Double trellis-coded CPM

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

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.

Continuous Phase Modulation (CPM) schemes are advantageous for low-power radios. The constant envelope transmit signal is more efficient for both linear and non-linear amplifier architectures. A standard, coherent CPM receiver can take advantage of modulation memory and is more complex than a coherent Phase Shift Keyed receiver. But the CPM signal can be demodulated non-coherently and still take advantage of the trellis structure inherent in the modulation. With this complexity reduction, the CPM receiver is comparable in performance to a Phase Shift Keyed radio with the power utilization of a Frequency Shift-Keyed design. In this paper, we discuss two methods for increasing the modulation memory of the CPM signal. In the first method, the distribution of the transmitted symbol across multiple phase pulses is investigated and the bit error rate analyzed. In the next method we address the addition of convolutioncodes. In both cases the effects of the CPM memory to quasi-coherent demodulation is analyzed and discussed. The differences in complexity will be analyzed and the overall performance enhancements of several different modulation schemes will be illustrated. 1

The paper shows that some continuous phase modulation (CPM) schemes have some properties that allow a near optimum reception with very low complexity. The proposed reception method applies simultaneously three techniques for complexity reduction of CPM receivers, which have been previously object of separate analysis with additive white Gaussian noise (AWGN). These techniques are: first-quadrant metrics calculus on a F-dimensional Walsh space, derivation of the other quadrant metrics using a no loss derivation algorithm and finally the use of constrained complexity maximum likelihood sequence detection (MLSD) using the M-algorithm. The cumulative effect on total performance loss is negligible and no more than the sum of the partial losses due to the Walsh space and the M-algorithm, known to be negligible when observing the respective standalone rules for the complexity reduction limits.

Joint source and channel (JSC) coding using combined trellis coded quantization (TCQ) and continuous phase modulation (CPM) is studied. The channel is assumed to be the additive white Gaussian noise (AWGN) channel. Analytical bounds on the channel distortion for jointly designed TCQ/CPM systems with maximum likelihood sequence detection (MLSD) are developed. For a memoryless uniform source, our upper bounds for the investigated TCQ/CPM systems are shown to be asymptotically tight for increasing channel signal-to-noise ratio (SNR) values. It is concluded that the minimum Euclidean distance of the CPM system alone is not enough to evaluate the performance of the combined TCQ/CPM systems. The number of the error events having the minimum Euclidean distance and the total distortion caused by those error events also affect the asymptotic performance of the investigated systems. This work provides an analysis tool to estimate the performance for a given combined TCQ/CPM system. The analysis method is very general, it may be applied to any trellis based JSC coding schemes.

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.

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 present a coherent detection technique for continuous phase modulation (CPM) operating in the Rayleigh flat fading channel. The technique is based on the idea of inserting periodically data dependent pilot symbols that force the CPM signal to pass through known phase states. This transmission format enables the receiver to extract from the received signal the channel fading gains at regularly spaced instants. When coupled with proper channel estimation filters, very accurate channel state information (CSI) can be estimated at the receiver for fading compensation. Moreover, the accuracy of the CSI can be further refined by adopting a multiple-pass decoding approach. The paper discusses (a) the pilot symbol encoding technique required to force a M-level CPM scheme with a modulation index of p/M, p is an integer, to return periodically to a set of known phase states, (b) the optimal channel estimation filters, (c) a trellis-based precoding technique that can reduce the bit error rate in M-level CPM systems by close to 50%, and (d) a multiple-pass channel estimator/demodulator. Analytical and simulation results are presented for minimum shift keying (MSK), Gaussian MSK, and four-level continuous phase frequency shift keying with a modulation index of 1/4. It is observed that our pilot symbol-assisted CPM schemes exhibit no irreducible error floor even at a channel fade rate of three percent the symbol rate. The implicit phase coding in CPM and the accurate CSI provided by the pilot symbols lead to a diversity effect in the bit error rate curves of these modulation schemes.

