Binary Continuous Phase Modulation Research Articles

Detection of Downlink Asynchronous NOMA With MSK-Type Signal

In this letter, motivated by the superiority of continuous phase modulation (CPM) signals, a binary CPM with modulation index 0.5 is considered into downlink symbol-asynchronous non-orthogonal multiple access (ANOMA) to enhance power and spectral efficiency, especially for resource-limited wireless communications. According to the maximum likelihood (ML) criterion, a Viterbi-based block-by-block detector (VB-BBD) is first proposed. Considering the asymptotics of Toeplitz matrices, a DFT matrix diagonalization-based symbol-by-symbol detector (DFTD-SSD) is also given. Finally, the detection complexity analysis is provided. Numerical results reveal the optimal time offsets with different modulation formats for a two-user system, and show that time asynchrony can bring about 3dB and 6dB performance gains at a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> . The relationship between BER performance and different power levels, frequency pulses, response lengths is also investigated.

Prefiltered Single-Carrier Frequency-Domain Equalization for Binary CPM over Shallow Water Acoustic Channel

The continuous phase modulation (CPM) technique is an excellent solution for underwater acoustic (UWA) channels with limited bandwidth and high propagation attenuation. However, the severe intersymbol interference is a big problem for the algorithm applying in shallow water. To solve this problem, an algorithm for prefiltered single-carrier frequency-domain equalization (PF-SCFDE) is presented in this paper. The regular whitening filter is replaced by a prefilter in the proposed algorithm. The output information sequence of this prefilter contains the forward information. To improve the performance, the output of the equalizer, combined with the forward information, is used to make the maximum likelihood estimation. The simulation results with minimum-shift keying and Gaussian-filtered minimum-shift keying signals over shallow water acoustic channels with low root mean square delay spread demonstrate that PF-SCFDE outperformed the traditional single-carrier frequency-domain equalization (SCFDE) by approximately 1 dB under a bit error rate (BER) of 10−4. A shallow sea trial has demonstrated the effectiveness of PF-SCFDE; PF-SCFDE had a reduction in BER of 18.35% as compared to the traditional SCFDE.

CPM modulation index estimation using LS and BLUE methods

SummaryIn this paper, we propose two methods for blind estimation of modulation index of full‐response binary continuous phase modulation (CPM) scheme. Most of previous works assume that there is a single sample for each symbol; thus, they cannot improve their performance when sampling rate is bigger than symbol rate. In our proposed methods, modulation index is estimated using samples of autocorrelation function of the received signal, which is a nonlinear function of modulation index. We propose Taylor expansion for approximating this nonlinear function by a linear function. Then, by choosing some samples of the autocorrelation function, we estimate the modulation index with the least square (LS) estimator. For decreasing estimation errors, in the second proposed method, we apply the statistical properties of the autocorrelation function estimation errors, to design the best linear unbiased estimation (BLUE) estimator. The numerical performance analysis in terms of mean‐squared error (MSE) and bit error rate (BER) shows that the proposed methods outperform the reference methods in accurate estimation of the modulation index.

An Improved Data-Aided Linear Estimator of Modulation Index for Binary CPM Signals

This letter considers the estimation of modulation index for binary continuous phase modulated (CPM) partial response signals. The actual value of modulation index in low-cost implementations turns out to be different than the nominal value used at the transmitter, leading to severe performance degradation. One possible solution is the deployment of an estimation algorithm at the receiver. The proposed data-aided best linear unbiased estimator (BLUE) is based upon a linear model approximation of the differential phase of pre-averaged CPM signal. Theoretical analysis of the variance of the estimator is presented to establish its improved performance. Simulation results also corroborate significant improvement of the proposed estimator at lower signal-to-noise ratio (SNR) values as compared to existing estimators, while retaining the linear bound performance at high SNRs. We show that the bit error rate (BER) performance at low SNRs is also improved when the modified BLUE estimator is deployed at the receiver.

