Equalization for continuous phase modulation over frequency-selective fading channels

This paper presents an equalization algorithm for continuous phase modulation （CPM） over frequency-selective channels. A specific training sequence is first embedded in each data packet. By recursive least-squares （RLS） estimation, the channel information parameters can be acquired, and a fractionally Simulation results show that the proposed algorithm can acquire the spaced equalizer performs joint decoding and equalization. channel information parameters rapidly and accurately, and that the fractionally spaced equalizer can eliminate the intersymbol interference （ISI） effectively, and is not sensitive to timing inaccuracy, so this algorithm can be exploited for demodulation system in burst mode.

SERIALLY CONCATENATED CONTINUOUS PHASE MODULATION WITH REDUCED ITERATIVE DEMODULATION AND DETECTION

A reduced state Soft Input Soft Output (SISO) a posteriori probability algorithm for Seri-ally Concatenated Continuous Phase Modulation (SCCPM) is proposed in this paper. Based on the Reduced State Sequence Detection (RSSD),it has more general form compared with other reduced state SISO algorithms. The proposed algorithm can greatly reduce the state number,thus leads to the computation complexity reduction. It also minimizes the degradation in Euclidean distance with decision feedback in the reduced state trellis. Analysis and simulation results show that the perform-ance degradation is little with proper reduction scheme.

Improved dichotomous search frequency offset estimator for burst-mode continuous phase modulation

A data-aided technique for cartier frequency offset estimation with continuous phase modulation （CPM） in burst- mode transmission is presented. The proposed technique first exploits a special pilot sequence, or training sequence, to form a sinusoidal waveform. Then, an improved dichotomous search frequency offset estimator is introduced to determine the frequency offset using the sinusoid. Theoretical analysis and simulation results indicate that our estimator is noteworthy in the following aspects. First, the estimator can operate independently of timing recovery. Second, it has relatively low outlier, i.e., the minimum signal-to-noise ratio （SNR） required to guarantee estimation accuracy. Finally, the most important property is that our estimator is complexity-reduced compared to the existing dichotomous search methods： it eliminates the need for fast Fourier transform （FFT） and modulation removal, and exhibits faster convergence rate without accuracy degradation.

A reduced state SISO iterative decoding algorithm for serially concatenated continuous phase modulation

In this paper, serially concatenated continuous phase modulation （SCCPM） system is analyzed and a reduced state soft input soft output （SlSO） a posteriori probability algorithm is proposed. Based on the reduced state sequence detection （RSSD）, it has the more general form compared with other reduced state SISO algorithms. The proposed algorithm can greatly reduce the state number, thus leads to the computation complexity reduction. It also minimizes the degradation in Euclidean distance with decision feedback in the reduced state trellis. Analysis and simulation results show that the performance degradation is little with proper reduction scheme.

CNN demodulation model with cascade parallel crossing for CPM signals

The continuous phase modulation(CPM)technique is widely used in range telemetry due to its high spectral efficiency and power efficiency.However,the demodulation performance of the traditional maximum likelihood sequence detection(MLSD)algorithm significantly deteriorates in non-ideal synchronization or fading channels.To address this issue,this work proposes a convolutional neural network(CNN)called the cascade parallel crossing network(CPCNet)to enhance the robustness of CPM signals demodulation.The CPCNet model employs a multiple parallel structure and feature fusion to extract richer features from CPM signals.This approach constructs feature maps at different levels,resulting in a more comprehensive training of the model and improved demodulation performance.Simulation results show that under Gaussian channel,the proposed CPCNet achieves the same bit error rate(BER)performance as MLSD method when there is no timing error,but with 1/4 symbol period timing error,the proposed method has 2 dB demodulation gain compared with CNN and convolutional long short-term memory deep neural network(CLDNN).In addition,under Rayleigh channel,the BER of the proposed method is reduced by 5%-87%compared to that of MLSD in the wide signal-to-noise ratio(SNR)region.

SYMMETRIC INFORMATION RATE OF CPM AND OPTIMAL DETECTOR DESIGN

This paper first calculates numerically the Symmetric Information Rate (SIR) of Cotinuous Phase Modulation (CPM) schemes over Additive White Gaussian Noise (AWGN) channel, modeling CPM and channel as a Memory-less Modulator (MM) plus a Markov Finite State Channel (FSMC), then proposes an optimal detector, which is of BCJR based Decision Feedback Detector (DFD) but non-iterative. It can achieve the SIR as the sequence length approaches infinity while the complexity is extremely low. Finally, both theoretic proof and numerical simulation are performed to show the op- timality. Simulation results show that it nearly achieves the theoretic bound and outperforms the Viterbi Detector (VD) with 2dB in low Eb/N0.

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.

Low-complexity detection based on maximum cumulative measure and Laurent decomposition for multi-h CPM signal

In order to solve the problem of high computational complexity in demodulation for multi-h continuous phase modulation(CPM) signal, a maximum cumulative measure combing with the Laurent decomposition(MCM-LD) scheme is proposed to reduce the number of the grid states and the required number of matched filters, which degrades the demodulation complexity at the receiver.The advanced range telemetry(ARTM) Tier Ⅱ CPM signal is adopted to evaluate the performance in simulation. The results show that, compared with the traditional maximum likelihood sequence detection(MLSD), MCM-LD can respectively reduce the numbers of grid states and matched filters from 256 to 32 and 128 to 48 with negligible performance loss, which effectively degrades the computational complexity for multi-h CPM signal.

Maximum-likelihood Block Detection for CPM Signals

This paper deals with noncoherent Maximum-likelihood Block Detection (MLBD) of uncodedCPM signals (full response CPM and parrtal response CPM) over an additive white noise (AWGN)channel. Based on the work of W. Osborne and M. Simon ,this paper generalizes Maximum-likelihoodBlork Detection. Then we focus on the error performance of MLBD, which is named one-symbol MLBDand N-symbol MLBD respectively. By computer simulation of CPFSK, 1RC and 2RC , it is found thatMLBD can improve the error performance over traditional noncoherent detection.