Continuous phase modulation (CPM) with noncoherent detection over a one-symbol interval is discussed. In order to obtain good performance with this simple demodulation strategy, the phase function of the modulation scheme has to be designed properly. An approach to shaping the purchase function to achieve noncoherent orthogonal performance for various values of the modulation index (h) is presented. Using the Gram-Schmidt orthogonality procedure, an entire family of orthogonal phase functions for h>or=0.68 is derived. All CPM schemes with these phase functions produce the same performance as noncoherent orthogonal signaling. For h=1 the phase function reduces to that of the FSK phase function. It is shown that there are CPM schemes that give the same SNR performance as noncoherent orthogonal FSK but have some spectral advantages over the FSK modulation format. >

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.

The paper considers a wireless transmission system in a multiple-user environment. It involves a combination of non-binary convolutional codes with Continuous-Phase Modulation (CPM) for transmission in an uplink channel using the Frequency Division Multiple Access (FDMA) method. For a more efficient available band utilization, the distances between individual system user carriers are decreased. In order to reduce the bit error rate (BER) a concatenation of CPM with convolutional codes over a ring has been used and a low-complexity iterative algorithm for inter-carrier interference (ICI) cancellation was employed on the receiver side. BER results obtained in computer simulations are presented for the proposed solution.

Space–time (ST) coding is a proved technique for achieving high data rates in 3G mobile systems that combines coding, modulation and multiple transmitters and receivers. A novel algorithm is proposed for ST ring trellis‐coded modulation (ST‐RTCM) systems with continuous‐phase modulation (CPM) when the channel coefficients are known to the receiver. This algorithm is based on the CPM decomposed model, which exploits the memory properties of this modulation method, resulting in a straightforward implementation of joint ST coding and CPM, which is particularly suitable for ring codes. This new scheme is used to investigate the performance of the delay diversity code with CPM over slow Rayleigh fading channels, in particular with MSK which is one of the most widely used modulation methods of continuous phase. Furthermore, a feedback version of delay diversity allowed by the decomposition is tested in 1REC and 1RC systems. This feedback configuration is seen to provide good results for low signal‐to‐noise ratios. Simulations results are also provided for multilevel ST‐RTCM codes that achieve a higher throughput than MSK‐coded systems. Additionally the serial concatenation of an outer Reed–Solomon code with an ST‐RTCM code is shown, this combination further reduces the error probability and achieves even more reliable communications. Copyright © 2005 John Wiley & Sons, Ltd.

The attractive properties of the digital constant amplitude modulation scheme CPM (continuous phase modulation) have been demonstrated in a previous paper in this journal.1 This concerned both the power and spectral efficiency of the large family of CPM schemes over the Gaussian channel.In this paper the considered channel can be both bandlimited or band‐ and amplitude‐limited at the same time. Analytical results as well as simulations are presented for a number of selected CPM schemes.In today's increasing demand for bandwidth, CPM is an attractive candidate for future satellite applications because of its spectral efficiency. In addition to this comes the fact that the transmitted signal has a constant amplitude and good detection performance when optimal coherent detection is performed.

Multicarrier transmission techniques like multicarrier code division multiple access (MC-CDMA) is the strongest contender for the future generation wireless networks which is supposed to cater to the need of very high data rate with mobility and at the same time combat multipath and intersymbol interference in a spectrally efficient manner. To enhance the spectral efficiency further, some form of adaptive modulation is being proposed (Wasantha et al. (2002)). In this paper, first of all, we simulate the performance of various single-h continuous phase modulation (CPM) schemes in an MC-CDMA system by varying the two CPM parameters - size of symbol alphabet (M) and modulation index (h). The parameter sets considered are {M=2, h=0.5}, {M=2, h=0.875}, {M=4, h=0.5} and {M=4, h=0.875}. Simulation results show that the higher order modulation schemes (M=4) need better channel conditions than the lower order schemes (M=2) for a given bit error rate (BER). Moreover, as expected (Xiong (2000)), h=0.875 (approximate optimum value) gives a better BER performance than h=0.5 for a given BER. Based on these simulation results, we then design two adaptive modulation based systems, one considering h=0.5 and the other with h=0.875, each with M=2 and 4. Results of the adaptive systems clearly indicate that the adaptive switching of the modulation formats in each of these two systems increases the system capacity per given bandwidth (spectrum efficiency) effectively without sacrificing the expected BER performance. Also, it is seen that the adaptive system with h=0.875 is superior to the h=0. 5 system, both in terms of BER performance and the number of simultaneous users, but obviously at the cost of reduced bandwidth efficiency as higher the value of h, the higher bandwidth it requires.