Reduced State Sequence Detection for Ring Convolutional Coded Continuous Phase Modulation

Continuous phase modulation (CPM) is known for its attractive spectral properties. Furthermore, CPM has the property that the modulation signal maintains a constant envelope, so CPM is effective for satellite communications. Recently, generalized nonlinear CPM (GNCPM), which can achieve a larger minimum Euclidean distance than ordinary CPM, was introduced. In this paper, we propose a convolutional coded GNCPM to improve the bit error rate (BER) performance of uncoded GNCPM without expanding bandwidth. Combination CPM with convolutional coding causes an increased number of phase trajectory patterns which can cause the bandwidth expansion. Therefore, in our proposed model, to control the bandwidth, we pay attention to the phase trajectory pattern which is already owned by uncoded GNCPM and change the modulation index appropriately, depending on the input symbols, to keep the number of phase trajectory patterns the same as in uncoded GNCPM. First, we consider the most suitable assignment of the modulation index which can increase the Euclidean distances without bandwidth expansion. Next, we theoretically derive the upper bound on the error event probability of the proposed model in additive white Gaussian noise (AWGN). The performance of the proposed convolutional GNCPM, obtained by computer simulation, shows that the proposed model can improve BER performance without bandwidth expansion. © 1998 Scripta Technica. Electron Comm Jpn Pt 1, 81(8): 42–50, 1998

It is known that space-time coding (STC) technology can improve the performance of MIMO continuous phase modulation (CPM) communication system, but it also leads to high receiver complexity. It is also known that any M-ary CPM signal can be exactly decomposed into a sum of time-offset pulse amplitude-modulated (PAM) waveforms based on the extended Laurent decomposition. In this paper, we develop a simplified detection algorithm using the CPM's PAM decomposition for the full response STC-CPM system which adopts space-time trellis coding. Analysis and simulation results show that this algorithm efficiently reduces the computation complexity with a very small degradation in error performance compared with the conventional maximum likelihood sequence detection.

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.

Continuous phase modulation (CPM) has been widely used in telecommunication and aeronautical telemetry system due to its high power and spectral efficiency. Non-coherent detection is a kind of feasible CPM detection method if there is large phase noise or residual carrier frequency offset. Near-optimal non-coherent sequence detection, which is based on Viterbi algorithm, has a performance close to that of maximum-likelihood sequence detection (MLSD). However, near-optimal non-coherent detection of CPM is very complicated to be implemented, and it is even more difficult to achieve a high speed due to feedback in the process of calculating branch metrics, add-compare-select (ACS), updating the beginning phase and phase reference symbol. In this paper, we first review near-optimal non-coherent detection of CPM, and then we present a high speed design of FPGA implementation for near-optimal non-coherent detection of a 64 state, 4-ary, length-3T raised cosine (3RC) CPM on Xilinx XC7VX690T device. In our scheme, the frequency pulse truncation is used to simplify the CPM detection. We propose a feedback processing in parallel for different states of CPM trellis to achieve a low latency. Furthermore, we develop a recursive implementation architecture for the process of updating the beginning phase. We achieve the CPM bit rate of 25Mbps for the on-chip processing clock of 100MHz. The results of simulation shows near-optimal non-coherent detection performs much better the coherent detection when residual carrier frequency offset or phase noise exists. It is found that the implementation can achieve a degradation in the Eb/N0 from computer simulation of as small as 0.3 dB for an average BER=10-5.

Continuous phase modulation (CPM) is a widely used modulation scheme in communication systems. However, difficulties arise with the design of CPM receivers, due to the nonlinear nature of CPM. One popular solution to this problem is to linearize CPM with pulse amplitude modulation (PAM) representation. In this paper, a reduced-complexity superbaud timing recovery method is proposed for PAM-based multi-h CPM receivers. The proposed method is non-data-aided, feedforward, and suitable for M-ary, multi-h CPM in general. The novelties of the proposed method are twofold. On one hand, the proposed method is reduced-complexity for PAM-based receivers, because it shares the same match filters with the PAM-based detectors. On the other hand, it is shown that the proposed method is able to outperform the existing method with some modulation schemes. Therefore, the proposed method provides an important synchronization component for PAM-based multi-h CPM receivers.

A decomposition approach to continuous phase modulation (CPM), mostly due to the work of Rimoldi (1988), is significant in the design of combined coding and communication signaling scheme. In this paper the generalized decomposition model is developed and applies to the multi-h CPM. It is shown that any multi-h CPM can also be realized by a continuous phase encoder (CPE) concatenated with a memoryless modulator (MM). Moreover, depending on the manner that the modulation indexes are selected for each symbol interval, the CPE can be either a linear or nonlinear feedback convolutional encoder, in which both the CPE and MM are time-variant. Finally, some applications are employed to verify the advantage of the proposed decomposition model, namely, (1) natural trellis representation of the CPE for M-ary single-h CPM with different modulation indexes that have the same denominator P, (2) a reduction of the number of states of the MLSD receiver for conventional multi-h CPM, (3) asymmetrical multi-h CPM has no gain over conventional multi-h CPM, (4) nonlinear CPM has a CPE that is nonlinear.

