Partial Response Continuous Phase Modulation Research Articles

Non-coherent Phase Compensated Sphere Detector for Partial Response CPM

Non-coherent Phase Compensated Sphere Detector for Partial Response CPM

Partial response continuous phase modulation with a prolate spheroidal wave function for compass system in the S-band

Continuous phase modulation (CPM) has the characteristics of high power efficiency, spectral efficiency, and less out-of-band radiation, which is very suitable for the Compass S-band (2483.5–2500 MHz) with limited power and bandwidth. However, as more and more navigation systems share the S-band, the mutual interference between different systems is gradually increasing, and the compatibility of CPM signals with rectangular or raised cosine pulses needs to be further improved. To enhance the navigation performance and compatibility of current CPM candidate signals, we propose to apply continuous phase modulation with prolate spheroidal wave function (CPM-PSWF) to S-band navigation. The proposed modulation scheme selects PSWF with excellent time-frequency energy aggregation and flexible time-bandwidth product as the frequency pulse function of CPM. Then, the influence of key modulation parameters such as M, L, h, and C on CPM-PSWF power spectral density is analyzed, and a specific partial-response CPM-PSWF signal is proposed as the S-band candidate navigation signal. Finally, the navigation performance evaluation criteria are derived, and the proposed signal scheme and existing candidate schemes are comprehensively evaluated. Theoretical analysis and simulation results indicate that compared with CPM with BM2RC(8), cos-phase binary offset carrier (BOCc(4,4)), sin-phase binary offset carrier (BOCs(4,4)), minimum shift keying-BOCs (MSK-BOCs(4,4)) and binary offset carrier (BPSK(8)), the proposed signal scheme not only delivers exceptional spectral performance but also exhibits superior performance in code tracking accuracy and multipath suppression. In addition, in the acquisition and tracking phase, compared with other candidate signals except for BOCc(4,4), the mutual interference between the proposed signal scheme and most S-band signals is the lowest, which is easier to realize the compatibility of the Compass system with IRNSS, Galileo, and Globalstar systems.

Non-coherent multi-symbol detection of PR-CPM for deep space relay satellites with physical-layer network coding

The demand for wireless spectrum and data transmission has increased dramatically with the rapid growth of deep-space exploration and communication. The satellite relay communication is an essential technique to solve the issues above. The method of combining Physical-layer Network Coding (PNC) with Continuous Phase Modulation (CPM) on relay satellites can improve communication efficiency and perform the collection and transmission of space data effectively. Partial-Response CPM (PR-CPM) signals possess excellent spectrum and power characteristics and are suitable for deep-space communications with limited bandwidth and massive data transmission. In this paper, a partial response non-coherent multi-symbol detection algorithm is proposed based on the Maximum-Likelihood principle. The proposed algorithm fully utilizes the memory properties of PR-CPM signals and makes decisions on specified symbols by observing a number of symbols each time. Simulation results indicate that the performance gain under the Bit Error Rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> is about 2 dB when 5 symbols are inspected, compared with the case where the observation length is 3.

Wideband partial response CPM demodulation via multirate frequency transformations and decision feedback equalization

■■■Continuous phase modulation (CPM) is a popular frequency modulation technique used in mobile communications due to its power efficiency and constant modulus properties. Conventional narrowband CPM demodulation employs the Viterbi algorithm after phase demodulation and requires that the phase states be rational and contain additive white noise. The complexity of the Viterbi approach further increases with the number of phase states. Frequency discrimination approaches that estimate the instantaneous frequency provide a simpler suboptimal approach but are primarily for full response CPM and are not well known for wideband partial response CPM.In this paper, we investigate an approach that combines multirate frequency transformations for wideband CPM demodulation with decision feedback equalization for memory removal. This combined approach avoids the problems of complexity and restrictive requirements of the Viterbi approach. Simulation results are used to demonstrate the validity of the combined approach.