Reconstruction of Finite-Alphabet Block-Sparse Signals From MAP Support Detection

This paper addresses finite-alphabet block-sparse signal recovery by considering support detection and data estimation separately. To this aim, we propose a maximum a posteriori (MAP) support detection criterion that takes into account the finite alphabet of the signal as a constraint. We then incorporate the MAP criterion in a compressed sensing detector based on a greedy algorithm for support estimation. We also propose to consider the finite-alphabet property of the signal in the bound-constrained least-squares optimization algorithm for data estimation. The MAP support detection criterion is investigated in two different contexts: independent linear modulation symbols and dependent binary continuous phase modulation (CPM) symbols. The simulations are carried out in the context of sporadic multiuser communications and show the efficiency of proposed algorithms compared to selected state-of-the-art algorithms both in terms of support detection and data estimation.

On the Estimation of Modulation Index for Binary Full Response CPM Signals

This letter considers a full response binary continuous phase modulation (CPM) scheme with a single modulation index. Two estimators are proposed for estimating the modulation index of the underlying CPM scheme. The first estimator is based on the method of moments (MoM) that makes use of the auto-correlation function of the received signal whereas the second estimator is the best linear unbiased estimator (BLUE), which is based on an approximate linear model. A closed-form expression of the modified Cramer-Rao bound (MCRB) is also derived. The MoM estimator is developed only for the rectangular phase shaping functions, while the MCRB expression and the BLUE estimator are applicable to signals with arbitrary phase shaping functions. Numerical performance analysis in terms of mean-squared error and bit-error rate shows that the method of moments estimator performs better at low signal-to-noise ratio (SNR), whereas the performance of the BLUE is close to MCRB at high SNR.

PAM Decomposition of Ternary CPM With Duobinary Encoding

In this paper, we investigate the pulse amplitude modulation (PAM) decomposition and the spectral efficiency of duobinary continuous phase modulation (CPM), where duo- binary CPM represents a ternary CPM whose symbols are generated using a duobinary encoder. We show that this precoder ensures a higher spectral efficiency compared with binary CPM and we propose a PAM decomposition characterized by the presence of a single main pulse and by uncorrelated pseudo-symbols for a half integer modulation index value for this ternary CPM. We show that shaped offset quadrature phase shift keying belongs to this CPM family and we provide a new reduced complexity trellis detector capable of reaching identical performance as the one introduced by Perrins as well as new linear detectors.

Low-Complexity Detection of Binary CPM With Small Modulation Index

Binary continuous phase modulation (CPM) with modulation index $h = 0.5$ can be approximated by a linear modulation, which leads to a low-complexity serial receiver. By reconstructing CPM signals generated with a small modulation index into equivalent CPM signals with modulation index $h = 0.5$ , a low-complexity detector (LCD) for binary CPM with small modulation index is proposed. The complexity of the resulting detector is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss. In addition, the detector can generate appropriate metrics for the soft decision decoding, which is desirable in a coded CPM system.

Binary CPMs With Improved Spectral Efficiency

We design new continuous phase modulation (CPM) formats which are based on the combination of a proper precoder with binary input and a ternary CPM. The proposed precoder constrains the signal phase evolution in order to increase the minimum Euclidean distance, and to limit the bandwidth expansion due to the use of a ternary CPM. The resulting schemes are highly spectrally efficient and outperform classical binary and quaternary formats in terms of coded and uncoded performance.

Binary Continuous Phase Modulations Robust to a Modulation Index Mismatch

We consider binary continuous phase modulation (CPM) signals used in some recent low-cost and low-power consumption telecommunications standard. When these signals are generated through a low-cost transmitter, the real modulation index can end up being quite different from the nominal value employed at the receiver and a significant performance degradation is observed, unless proper techniques for the estimation and compensation are employed. For this reason, we design new binary schemes with a much higher robustness. They are based on the concatenation of a suitable precoder with binary input and a ternary CPM format. The result is a family of CPM formats whose phase state is constrained to follow a specific evolution. Two of these precoders are considered. We will discuss many aspects related to these schemes, such as the power spectral density, the spectral efficiency, simplified detection, the minimum distance, and the uncoded performance. The adopted precoders do not change the recursive nature of CPM schemes. So these schemes are still suited for serial concatenation, through a pseudo-random interleaver, with an outer channel encoder.

