Coded continuous-phase FSK: Information theoretic limits and receiver design.

An optical continuous phase FSK modulation scheme with an arbitrary modulation index over long-haul transmission fiber link

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> .

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) codes and continuous phase frequency shift keying (CPFSK) modulation and introduce a new scheme, called ‘low density parity check coded‐continuous phase frequency shift keying (LDPCC‐CPFSK)’. Since LDPC codes have very large Euclidean distance and use iterative decoding algorithms, they have high error correcting capacity and have very close performances to Shannon limit. In all communication systems, phase discontinuities of modulated signals result extra bandwidth requirements. Continuous phase modulation (CPM) is a powerful solution for this problem. Beside CPM provides good bandwidth efficiency; it also improves bit error performance with its memory unit. In our proposed scheme, LDPC and CPFSK, which is a special type of CPM, are considered together to improve both error performance and bandwidth efficiencies. We also obtain error performance curves of LDPCC‐CPFSK via computer simulations for both regular and irregular LDPC code. Simulation results are drawn for 4‐ary CPFSK, 8‐ary CPFSK and 16‐ary CPFSK over AWGN, Rician and Rayleigh fading channels for maximum 100 iterations, while the frame size is chosen as 504. Copyright © 2006 John Wiley &amp; Sons, Ltd.

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

The required high-frequency laser diode (LD) FM responses for a continuous phase frequency shift keying (CPFSK) heterodyne delay modulation system were investigated. The degradations due to insufficient high-frequency FM response are evaluated, considering the FSK waveform distortion, which gives undesired phase error at the demodulation circuit. From the phase error, bit error rate (BER) degradation is calculated. The calculated results indicate that the delay-time adjustment for the demodulation circuit is effective in minimizing the power penalty. The theoretical evaluation, including the demodulation circuit optimization, explains the experimental results fairly well. Using the same evaluation procedure, required high-frequency LD FM responses are derived. The results, together with the required low-frequency FM responses, give guidelines for transmitter LD selection for coherent CPFSK systems. >

A combined source/channel coding and modulation technique is developed for the transmission of memoryless sources over an AWGN channel. Combined source/channel coding is implemented using the concepts of trellis coded quantization (TCQ) in conjunction with an Ungerboeck code defined for a continuous phase frequency shift keying (CPFSK) signaling scheme. The Viterbi algorithm is employed by the source encoder to find a minimum mean-square-error (MSE) path through the source code trellis. The resultant minimum distortion sequence is mapped to an appropriate set of CPFSK symbols for transmission. A mapping is pragmatically developed to simultaneously preserve the original branch labelings of both the source and channel code trellises. Source symbol recovery is performed by maximum likelihood sequence estimation. The total distortion is experimentally determined over a range of channel signal-to-noise ratios. Furthermore, it is demonstrated that the use of a CPFSK signaling scheme avoids the production of spectral line components in the transmitted waveform spectrum that are usually associated with joint source/channel coding schemes.

Designing communication techniques for non-Gaussian impulsive noise has been attracting considerable attention from the research community. In this paper, we focus on the continuous phase frequency shift keying (CPFSK) signal detection for both white and bursty impulsive noises. The independent and identically distributed (i.i.d.) symmetric $\alpha $ -stable ( ${S\alpha S}$ ) process and the stationary $m$ -order $\alpha $ -sub-Gaussian [ ${{\alpha \mathit {SG}}}(m)$ ] model are adopted to model the white and the bursty impulsive noises, respectively. At first, both coherent and non-coherent detections of CPFSK signals are investigated for white ${S\alpha S}$ noises. For the coherent sequence detection, the Viterbi algorithm is used by replacing the maximum likelihood (ML) measure with the myriad measure. In non-coherent detection, a multiple symbol aided scheme is proposed, for which both the ML and myriad measures are considered. Subsequently, the detection of CPFSK signals is further addressed in ${{\alpha \mathit {SG}}}(m)$ noise. For coherent detection, based on the Markov property of ${{\alpha \mathit {SG}}}(m)$ noise, we first express the likelihood function as the sum of branch measures, and the myriad measure is also provided to replace the ML measure. The multiple symbol-aided methods are also applied to the non-coherent detection in ${{\alpha \mathit {SG}}}(m)$ noise, and the corresponding ML and myriad measure-based algorithms are given as well. For the sake of comparison, the Gaussian measure is also considered. The simulation results show that the performance of the myriad measure-based algorithms can closely approach that of the ML measure-based algorithms for both coherent and non-coherent detection, and is much better than that of the Gaussian measure-based algorithms.

