Multi-h Continuous Phase Modulation Research Articles

Design and Implementation of a Low-Complexity Multi-h CPM Receiver with Linear Phase Approximation Synchronization Algorithm.

Multi-h continuous phase modulation (CPM), with extremely high spectral efficiency, involves the plague of high demodulation complexity with a large number of matched filters and a complex trellis. In this paper, an efficient all-digital demodulator for multi-h continuous phase modulation (CPM) is proposed based on a low-complexity decision-directed synchronization algorithm. Based on the maximum-likelihood estimation of the carrier phase and timing errors, we propose a reduced-complexity timing error detector with linear phase approximation (LPA) to the phase of the multi-h CPM. Compared with the traditional synchronization methods, it avoids derivative matched filtering and reduces about 2/3 of matched filters. The estimated accuracy and bit error rate (BER) performance of the LPA-based synchronization algorithm have no loss, as shown by the numerical simulation. Its stability is verified by the derived S-curve. Then, the receivers with the LPA-based synchronization for the three kinds of promising multi-h CPM are implemented on a Xilinx Kintex-7 FPGA platform. The experimental results show that the onboard tested BER of the proposed design has an ignorable loss in the numerical simulation. The implementation overhead on FPGA is significantly reduced by about 27% slices, 64% DSPs, and 70% block RAMs compared with the conventional method.

Spatial Diversity, Low PAPR and Fast Decoding for OFDM using L2-Orthogonal CPM ST-Codes

Orthogonal Frequency Division Multiplexing (OFDM) schemes provide high data rates and good robustness against frequency selective fading for communication systems. Space-Time Block Coding (STBC) is an efficient way to introduce space-time diversity in Multiple-Input Multiple-Output (MIMO) systems. Using non-linear modulations such as Continuous Phase Modulation (CPM) with its constant envelope property may be a way to construct MIMO OFDM systems that alleviates the typical Peak to Average Power Ratio (PAPR) issue of OFDM. However, CPM based systems are usually plagued by decoding complexity issues. In this paper, we introduce space-time-frequency diversity techniques based on L2-orthogonal multi-h CPM Space-Time codes designed for OFDM transmission. We benchmark these codes under frequency selective Rayleigh channels and show how they achieve full spatial diversity at full rate for any number of antennas, good spectral compactness, low PAPR and robustness to frequency fading. Furthermore, L2-orthogonality allows fast decoding with complexity growing only linearly in the number of Tx antennas.

A Flexible Modulation Scheme Design for C-Band GNSS Signals

Due to the spectrum congestion of current navigation signals in L-band, C-band has been taken into consideration as a candidate frequency band for global navigation satellite system (GNSS). As is known, modulation scheme is the core part of signal structure, and how to design a modulation waveform that could make full use of narrow bandwidth 20 MHz and satisfy the constraint condition of frequency compatibility in C-band is the main research content of this paper. In view of transmission characteristics and constraint condition of compatibility in C-band, multi-hcontinuous phase modulation (CPM) is proposed as a candidate modulation scheme. Then the classical channel capacity estimation and a comprehensive evaluation criterion for GNSS modulation signals are employed to assess the proposed scheme in the aspects of the capacity over additive white Gaussian noise (AWGN), tracking accuracy, multipath mitigation, antijamming, and so on. Simulation results reveal that, through optimizing the number and size of modulation indexes, the flexible scheme could offer better performance in terms of code tracking, multipath mitigation, and antijamming compared with other candidates such as MSK and GMSK while maintaining high band efficiency and moderate implementation complexity of receiver. Moreover, this paper also provides a reference for next generation modulation signals in C-band.

Frequency-domain Equalization Techniques for Multi-h Continuous Phase Modulation

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.

Wireless Robotics: Generalization of an Efficient Approach with Multi-h CPM Signaling and L2-Orthogonal Space-Time Coding

Wireless Robotics has become an important research topic in the last two decades. The need of controlling a robot to perform tasks remotely has significantly increased with the number of applications in fields like medicine and military, among many others. Taking advantage of current standards like Bluetooth and Wifi, Wireless Robotics calls for low power consumption components, robustness and high data rate through the wireless channel. This call can be fulfilled with a reliable signaling format, satisfying the needs of low power consumption and high spectral efficiency. Besides, continuous phase modulation (CPM) has gained increasing attention due to its favorable trade-off between power and bandwidth efficiency. Multi-h CPM recently appeared as a generalization of single-h schemes so as to further decrease the need for bandwidth expansion over the wireless channel. Despite the interesting characteristics of CPM, the decoding of the received signal is particularly difficult in a multi-path wireless environment with no diversity. To provide some level of diversity, several authors have proposed to combine CPM with space-time block coding. A new family of codes for CPM, based on $$L^2$$ -orthogonality was recently introduced in Hesse et al. (IEEE Trans Commun 59(11): 3158---3166, 2011). These full rate codes achieve full diversity and a low decoding complexity. In this paper, we detail a non trivial extension of these $$L^2$$ -orthogonal space-time codes using multi-h signaling schemes. These new codes still achieve full diversity but a better spectral compactness by utilizing the available communication bandwidth more efficiently. Also, the decoding complexity is greatly decreased by using only one correlation filter bank for the detection of all transmitted signals.