Adaptive Coded Modulation Based on Continuous Phase Modulation for Inter-Satellite Links of Global Navigation Satellite Systems

The inter-satellite links (ISLs) will play an increasingly important role in improving the service performance and enhancing the survivability of global navigation satellite systems. The current signal transmission schemes in ISLs primarily employ constant coded modulation to guarantee a high reliable communication even for the worst channel status, and the adaptive coded modulation (ACM) schemes, such as binary low-density parity-check (LDPC) coded quadrature phase shift keying or $M$ -ary quadrature amplitude modulation ( $M$ QAM) have been introduced to improve spectral efficiency over inter-satellite channels recently. However, the phase discontinuity of the above modulations will widen frequency spectrum and cause the high-voltage transient of transmitter, and the $M$ QAM signal through high power amplifier onboard will result in non-linear distortion because of non-constant envelope. In this paper, the association between non-binary LDPC codes and high-order partial response continuous phase modulation with iterative detection is presented as the source of ACM schemes, which effectively inhibits information loss in the process of conversion between bit and symbol probabilities. According to the constellation of BeiDou navigation satellite system in 2020, an open loop ACM control mechanism based on inter-satellite distance is introduced, and implemented by the target bit error rate (BER) and the maximum ratio between the throughput and bandwidth algorithms. Simulation results show that the proposed ACM scheme can reduce the BER and improve the power efficiency in the requirement of target BER limit, and provide a higher spectral efficiency under the same transmitting power compared with the existing ACM scheme.

Estimation of Modulation Index for Partial Response CPM Signal

Continuous phase modulation (CPM) is a power and bandwidth efficient modulation scheme used in cellular, personal, and satellite communications among other applications. If the modulation index of the CPM waveform used by the transmitter is unavailable at the receiver, serious performance degradation may occur. This paper investigates the problem of modulation index estimation for partial response continuous phase modulation schemes. Specifically, we propose two novel estimators for the CPM signal observed in an additive white Gaussian noise channel. A non-data aided method of moments (MoM) estimator based upon the fourth-order cumulants and a data-aided best linear unbiased estimator (BLUE) based upon an approximate linear phase model of the received CPM signal have been proposed. Modified Cramer-Rao lower bound is derived for the partial response CPM schemes to assess the performance of the estimators. We also perform numerical simulations to compare the mean-squared error (MSE) performance of the proposed MoM and BLUE estimators with previously proposed estimators in the literature. It is shown that the MoM estimator exhibits good MSE performance at low signal-to-noise ratio (SNR) while the BLUE estimator performs very well at high SNRs. Moreover, the proposed estimators have lower complexity than existing methods and are based upon non-iterative algorithms.

Improved iterative convergence method in Q-ary LDPC coded high order PR-CPM

The Q-ary low-density parity-check (LDPC) coded high order partial response continuous phase modulation (PR-CPM) with double iterative loops is investigated. This scheme shows significant improvements in power and bandwidth efficiency, but at the expense of long iterative decoding delay and computational complexity induced by the improper match between the demodulator and the decoder. To address this issue, the convergence behavior of Q-ary LDPC coded CPM is investigated for the Q=2 and Q>2 cases, and an optimized design method based on the extrinsic information transfer chart is proposed to improve the systematic iterative efficiency. Simulation results demonstrate that the proposed method can achieve a perfect tradeoff between iterative decoding delay and bit error rate performance to satisfy real-time applications.

Dynamic iteration stopping algorithm for non-binary LDPC-coded high-order PRCPM in the Rayleigh fading channel

This paper mainly studies the association between non-binary low-density parity-check codes and high-order partial response continuous phase modulation, which prevents information loss in the mutual conversion of bit and symbol probabilities. Although the iterative detection and decoding technique applied in this system can obtain good performance/complexity tradeoff, the iterative process still encounters the problems of positive feedback and relatively large decoding delay, similar to other iterative coded modulation systems. The inhibitory effects of different extrinsic information exchange methods on positive feedback under different signal-to-noise ratio (SNR) conditions are investigated in this work to address this issue. Two dynamic iterative stopping algorithms, namely, cross entropy and hard decision aided combined with weighted extrinsic information exchange for cases with medium and high SNRs, are then proposed. Extrinsic information exchange between the demodulator and the decoder is conducted in the two algorithms through weighted processing. Iterative detection is subsequently performed based on two stopping criteria of dynamic iterative decoding. Theoretic analysis and simulation results for the Rayleigh fading channel show that the combination of weighted extrinsic information exchange and the two dynamic iterative stopping algorithms effectively resists positive feedback and improves the convergence of iterative detection and bit error rate performance. Such a combination also reduces the average iteration number to improve the real-time performance of iterative detection and decoding.

