A system-theory approach to decompose CPM signals into PAM waveforms

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.

The complexity of the multiple-symbol detection structures for partial response continuous phase modulation (CPM) signals goes exponentially with the length of the pulse shaping filter and the observation length as well. Simple no coherent trellis receivers for partial response CPM signals are proposed in this paper. Parallel to the simple coherent detectors, where CPM signals are approximately represented by a sum of Phase Amplitude Modulation waveforms, Laurent decomposition is applied to reduce the complexity. The proposed no coherent receiver is structured with only fixed K matched filters in the front-end and a processor which uses Viterbi algorithm with a 2N-1 states trellis to perform the sequence estimation. It is attractive because the structure does not involve any matrix calculations. The good error performance is confirmed by simulation results.

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.

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.

In this paper a general soft-based synchronization technique for continuous phase modulations (CPM) is presented. In particular two soft carrier phase estimation algorithms are derived, being the phase the parameter that shows the lower implementation complexity. These algorithms exploit the trellis structure inherent in the modulator of CPM signals and make use of a symbol-based BCJR, developed in an ad-hoc way for an uncoded CPM signal. The algorithms are blind and are designed to work with all CPM family. Simulation results for the soft carrier phase estimation are presented in terms of Root Mean Square Estimation Error (RMSEE). The modified Cramer-Rao bound (MCRB) is also shown for reference. RMSEE of soft recovery approach is very close to MCRB for all the examined formats.

In this paper we develop a reduced-complexity detection scheme for shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient constant-envelope modulation. The detector is based on the well-known pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM). Since SOQPSK is a ternary CPM, we show how the binary-based PAM technique is extended to accommodate the ternary case. We demonstrate that a detector based on the first two PAM components requires a simple trellis of only 4 states. We show that near-optimum performance is achieved using this reduced-complexity detector. The potential complexity reduction can be quite large, since one version of SOQPSK requires a trellis of 512 states.

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.

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.

We present an optimal maximum likelihood sequence estimating (MLSE) receiver which is based on the pulse amplitude modulation (PAM) representation of multilevel multi-h continuous phase modulation (CPM). We also give four different approaches to constructing suboptimal receivers which use a significantly reduced number of signal terms. We apply these techniques to two multi-h schemes in current use and evaluate receiver performance with computer simulations. In one instance we reduce the number of trellis states from 512 to 32, and the number of matched filters from 96 to 3, with a degradation of 0.7 dB. The simulations also show that the complexity reductions preserve the performance advantage multi-h CPM schemes have over single-index schemes.

Maximum Likelihood Sequence Estimation (MLSE) of Continuous Phase Modulated (CPM) signals can be realized in a few different manners. For the special case of transmission over a Rayleigh flat-fading channel, an attractive receiver is in the form of the Viterbi algorithm with the trellis updates being computed using a bank of FIR filters and square operations. The FIR filters are functions of the CPM pulse shape, of the channel model and of the transmitted sequence. The channel modeling being performed by using a finite order linear predictor, the receiver has been called a linear predictive receiver. For signaling with a symbol set larger than two symbols, this type of receiver can become too complex to even contemplate a practical implementation. The problems of complexity reduction and Viterbi soft-output decoding for quaternary CPM signals are examined. State-reduction techniques coupled with a q-ary Soft-Output Viterbi Algorithm (QSOVA) are presented. The performance of the algorithms is evaluated by simulations, showing the trade-off between performance and complexity reduction in some important practical cases.KeywordsFilter BankConvolutional CodeViterbi AlgorithmChannel EstimatorFading RateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The maximum a posteriori (MAP) detection of a continuous phase modulation (CPM) signal deploys the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm that utilises the trellis structure of the CPM signal. For optimal results the start as well as the end state must be known to the MAP detector. While the start state is usually the zero state by convention, the end of the trellis must be terminated properly to yield a defined end state. This leads to an overhead, which size is dependent on the particular CPM parameters. To overcome the decrease of spectral efficiency, a tail-biting technique is presented and compared to termination and truncation in a fair comparison regarding spectral efficiency.

We propose a new spread spectrum (SS) system based on continuous phase modulations (CPMs). The main idea is to exploit the sequence of modulation indices of a multi-h CPM as a frequency hopping (FH) sequence. We will show how the sequence of indices impacts on the CPM signal bandwidth and power spectral density (PSD). Spectral spreading, flatness and smoothness can be easily achieved by an appropriate choice of the maximum value of the modulation index and of the length of the index sequence. We will show that a CPM-based spread spectrum system achieves an overall spectral efficiency larger than that of a single-user single-h CPM signal even when a single-user detector is employed at the receiver.

Frequency-domain equalization for continuous phase modulation (CPM) is investigated. A discrete representation of the CPM signal is obtained by using the Gram-Schmidt orthonormalization procedure. The CPM discrete signal representation admits frequency-domain equalization for the purpose of mitigating intersymbol interference. General full- and partial-response CPM waveforms, and specific examples of MSK and GMSK with BT=0.3 are considered. Frequency-domain equalization is shown to be effective for CPM on severe frequency-selective fading channels.

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

A coherent receiver for CPM signals with RC (raised-cosine) pulse shaping is introduced. The receiver mainly consists of a multilayer ANN (artificial neural network) that evaluates the first derivative of the phase of the IF (intermediate frequency) signal. After training the ANN transforms the signal phase into the appropriate digital symbols. Further an easy to implement symbol synchronisation scheme is introduced. The symbol synchronisation also exploits the differentiated phase of the received signal. Therefore, the coherent receiver, does not need any extra synchronisation signal. Both applications are described in detail and a performance analysis is presented.