Convolutional Coding Combined with 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

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.

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.

We study a serially interleaved concatenated code construction, where the outer code is a standard convolutional code, and the inner code is a recursive convolutional code of rate 1. We focus on the ubiquitous inner differential encoder (used, in particular, to resolve phase ambiguities), double differential encoder (used to resolve both phase and frequency ambiguities), and another rate 1 recursive convolutional code of memory 2. We substantiate analytically the rather surprising result, that the error probabilities corresponding to a maximum-likelihood (ML) coherently detected antipodal modulation over the additive white Gaussian noise (AWGN) channel for this construction are advantageous as compared to the stand-alone outer convolutional code. This is in spite of the fact that the inner code is of rate 1. The analysis is based on the tangential sphere upper bound of an ML decoder, incorporating the ensemble weight distribution (WD) of the concatenated code, where the ensemble is generated by all random and uniform interleavers. This surprising result is attributed to the WD thinning observed for the concatenated scheme which shapes the WD of the outer convolutional code to resemble more closely the binomial distribution (typical of a fully random code of the same length and rate). This gain is maintained regardless of a rather dramatic decrease, as demonstrated here, in the minimum distance of the concatenated scheme as compared to the minimum distance of the outer stand-alone convolutional code. The advantage of the examined serially interleaved concatenated code, given in terms of bit and/or block error probability which is decoded by a practical suboptimal decoder, over the optimally decoded standard convolutional code is demonstrated by simulations, and some insights into the performance of the iterative decoding algorithm are also discussed. Though we have investigated only specific constructions of constituent inner (rate 1) and outer codes, we trust, hinging on the rational of the arguments here, that these results extend to many other constituent convolutional outer codes and rate 1 inner recursive convolutional codes.

CPM waveforms which are utilized in both MIL-STD-188-181B (181B) and high performance waveform SATCOM operation undergo appreciable distortion due to the effects of the bandlimiting and hard-limiting satellite transponder. In this application, the traditional LMS equalizer can remove some of the intersymbol interference, but at the higher symbol rates, the modem performance is still far off from the same bit error rate achieved in an environment which only contains additive white Gaussian noise. Observation of the SATCOM channel has shown that the CPM waveform is predictable, distorted in phase during symbol transitions. Large phase transitions incur a larger, proportional amount of distortion when compared to smaller phase transitions. A characterization of the phase error as a function of all the possible clockwise and counterclockwise adjacent phase transitions for the CPM phase constellation illuminates this proportion property of the distortion caused by the intersymbol interference. Once this error is characterized for all the symbols, it can be removed via complex multiplication. This method has been shown to outperform the traditional LMS equalizer in this application especially when considering the noise enhancement inherent in the LMS equalizer implementation. This paper documents the simulation comparison of the LMS equalizer and the new non-linear equalizer approach along with actual radio bit error rate curves.

The detection of convolutional codes over rings suitable for continuous phase modulation (CPM) are presented based on the Rimoldi's Decomposition of CPM. Because the ring convolutional codes are on the same ring as the inner codes of CPM, We can use reduced state sequence detection (RSSD) to analyze and detect the overall encoder. Numerical result shows the detection complexity of this RSSD is significantly reduced with a very small degradation in error performance.

Constant envelope and high spectral efficiency are among the key properties which make continuous phase modulation (CPM) a preferred choice for many applications. Numerous methods are available for designing concatenated CPM systems to achieve additional coding gains. In this paper, we propose a new serial concatenated CPM scheme. Our design uses a multi-alphabet binary CPM as an inner code, a modified turbo code as an outer code, and specially designed interleavers. The extrinsic information transfer (EXIT) chart technique has been employed to assist the outer code design. Using soft decision decoding, we show that our design gives noticeable improvements compared with previous concatenated CPM schemes over additive white Gaussian noise (AWGN) channel.

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.

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.

Some properties of digitally phase modulated (DPM) signals are presented. Phase modulation with (overlapping) pulses generated by a digital FIR filter belong to this class, which may be considered to be a practical approximation to continuous phase modulated (CPM) signals. The power spectra of DPM signals are derived analytically. The ability of these signals to operate through an additive white Gaussian noise channel is assessed by calculating their minimum Euclidean distance. Their noise and spectral properties are found to be similar to those of CPM signals. Assuming that a Viterbi decoder is used to resolve symbol interference, the out-of-band power tends to decrease as the pulse duration increases, and the noise immunity is enhanced. At the same time the receiver complexity grows exponentially. Hence, noise immunity and spectrum compactness are achieved at the cost of higher received complexity. Modems for DPM signals are believed to be easier to implement than those for CPM signals. This is because filter design is simple and a residual carrier component can be retained to facilitate carrier regeneration. Furthermore, the accumulated carrier phase does not need to be continuously evaluated in order to perform matched filtering. The analytic results derived are supported by measurements and simulations.

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.

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.

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.