A generalized decomposition approach to multi-h continuous phase modulation

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.

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.

This 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) 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

Two receiver architectures are presented for equalization of multi-h continuous phase modulation (CPM). In the first approach, the receiver front end is a matched-filter bank, which is derived from Laurent decomposition of the signal. A circulant-matrix model derived for the samples of the matched filter is used to perform the equalization in frequency domain. The second technique employs a receiver with a simple front end consisting of a low-pass filter and a fractional sampler. We also develop a circulant matrix model for the latter approach, which relates the Laurent pseudo-symbols to each polyphase component at the output of the sampler. A linear frequency-domain equalizer (FDE) is also proposed using this model. In addition to providing the details of these approaches, the paper proposes several simplifications applicable to each of the two cases, and provides a detailed discussion on the performance/complexity trade-off. Bit-error rate (BER) results are presented for the IRIG-106 aeronautical telemetry dual-h CPM waveform.

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.

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) 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

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) 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.

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.

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.

In 1986, Laurent showed that binary continuous phase modulated (CPM) signals can be decomposed into pulse amplitude modulated (PAM) waveforms. This result, later extended to multilevel CPM signals by Mengali and Morelli, has attracted much attention, especially for the design of simplified receivers. The paper proceeds from the premise that the decomposition into PAM waveforms is not unique, and follows a systemtheory approach that leads to a natural formulation. First, the CPM modulator is represented by a nonlinear part (encoder) followed by a linear part (bank of PAM modulators).The two parts are then rearranged with the aim of obtaining real-valued continuous PAM waveforms and to reduce their number. Several classes of decompositions arise with this approach, each of which admits an infinite number of different decompositions of the same CPM signal, among which the Laurent and MengaliMorelli results appear as special cases. Throughout the paper, a systematic use is made of the Kronecker product, which appears to be the natural tool for dealing with CPM decompositions and for expressing results in a very simple form.

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.