretical complement for evaluating the performance of a line-coded continuous phase frequency shift keying (CPFSK) optical transmission system with a direct detection receiver. The analysis is carried out for two different line-coding schemes, i.e. alternate mark inversion (AMI) and order-1 coding, to investigate the effectiveness of the line coding in counteracting the effect of PMD in a CPFSK direct detection transmission system in the presence of group velocity dispersion (GVD) and receiver noise in a single mode fiber. The average bit error rate (BER) performances are evaluated without and compared to that of line codes at a bit rate of 10 Gb s−1 considering Maxwellian distribution for the mean differential group delay (DGD). We found that the amount of power penalty improvement of line-coded systems is within 0.65 to 2.25 dB with respect to NRZ data at a BER of 10−9.

Robust Frequency Hopping for Interference and Fading Channels

A robust frequency-hopping system with noncoherent detection, iterative turbo decoding and demodulation, and channel estimation is presented. The data modulation is the spectrally compact nonorthogonal continuous-phase frequency-shift keying, which strengthens the frequency-hopping system against multiple-access interference and multitone jamming. An analysis based on information theory provides the optimal values of the modulation index when there is a bandwidth constraint. The channel estimator, which is derived by applying the expectation- maximization algorithm, accommodates both frequency-selective fading and interference. Simulation experiments demonstrate the excellent system performance against both partial-band and multiple-access interference.

Cooperative Relaying with CPFSK and Distributed Space-Time Trellis Codes

Cooperative relaying allows single antenna users to achieve diversity and coding gains by utilizing nearby users' transmitting capabilities. We consider a relay system employing constant envelope continuous phase frequency shift keying. Distributed space-time trellis codes are implemented with a novel multiple relay protocol.

Performance of Systematic Distance-4 Binary Linear Block Codes with Continuous Phase Frequency Shift Keying over MIMO Systems

Codes with full information rate (optimal), for example Hamming codes, provide the highest possible code rate R (R = k/n where k and n are the code dimension and length respectively) and it is an important property for a block code. Recently, the Systematic Distance-4 (SD-4) codes are proposed that allows generating all the optimal Hamming distance-4 binary linear block codes. Continuous Phase Frequency Shift Keying (CPFSK) provides low spectral occupancy and is suitable for power and bandwidth-limited channels such as satellite communication channels. MIMO technique is essential for modern wireless communication systems. In this article, we evaluated the error performances of SD-4 codes utilizing CPFSK modulation over MIMO Rician and Rayleigh channels via computer simulations and obtained outstanding results regarding coding gain.

Woven Coded CPFSK With Hierarchical Code Structure

We introduce hierarchical woven coded continuous phase frequency-shift keying (hierarchical WCCPFSK) as the serial concatenation of different outer convolutional codes and inner CPFSK. We compare it to WCCPFSK with identical outer convolutional codes. With the proposed code combinations, hierarchical WCCPFSK achieves superior decoding capability. Simulations show that it performs better at medium SNRs.

Performance limitations of an optical heterodyne continuous-phase frequency-shift keying transmission system affected by polarization mode dispersion in a single-mode fiber

A theoretical analysis is developed to evaluate the conditional and average bit error rate (BER) performance degradation of an optical heterodyne continuous-phase frequency-shift keying (CPFSK) system caused by signal phase distortion due to polarization mode dispersion (PMD) in a single-mode fiber. The probability density function (pdf) of the random phase fluctuation due to PMD at the output of the receiver is determined analytically. The average BER performance results are evaluated at a bit rate of 10 Gb/s, considering Maxwellian distribution for the differential group delay (DGD) based on the pdf of the random phase fluctuation. The results show that the performance of the optical heterodyne CPFSK direct detection system suffers power penalties of 0.75, 1.95, 4.00, and 9.15 dB, corresponding to mean DGD of 20, 30, 40, and 60 ps, respectively, at a average BER of 10 -9 operating at 10 Gb/s. Furthermore, at increased values of the mean DGD, there occur BER floors above 10 -9 , which cannot be lowered by further increasing the signal power. It is noticed that BER floors occur at about 2×10 -8 , 10 -5 , and 2.5×10 -4 , corresponding to mean DGD of 60, 70, and 80 ps, respectively, at 10 Gb/s and a modulation index of 0.50. The effect of PMD is found to be more detrimental at higher modulation indexes and bit rates.

Performance of low density parity check coded continuous phase frequency shift keying (LDPCC-CPFSK) over fading channels

In this paper, in order to improve bit error performance, bandwidth efficiency and reduction of complexity compared to related schemes such as turbo codes, we combine low density parity check (LDPC...

Space Time Codes for CPFSK With Arbitrary Number of Receive Antennas

In this letter, space time (ST) trellis codes are developed for systems with an arbitrary number of receiver antennas in quasi-static fading channels applying M-ary continuous phase frequency shift keying (CPFSK) modulation with M = 4 and 8 for h = 1/M. The maximizing minimum squared Euclidean distance criterion (MMSEDC) is applied in the code search algorithm when obtaining the ST codes. The results show that a significant performance gain can be obtained by using the ST codes from the MMSEDC code search algorithm compared to the ST codes obtained in X. Zhang and M.P. Fits (2003) for CPFSK modulation systems