Continuous Phase Encoder Research Articles

A Novel Serially Concatenated GMSK System for Satellite Communications

A novel serially concatenated GMSK system is proposed for satellite communications subject to low SNR, limited power and spectrum resources. First, we design a Nonrecursive continuous-phase encoder (NRCPE) based GMSK based on the Rimoldi’s decomposition. Then, a corresponding pilot-aided quasi-coherent demodulation algorithm is developed, whose basic principle is that a modified BCJR-based detection performs on the received signals with initial and ending trellis states being determined using the very limited pilot overhead. Finally, we choose proper modulation parameters for the NRCPE based Gaussian minimum shift keying GMSK signaling according to the trade-offs between the power and spectral efficiency. The simulation results show that the LDPC coded GMSK system using the proposed algorithm can achieve excellent performance and can also work well in the presence of the large Doppler shifts and some burst errors.

Design of Efficient LDPC Coded Non-Recursive CPE-Based GMSK System for Space Communications

We consider a low-density parity-check (LDPC) coded non-recursive Gaussian minimum shift keying (GMSK) scheme for space communications subject to low signal-to-noise ratio (SNR), limited power, and spectrum resources. First, we design a non-recursive continuous-phase encoder (NRCPE)-based GMSK modulator to alleviate the impact of the error propagation existed in a recursive CPE (RCPE)-based one. Then, a corresponding pilot-aided quasi-coherent demodulation algorithm (PA-QCDA) is developed for improving the performance of the non-coherent demodulation and the impact of the Doppler shift in the coherent demodulation, whose basic principle is that a modified Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm-based detection performs on the received signals with initial and ending trellis-states being determined using the very small pilot overhead. Finally, we choose proper modulation parameters for the NRCPE-based GMSK signaling according to the tradeoffs between power and spectral efficiency. The simulation results show that the proposed system using the PA-QCDA can achieve excellent performance and can also work well in the presence of the large Doppler shifts and some burst errors.

Code design and performance analysis in TCCPM system based on super trellis

AbstractThis paper describes a technique related to the design of a trellis encoder, combined with the continuous phase modulation (CPM). Based on the idea of decomposing CPM into continuous phase encoder (CPE) and memoryless modulator (MM), superior trellis encoders are designed following Ungerboeck's set partitioning rules. Combinations are optimized with the squared minimum Euclidean distance based on the super trellis structure constructed by the trellis structure of trellis coded modulation (TCM) and CPE. Simulation results show that this new coding scheme consistently obtains better performance than previous schemes. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Continuous Phase Modulation (CPM) Revisited: Using Time-Limited Phase Shaping Pulses

Conventional CPM signals employ information sequence with time-unlimited phase shaping pulse (PSP) to achieve power and bandwidth efficient transmission. On the contrary, information sequence using time-limited PSP was believed to produce power-wasting data-independent discrete spectral lines in CPM spectra, and was suggested to be avoided. In this paper, we revisit this problem and adopt the time-limited PSP to replace the one with time-unlimited, it turns out to have an alternative solution to the CPM scheme. We first modify the spectral computing formula for the CPM with time-limited PSP (or CPM-TL) from conventional CPM formula and show that the discrete spectral lines appeared in the power density spectrum of CPM-TL signals can be diminished or become negligible by appropriately choosing PSP. We also show that this class of CPM can use any real number modulation index (h) and the resultant trellis structure of CPM guarantees the maximum constraint length allowed by the number of states in the MLSD receiver. Finally, the energy-bandwidth performance of CPM using time-limited PSP is investigated and compared with conventional CPM with time-unlimited PSP. From numerical results we show that, under the same number of states in the MLSD receiver and bandwidth occupancy, this subclass of CPM could outperform the conventional CPM up to 6 dB coding gain, for h < 1, in many cases. key words: continuous phase modulation, time-limited phase shaping pulse, power spectrum, euclidean distance, constraint length, continuous phase encoder

The Study of Coded CPM Schemes

Continuous Phase Modulation (CPM) schemes belong to a class of constant-envelope digital modulation schemes, the constant-envelope nature of the CPM signals makes them robust for the nonlinear and fading channels, and very useful for the satellite and/or the mobile radio channels. Comparing to PSK modulation, CPM modulation can not only provide spectral economy, but also exhibit a “coding gain”. CPM can be decomposed into a Continuous Phase Encoder (CPE) followed by a Memoryless Modulator (MM), this allows many new coded modulation schemes of combination of convolutional encoder and CPM modulator to be possible, such as serially-concatenated CPM (SC-CPM), SC-CPM with Convolutional Codes over Rings, pragmatic CPM (P-CPM), Concatenation of convolutional endocder and extended CE（CCEC）, etc. Some simulations show that these new CPM schemes can offer superior performance.