A low complexity detection/decoding algorithm for NB-LDPC coded PRCPM system

This paper studies the combination of non-binary low-density parity-check (NB-LDPC) codes and M-ary partial response continuous phase modulation (PRCPM). A low-complexity joint detection/decoding algorithm is proposed, which is referred to as the Max-Log-MAP/X-EMS algorithm. In this joint algorithm, the CPM detector is implemented by the Max-Log-MAP algorithm while the LDPC decoder is implemented by the extended min-sum (EMS) algorithms. Three kinds of EMS algorithms, including D-EMS, T-EMS, and M-EMS algorithms, are compared, which are referred to as X-EMS algorithm for convenience. Simulation results show that the Max-Log-MAP/X-EMS algorithm performs as well as the traditional iterative detection/decoding algorithm based on the BCJR algorithm and the q-ary sum–product algorithm, but with lower complexity. In addition, comparison of the proposed NB-LDPC coded PRCPM system with the eBCH coded PRCPM system is given, which shows the performance advantages of our system.

A Timing False Lock Detector for M-ary Partial-Response CPM

We consider a timing false lock detector for continuous phase modulation (CPM), which is needed for M-ary partial-response CPM schemes. Our approach maintains a running count of successive, simple, short-term false lock decisions, rather than conducting a single, long-term decision. Using a Markov chain model, we show that our scheme can provide accurate and rapid synchronization for capacity-approaching CPMs that operate at very low signal-to-noise ratios.

An All Digital Implementation of Constant Envelope: Bandwidth Efficient GMSK Modem using Advanced Digital Signal Processing Techniques

Gaussian Minimum Shift Keying (GMSK) has been the most common modulation format belonging to the class of partial response Continuous Phase Modulation (CPM) scheme. It is primarily adopted in the GSM standards (B=0.3) for land mobile radio communication systems because of its high bandwidth efficiency and constant envelope modulation characteristics. The focus of this paper is the design of the demodulator wherein we demonstrate an all digital implementation of sub-optimal synchronization techniques for a GMSK modem based on two Laurent Amplitude modulation pulse (AMP) streams approximation representing the matched filter. In this all digital implementation, we perform a joint estimation of the symbol timing and carrier offset wherein the symbol timing is performed using interpolation techniques.

A wireless MIMO CPM system with blind signal separation for incoherent demodulation

Abstract. A multiple-input multiple-output (MIMO) wireless transmission system with continuous phase modulation (CPM) is considered. A novel MIMO CPM receiver with incoherent modulation is presented. The incoherent demodulation of CPM allows an uncomplicated handling of a frequency offset compared to coherent approaches requiring exact knowledge of the carrier frequency. Blind signal separation (BSS) is applied in the proposed MIMO CPM receiver to separate the signals without any knowledge of the MIMO channel. The BSS permits the demodulation of each separated signal by an incoherent CPM demodulator. For bandwidth efficient transmission partial response CPM and non-binary modulation is applied. The applicability of the proposed system is verified by simulation results.

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

An orthogonal space-time coded partial response CPM system with fast decoding for two transmit antennas

In this paper, an orthogonal space-time coded partial response continuous phase modulation (OST-PCPM) system with two transmit antennas is proposed. It can achieve full diversity with arbitrary inner memory length and phase smoothing functions of CPM schemes. Based on the orthogonality between signals from two transmit antennas and the proposed differential encoding scheme, a fast decoding algorithm is developed for some special cases. Simulation results show that this scheme can provide much better performance with a reasonable complexity, as compared to one transmit antenna CPM scheme. We also give a suboptimal decoding method that provides a tradeoff between complexity and performance.

Frequency-domain equalization for continuous phase modulation

Single-carrier frequency-domain equalization (SC-FDE) is proposed for continuous phase modulation (CPM). Two different discrete representations of the CPM signal are obtained. One is an orthogonal representation obtained from the Gram-Schmidt orthonormalization procedure, and the other is obtained from Laurent's decomposition for binary CPM. The methodology for maintaining phase continuity with a cyclic guard interval is presented. Various optimal and suboptimal reduced-complexity approaches are suggested for SC-FDE of CPM signals. General full- and partial-response CPM waveforms, and specific examples of minimum-shift keying (MSK) and Gaussian MSK (GMSK) with BT=0.3 are investigated. Simulation results show that SC-FDE for CPM is an effective approach for CPM on channels having long impulse responses.