There are several ways to use iterative decoding techniques with coded continuous phase modulation (CPM). This paper presents a method using parallel concatenation of convolutionally-coded CPM. All CPM schemes can be decomposed into a ring convolutional code and a memoryless signal mapper. This allows a properly designed convolutional code trellis to be combined with the CPM trellis, producing the joint trellis of a constituent code. Parallel concatenation of such constituent codes combined with iterative decoding yields very good performance. We present the results of code searches for two binary CPM schemes, each using bit interleaving and symbol interleaving. Simulation results using various length interleavers are also provided. Low complexity encoders are shown to perform better using bit interleaving, whereas encoders with higher complexity perform better with symbol interleaving.

Existing space-time codes have focused on multiple- antenna systems with linear modulation schemes such as phase- shift keying and quadrature amplitude modulation. Continuous phase modulation (CPM) is an attractive scheme for digital transmission because of its constant envelope which is needed for power efficient transmitters. Recent research has shown that space-time coded CPM can achieve transmit diversity to improve performance while maintaining the compact spectrum of CPM signals. However, these efforts mainly combine space- time coding (STC) with CPM to achieve spatial diversity at the cost of a high decoding complexity. In this paper, we design space-time block codes (STBC) for binary CPM with modulation index h = 1/2 and derive low-complexity receivers for these systems. The proposed scheme has a much lower decoding complexity than STC CPM with the Viterbi decoder and still achieves near-optimum error performances.

Continuous phase modulation (CPM) and trellis-coded modulation are well-understood schemes that layer trellis codes with multilevel modulation to produce efficient bandwidth waveforms. This paper describes a novel modulation scheme which takes advantage of existing trellis codes and adds parallel branches to create a new modulation with greater spectral efficiency and reduced receiver complexity. The first part of the paper discusses the trade-off between Euclidean distance and modulation bandwidth for the standard 1-REC CPM waveform. A set of orthogonal signals can be added to the CPM constellation which provides a series of parallel branches in the natural trellis structure of the CPM modulation. The corresponding bandwidth expansion and throughput improvement is analyzed and the advantages of this modulation technique are discussed. This new, non-constant envelope CPM waveform is compared to the multi-level, multi-amplitude CPM waveform (described in Proakis). In similar fashion, a trellis-coded, shaped PSK modulation is expanded to include orthogonal signal shaping and the power and spectral efficiencies are discussed.

This paper shows that under certain scenarios continuous phase modulation (CPM) is an attractive option for space-time modem implementations. CPM is attractive in the sense that nonlinear power amplifiers can be used to reduce the cost of individual transmitters. However, receiver complexity and bandwidth inefficiency have reduced the utility of CPM in single transmit antenna scenarios. We would show that in a multiple transmit antenna scenario CPM modulation can reduce the cost of individual transmitters and while still achieving the multiple antenna throughput advantage. A constrained outage capacity analysis is completed and the results show that if outage probability is the design constraint then using CPM results in little loss in terms of the achievable rate and performance. CPM, like linear modulations, can achieve a tradeoff between rate and performance, and this paper examines some of the signaling options available for CPM in multiple antenna modems.

In order to understand the optimal parameter settings of spectrally efficient continuous phase modulation (CPM), we elaborate on our previous work on numerically optimized CPM. An empirical model is developed based on an expression for the effective bandwidth of CPM, an approximate expression for the smallest Euclidean distances of spectrally efficient CPM and observed properties of the numerically optimized phase pulses. We find that the optimized phase pulses, which resulted from a joint optimization of modulation index and phase pulse, share common properties for different alphabet sizes and different spectral efficiencies. These properties are described by three phase pulse parameters, and we show that they attain approximately equal values at the so-called saturation length. The model can predict the minimum Euclidean distance at the saturation length for a CPM system using an even-integer alphabet and jointly optimized modulation index and phase pulse, and it partly extends to less spectrally efficient CPM systems.

The SA(B,C) algorithm is considered for continuous phase modulation (CPM). The SA(B,C) detector performs a breadth first maximum likelihood sequence detection in the trellis under structural and complexity constraints. Given a trellis, the SA(B,C) detector partitions the states into C classes and for every time interval selects B paths into each class. To find a partition that minimizes C for a given B and CPM system, such that the performance (error event probability) approaches unconstrained MLSD when the signal to noise ratio goes to infinity, is an NP-hard problem. Here a suboptimum method for finding the partitioning is considered. Substantial savings in complexity can be made by using the SA(B,C), while achieving almost optimal (unconstrained) error performance.

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 & Sons, Ltd.

Continuous phase modulation (CPM) consists of a large family of signals that are especially suitable for wireless communication. CPM signals have not been represented by discrete points in signal space because the phase of the carrier is time-variant. However, in this paper we present a new method to represent the binary CPM signals by discrete points in signal space by utilizing the amplitude modulated pulse (AMP) representation of the CPM signals. We use this new signal space representation to compute the Euclidean distance for any CPM signal and we compare the performance of CPM signals with each other and with other modulation schemes.

We consider the serial concatenation of a convolutional code and a continuous phase modulation separated by a random interleaver. It is shown that the continuous phase modulator has the same behavior as a recursive systematic convolutional code in serial turbo codes. The interleaver gain produced by the modulator and the random interleaving depends only on the minimum Hamming distance of the outer code. A soft-input soft-output detection algorithm is described and applied in an iterative joint detection-decoding scheme. Simulated performance over Gaussian and Rayleigh channels shows a dramatic gain over both uncoded modulation and classic detection.