A continuous-phase frequency-shift-keying (CPFSK) signaling technique is suggested that combines convolutional encoding and multi-h signaling. In contrast to regular multi-h signaling, this technique changes the modulation index in a preselected pattern in order to maximize the minimum Euclidean distance. A rate-1/2 convolutional encoder along with a 2-h quaternary CPFSK modulator which uses two fixed modulation indexes is considered. Minimum Euclidean distances are calculated corresponding to the best encoder/mapper combinations for different modulation index patterns at attractive pairs of modulation indexes. Numerical results obtained for encoder memory lengths of one and two are used to illustrate that the minimum Euclidean distance of coded CPFSK signals can be significantly increased by combining with multi-h signaling. Modulation index patterns which perform significantly better than regular multi-h signals are determined. An error event analysis over the additive-white-Gaussian noise channel is carried out to investigate the actual error rate performance and to verify the theoretical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Aiming at the application of full-duplex (FD) method in phased array for different kinds of waveforms for different functions, based on the modeling of coupling path characteristics for different spatial links using adaptive system identification method, five representative waveforms, including linear frequency modulation (LFM), pseudorandom frequency shift keying (FSK), continuous phase frequency shift keying (CPFSK), dense repeated jamming (DRJ), and wide-band noise (WBN), are designed and applied in full-duplex mode to validate their self-interference cancellation (SIC) performance in practical experiments. From the experiments' results, where the best SIC is about 38dB for LFM, while the worst SIC is just 5∼7dB for DRJ and WBN, we can draw the conclusion that different kinds of waveforms used for different functions can bring on obviously inconsistent SIC, even in the same frequency bandwidth of 300MHz. Thus it can be seen that waveform characteristics used in multifunction phased array play an important role for self-interference cancellation of simultaneous transmit and receive (STAR).

The performance of a coherent optical M-ary continuous-phase frequency-shift-keying (CPFSK) receiver using limiter-discriminator (L-D) detection is investigated. It is shown that L-D detection of CPFSK optical signals offers the best performance for a large normalized IF beat spectral linewidth, Delta nu T. When the modulation index is unity, the receiver is immune to laser phase noise and can produce (M/4) exp (-SNR) symbol error probability, which may be considered as the upper bound if the optimal modulation index is used (SNR is the signal-to-noise ratio per symbol). Optimum modulation indexes are 0.8 and 1 at Delta nu T=1% and Delta nu T=2%, respectively, for M=4, 8, and 16.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In digital IQ modulators generating continuous phase frequency shift keying (CPFSK) signals, departures from flat-magnitude, linear phase in the pass bands of signal reconstruction filters in the I and Q channels cause ripple in the output signal envelope. Amplitude modulation (AM) in the signal envelope function produces undesirable sidelobes in the FSK signal spectrum when the signal passes through nonlinear elements in the transmission path. A structure is developed for digitally pre-compensating for the magnitude and phase characteristics of signal reconstruction filters. Optimum digital pre-compensation filters are found using least squares (LS) techniques and we propose a method by which the optimum pre-compensation filters can be estimated using test input signals. This method can be used as part of an automatic compensation process.

We consider digital signal processor (DSP) based inphase/quadrature (IQ) modulators generating continuous phase frequency shift keying (CPFSK) signals. Departures from a flat-magnitude, linear phase frequency response in the pass bands of signal reconstruction filters in the I and Q channels cause ripple in the modulator output signal envelope. Amplitude modulation (AM) in the signal envelope function produces undesirable sidelobes in the FSK signal spectrum when the signal passes through nonlinear elements in the transmission path. A structure was developed for digitally compensating for the magnitude and phase characteristics of the signal reconstruction filters by Tuthill and Cantoni (see IEEE Trans. Comm., vol.47, no.10, p.1466-69, 1999) and by Tuthill, (see Australian PhD Dissertation, Telecommunications Research Institute, Curtin University of Technology, 2000). However, this approach results in finite impulse response (FIR) filters that have a large number of coefficients. Implementation of these filters on a DSP is computationally demanding. In this paper we have generalised the technique of Tuthill and Cantoni to include infinite impulse response (IIR) filters, which have fewer coefficients. We then investigate whether a reduction in the number of filter coefficients leads to a reduction in the computational load in implementation.

This paper consists of an overview of recent results on combined constant amplitude continuous phase modulation (CPM) and convolutional channel codes. We also compare the best coded CPM systems to trellis-coded amplitude/phase modulations. The ideal additive white Gaussian channel and systems with perfect carrier phase and symbol time synchronization are considered in this paper. Signals which have a constant amplitude at all times are sometimes needed when highly nonlinear amplifiers are used. Memory is introduced into the constant amplitude signals by means of continuous phase at all times, controlled intersymbol interference to further smooth the phase changes and combinations of CPM and convolutional codes. Analytical tools for calculating the power spectrum and upper bounds on the error probability are given. Results for the special case of Continuous Phase Frequency Shift Keying (CPFSK) with up to 256 levels are considered. Some new results on bounds on more advanced coded systems of higher complexity where the coding is performed jointly over several consecutive channel symbols are also given. Current research topics such as trellis-coded modulation for fading channels, and practical implementations and applications are also briefly discussed.

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.

Multi-h full response CPM (continuous-phase modulated) signals are analyzed at preselected numbers of states in contrast to the standard method of analyzing them at preselected numbers of modulation indices. Optimal multi-h phase codes which produce the highest minimum Euclidean distance are presented according to the number of states. Three orders of multi-h signaling are considered in the optimal code search. Numerical results are presented for binary CPFSK (continuous-phase frequency shift keying) and binary 1RC (1 raised cosine) signals at number of states from four through 12. >