Blind equalization of turbo trellis-coded partial-response continuous-phase modulation signaling over narrow-band Rician fading channels

In this paper, a blind maximum-likelihood channel estimation algorithm is developed for turbo trellis-coded/continuous-phase modulation (TTC/CPM) signals propagating through additive white Gaussian noise (AWGN) and Rician fading environments. We present CPM for TTC signals, since it provides low spectral occupancy and is suitable for power- and bandwidth-limited channels. Here, the Baum-Welch (BW) algorithm is modified to estimate the channel parameters. We investigate the performance of TTC/CPM for 16-CPFSK over AWGN and Rician channels for different frame sizes, in the case of ideal channel state information (CSI), no CSI, and BW estimated CSI.

Partial response CPM in satellite mobile systems

It is known that Gaussian minimum shift keying (GMSK) is an attractive signaling technique in mobile communications. In this study, it is demonstrated using partial response raised cosine (ZRC) modulation that other partial-response continuous phase modulation (PR-CPM) techniques can perform better than GMSK in a mobile system. ZRC signals are analyzed and compared with GMSK signals in a mobile channel. Differential phase detection (DPD) and limiter discriminator detection (LDD) receivers with decision feedback are separately considered for the detection of the two types of signals. In case of ZRC signals, the delay of the DPD receiver, and the sampling instant of the LDD receiver are selected to minimize the error probability. Numerical results are presented for land mobile, satellite mobile and Gaussian channels at different bandwidths and Doppler shifts. It is shown that ZRC signals can perform better than GMSK signals at the same bandwidth.

Adaptable Viterbi detector for a decomposed CPM model over rings of integers

A novel, practical and flexible way of implementing continuous phase modulation (CPM) using a decomposed model and a Viterbi detector is presented. The decomposed CPM modulator, comprising a continuous phase encoder (CPE) and a memoryless modulator (MM), is implemented and can be concatenated with a ring convolutional encoder (CE) such that the detector may be readily adapted to the ring of integers over which the CE/CPE operates. A partial-response CPM system is simulated over additive white Gaussian noise (AWGN) and Rayleigh flat fading (RFF) channels, and results, in terms of the bit error rate (BER) against the signal to noise ratio (SNR), are presented, discussed and evaluated.

Multiple-symbol noncoherent decoding of uncoded and convolutionally coded continuous phase modulation

Recently, a method for combined noncoherent detection and decoding of trellis-codes (noncoherent coded modulation) has been proposed, which can practically approach the performance of coherent detection. Here, we successfully apply the technique to the detection of Continuous Phase Modulation (CPM), coded or uncoded. Both full and partial response CPM schemes with arbitrary modulation index are considered. This method is based on multiple-symbol observations, such that the observations are time-overlapped. The results show that most CPM schemes require short observations to achieve almost the same power efficiency as optimally detected coherent CPM. Compared to the previously proposed methods for noncoherent detection that can approach the coherent performance, the required observation length is much shorter and also the decoding complexity is much lower. A new trellis diagram for noncoherent CPM is suggested for simplifying the analysis and the decoder structure. The error performance for uncoded CPM is evaluated by using the union bound technique applied on the symbol-difference trellis diagram. For the coded case a pair-state trellis is required. Very efficient sub-optimal decoding algorithms with very small degradation may implement the noncoherent decoder. The performance achieved with these algorithms is demonstrated by simulations.

Coded and uncoded CPM schemes over rings of integers for AWGN and Rayleigh fading channels.

Coded and uncoded modulation schemes based on continuous phase modulation (CPM) over rings of integers are investigated. A baseband modulator utilising a decomposed model of CPM is used at the transmitter and a Viterbi soft-decision decoder is employed at the receiver. The performances of a number of partial-response CPM schemes are investigated when operating over an additive white Gaussian noise (AWGN) channel and Rayleigh flat fading (RFF) channel. The simulation results obtained are shown to compare favourably with theoretical bounds.