Design of Efficient Joint eIRA-Coded MSK Modulation Systems for Space Communications

An efficient scheme of extended irregular repeat-accumulate (eIRA-) coded minimum shift keying (MSK) is presented. Based on an extrinsic information transfer (EXIT) chart, it is designed as an eIRA code, incorporating a continuous-phase encoder (CPE) decomposed from MSK. Our scheme and a contrasting scheme of another eIRA-coded MSK are simulated in an additive white Gaussian noise (AWGN) channel. Simulation results show that our scheme outperforms the contrasting scheme by about 2 dB at a bit error rate (BER) of and has the same performance of an optimal eIRA-coded binary phase shift keying (BPSK). In addition, our scheme obtains lower complexity and less decoding latency because all differential encoders in the eIRA code are eliminated, while adding some differential decoders. Thus, the two-level Tanner graph-based decoding in the contrasting scheme is reduced. Therefore, the proposed scheme can be efficiently applied to satellite and deep space communications.

Trellis Termination of Multi-h CPM and the Diophantine Frobenius Problem

This paper presents a method for terminating the phase trellis in multi-h continuous phase modulation (CPM). It is shown that tilted phase trellis for multi-h CPM signals is periodic and enables the representation of the multi-h CPM modulator as a cascade of a periodic recursive continuous phase encoder (CPE) and a phase modulator (PM). We then pose the problem of finding the minimum number of symbols that will terminate the phase trellis in a known state of the modulator and establish a connection of its solution to the Diophantine Frobenius Problem (FP). Analytical results are established for the existence of a terminating sequence and upper and lower bounds are derived on its length for arbitrary modulation parameters. We show that the trellis terminating symbols and their quantity depends upon the initial state of the encoder, the set of modulation indices, the CPE memory order, and the number of bits per modulated symbol. It is shown that required overhead for trellis termination can be significant for schemes with integer modulation indices.

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.

Design of Ring Convolutional Trellis Codes for MAP Decoding of MPEG-4 Images

We propose a trellis-coded modulation system using continuous-phase frequency-shift keying (CPFSK) and ring convolutional codes for transmitting the bits generated by an embedded zerotree wavelet encoder. Improved performance is achieved by using maximum a posteriori decoding of the zerotree symbols, and ring convolutional trellis codes are determined for this decoding method. The CPFSK transmitter is decomposed into a memoryless modulator and a continuous phase encoder over the ring of integers modulo 4; the latter is combined with a polynomial convolutional encoder over the same ring. In the code design process, a search is made of the combined trellis, where the branch metrics are modified to include the source transition matrix. Simulation results of image transmission are provided using the optimized system, including mismatched channel cases.

Design of serial concatenated msk schemes based on density evolution

We consider the design of convolutional codes and low density parity check (LDPC) codes with minimum-shift keying (MSK) when the receiver employs iterative decoding and demodulation. The main idea proposed is the design of coded schemes that are well matched to the iterative decoding algorithm being used rather than to hypothetical maximum-likelihood decoding. We first show that the design is crucially dependent on whether the continuous phase encoder (CPE) is realized in recursive form or in nonrecursive form. We then consider the design of convolutionally coded systems and low density parity check codes with MSK to obtain near-capacity performance. With convolutional codes, we show that it is possible to improve the performance significantly by using a mixture of recursive and nonrecursive realizations for the CPE. For low density parity check codes, we show that codes designed for binary phase shift keying are optimal for MSK only if the nonrecursive realization is used; for the recursive realization, we design new LDPC codes based on the concept of density evolution. We show that these codes outperform the best known codes for MSK and have lower decoding complexity.

Adaptable Viterbi detector for a decomposed CPM model over rings of integers

A novel, practical and flexible way of implementing continuous phase modulation (CPM) using a decomposed model and a Viterbi detector is presented. The decomposed CPM modulator, comprising a continuous phase encoder (CPE) and a memoryless modulator (MM), is implemented and can be concatenated with a ring convolutional encoder (CE) such that the detector may be readily adapted to the ring of integers over which the CE/CPE operates. A partial-response CPM system is simulated over additive white Gaussian noise (AWGN) and Rayleigh flat fading (RFF) channels, and results, in terms of the bit error rate (BER) against the signal to noise ratio (SNR), are presented, discussed and evaluated.