Trellis Termination of Multi-h CPM and the Diophantine Frobenius Problem

This paper presents a method for terminating the phase trellis in multi-h continuous phase modulation (CPM). It is shown that tilted phase trellis for multi-h CPM signals is periodic and enables the representation of the multi-h CPM modulator as a cascade of a periodic recursive continuous phase encoder (CPE) and a phase modulator (PM). We then pose the problem of finding the minimum number of symbols that will terminate the phase trellis in a known state of the modulator and establish a connection of its solution to the Diophantine Frobenius Problem (FP). Analytical results are established for the existence of a terminating sequence and upper and lower bounds are derived on its length for arbitrary modulation parameters. We show that the trellis terminating symbols and their quantity depends upon the initial state of the encoder, the set of modulation indices, the CPE memory order, and the number of bits per modulated symbol. It is shown that required overhead for trellis termination can be significant for schemes with integer modulation indices.

Reduced-complexity detectors for Multi-h CPM in aeronautical telemetry

A two-index, partial response continuous-phase modulation (CPM) known as ARTM CPM was adopted for use in aeronautical telemetry in the IRIG 106 standard in 2004. This waveform was selected because it achieves approximately three times the spectral efficiency of PCM/FM, the legacy modulation in IRIG-106. However, the optimum receiver requires 128 real-valued matched filters and keeps track of the waveform state with a trellis of 512 states and 2048 branches. Various complexity-reducing techniques are applied and the resulting loss in detection efficiency is quantified. It is shown that the full 512-state trellis is not required to achieve desirable detection efficiency: two different 32-state configurations were found to perform within 0.05 dB of optimal; two different 16-state configurations were found to perform within 0.80 dB of optimal; and an 8-state configuration was found to perform within 1.05 dB of optimal. The analysis and simulation results show that to achieve a given state complexity, proper combination of two or more complexity-reducing techniques generally outperforms the use of a single complexity-reducing technique

New Results on the Spectral Analysis of Multi-h CPM Signals

This paper deals with the spectral analysis of multi-h continuous phase modulation (CPM) signals. A new solution to the problem is obtained by identifying an inner hidden Markov model in the CPM signal, which can be accomplished by expressing the modulator as the cascade of a sequential machine (SM), and a bank of PAM modulators. An in-depth study of the resulting Markov chain shows that it is both cyclostationary and reducible, and proper tools are identified to address these peculiarities. As a result, the multi-h CPM spectrum is expressed as a combination of Fourier transforms of portions of a CPM signal, thus allowing an efficient numerical evaluation through fast Fourier transforms (FFTs).

A New Performance Bound for PAM-Based CPM Detectors

It is well understood that the pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM) can lead to reduced-complexity detectors with near optimum performance. It has recently been shown that the PAM representation also extends to CPM schemes with multiple modulation indexes (multi-h CPM). In this paper, we present a detector for multi-h CPM which is based on the PAM representation. We also give an exact expression for the pairwise error probability for the entire class of PAM-based CPM detectors (single- and multi-h, optimal, and reduced-complexity) over the additive white Gaussian noise (AWGN) channel and show that this bound is tighter than the previously published bound for approximate PAM-based detectors. In arriving at this expression, we show that PAM-based detectors for CPM are a special case of the broad class of mismatched CPM detectors. We also show that the metrics for PAM-based detectors accumulate distance in a different manner than metrics for other CPM detectors. These distance properties are especially useful in applications with greatly reduced trellis sizes. We give thorough examples of the analysis for different single- and multi-h signaling schemes. We also apply the new bound in comparing the performance of PAM-based detectors with other reduced-complexity detectors for CPM.

Symbol and superbaud timing recovery in multi-h continuous-phase modulation

This paper is concerned with the estimation of two synchronization parameters that play a key role in multi-h continuous-phase modulation receivers-the ordinary symbol timing phase and the so-called superbaud timing phase. The recovery of symbol and superbaud timing is implemented by means of feedforward nondata-aided algorithms. The novelty of the proposed method is that it can be applied to any modulation format, either full or partial response, with binary or multilevel symbols and with arbitrary modulation indices.