Multiple symbol trellis coding of CPFSK

This paper describes a technique related to the design of a trellis encoder, combined with the full response M-ary continuous phase frequency shift keying (CPFSK) with modulation index 1/M. A new representation of CPFSK waveforms in N signaling intervals, is proposed as a function of an (N+1)-D vector. We also decompose the generation of the proposed CPFSK waveform into two stages, an N-consecutive continuous phase encoder (NCPE) and a memoryless modulator (MM). This decomposition makes it possible to design binary convolutional encoders with various code rates, cascaded to the NCPE. Specific optimal outer convolutional encoders of two and three-consecutive full response four-ary CPFSK with modulation index 1/4 are designed following Ungerboeck's (1982) set partitioning approach. These codes achieve asymptotic coding gains up to 4.77 dB for the two consecutive case with code rate 3/4, and asymptotic coding gains up to 5.45 dB for the three-consecutive case with code rate 5/6.

Coded continuous phase modulation using ring convolutional codes

Rate 1/2 convolutional codes over the ring of integers modulo M are combined with M-ary continuous phase modulation (CPM) schemes whose modulation indices are of the form h=1/M. An M-ary CPM scheme with h=1/M can be modeled by a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is linear over the ring of integers modulo M. The fact that the convolutional code and the CPE are over the same algebra allows the state of the CPE to be fed back and used by the convolutional encoder. A modified Euclidean distance function that substantially simplifies the search for good codes has been derived and used to find new codes. Numerical results show that this approach consistently improves the performance as compared to coded schemes using binary convolutional codes with the same decoding complexity.

Trellis-coded continuous-phase frequency-shift keying with ring convolutional codes

Trellis-coding techniques are applied to continuous-phase frequency-shift keying (CPFSK). A new coding scheme based on convolutional codes on the ring of integers modulo-P is shown to be a natural way to apply trellis coding to CPFSK. Previous work has decomposed CPFSK into two parts: a linear encoder, with memory called the continuous phase encoder (CPE), and a memoryless modulator (MM), where the CPE often has a code structure defined over the ring of integers modulo-P. The combination of a modulo-P convolutional channel encoder (CE) and the CPE is a linear modulo-P encoder. Design examples are given for rate-1/2 coded quaternary CPFSK with modulation indexes 1/2 and 1/4, and rate-2/3 coded octal CPFSK with modulation index 1/8. Combinations are optimized in the normalized minimum Euclidean distance sense for a given total number of states in the overall MLSE receiver. Numerical results show that this new coding scheme consistently obtains better performance than previous schemes. >

Catastrophic continuous phase modulation schemes and their noncatastrophic equivalents

Continuous phase modulation (CPM) schemes are bandwidth and energy efficient constant-envelope modulation schemes that can be viewed as a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is of convolutional type. It is observed that CPM schemes can be catastrophic in the sense that pairs of input sequences that differ in an infinite number of positions can be mapped into pairs of signals with finite Euclidean distance. This can happen in spite of the fact that the CPE is never catastrophic when considered as a stand alone convolutional encoder. The necessary and sufficient condition for a general CPM scheme to be catastrophic is given. Each member of the two major families of CPM schemes, namely the LREC and the LRC, has been classified as a catastrophic or noncatastrophic scheme. For the catastrophic schemes, the probability that a catastrophic event occurs is determined. A canonical precoder which transforms each scheme of both families into an equivalent noncatastrophic scheme is derived. The equivalent noncatastrophic scheme has the same number of states as the original one. Moreover, it has the property that if two input sequences differ in the ith position, the corresponding output signals have nonzero Euclidean distance in the ith interval. >

A decomposition approach to CPM

It is shown that any continuous-phase-modulation (CPM) system can be decomposed into a continuous-phase encoder and a memoryless modulator in such a way that the former is a linear (modulo some integer P) time-invariant sequential circuit and the latter is also time invariant. This decomposition is exploited to obtain alternative realizations of the continuous-phase encoder (and hence of CPM) and also to obtain alternative forms of the optimum decoding algorithm. When P is a prime p so that the encoder is linear over the finite field GF(p), it is shown that cascading it with an outside convolutional encoder is equivalent to a single convolutional encoder. It is pointed out that the cascade of the modulator, the waveform channel (which it is assumed is characterized by additive white Gaussian noise), and the demodulator that operates over one symbol interval yield a discrete memoryless channel that can be studied without the distractions introduced by continuous-phase encoding. >