Robust Detection of Binary CPMs With Unknown Modulation Index

We consider soft-output detection of a binary continuous phase modulation (CPM) generated through a low-cost transmitter, thus characterized by a significant modulation index uncertainty, and sent over a channel affected by phase noise. The proposed detector is designed by adopting a simplified representation of a binary CPM signal with the principal component of its Laurent decomposition and is obtained by using the framework based on factor graphs and the sum-product algorithm. It does not require an explicit estimation of the modulation index nor of the channel phase and is very robust to large uncertainties of the nominal value of the modulation index. Being soft-output in nature, this detector can be employed for iterative detection/decoding of practical coded schemes based on a serial concatenation, possibly through a pseudo-random interleaver, of an outer encoder and a CPM modulation format.

Simplified receiver design for STBC binary continuous phase modulation

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.

Doubly Iterative Equalization of Continuous-Phase Modulation

In this paper, a doubly iterative receiver is proposed for joint turbo equalization, demodulation, and decoding of coded binary continuous-phase modulation (CPM) in multipath fading channels. The proposed receiver consists of three soft-input soft-output (SISO) blocks: a front-end soft-information-aided minimum mean square error (MMSE) equalizer followed by a CPM demodulator and a back-end channel decoder. The MMSE equalizer, combined with an a priori soft-interference canceler (SIC) and an a posteriori probability mapper, forms a SISO processor suitable for iterative processing that considers discrete-time CPM symbols which belong to a finite alphabet. The SISO CPM demodulator and the SISO channel decoder are both implemented by the a posteriori probability algorithm. The proposed doubly iterative receiver has a central demodulator coupled with both the front-end equalizer and the back-end channel decoder. A few back-end demodulation/decoding iterations are performed for each equalization iteration so as to improve the a priori information for the equalizer. As presented in the extrinsic information transfer (EXIT) chart analysis and simulation results for different multipath fading channels, this provides not only faster convergence to low bit error rates, but also lower computational complexity.

A New Finite Series Expansion of Continuous Phase Modulated Waveforms

The Laurent Decomposition expresses any binary single-h continuous phase modulated (CPM) signal as the summation of a finite number of pulse amplitude modulated (PAM) waveforms, and the resulting signal space is so constructed that the waveform can usually be synthesized with a reasonable degree of accuracy by using only the ldquomainrdquo component pulse. This derivation has been very useful for reduced complexity demodulation of binary CPM signals. Subsequent to Laurent's work, it was shown that commensurate expressions could be obtained for multilevel and multi-h CPM, but with an exponential increase in the total number of PAM component pulses in the signal representation. In this paper, we show that by expressing a CPM signal in its equivalent binary multi- form, we can derive a generalization of Laurent's result for the general class of such waveforms that use noninteger modulation indices. In this new signal representation, there is a clearly identifiable data-dependent ldquomainrdquo expansion pulse during each symbol interval which carries most of the signal energy. As in the Laurent Decomposition, the number of terms in this decomposition is only dependent on the CPM signal memory.

Space-time trellis code design with binary CPM

Binary continuous phase modulation (CPM) is considered with space-time trellis codes (STTCs) for multiple-input multiple-output systems. Single-h CPM with rectangular, raised cosine and half cycle sinusoid is considered. The upper bound on the minimum product distance of this signalling scheme is determined over a quasi-static Rayleigh fading channel. Based on the rank and determinant criterion, best STTC/CPM combinations are identified for two transmit and an arbitrary number of receive antennas.

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.

Reduced complexity receivers for layered space-time CPM

Layered space-time (LST) transmissions employing continuous phase modulations (CPM) are well motivated for both bandwidth- and power-limited multiantenna communications. However, one of the major challenges for LST-CPM is the high complexity it incurs with maximum likelihood (ML) detection. In this paper, we develop reduced complexity LST-CPM receivers. First, we consider single antenna systems. Specifically, we study a reduced complexity Viterbi receiver for binary CPM. Based on this design, we introduce differential encoding for a class of CPM signals and analyze its performance gain both theoretically and with simulations. Second, we focus on multiantenna LST systems with minimum shift-keying (MSK)-type modulations. With group nulling-canceling (NC) and low-complexity linear equalization, we convert a coded multiuser detection problem into an uncoded one with small equalization loss. We also find that the combination of sphere decoding with hard-decision iterative processing is effective in boosting performance with a controllable complexity increase. Both analytical and simulated performance confirm that the novel LST-MSK receiver exhibits markedly improved performance relative to conventional NC detectors with moderate complexity increase.

Supplementary Proof for “Exact and Approximate Construction of Digital Phase Modulations by Superposition of AMP” by P. A. Laurent

In this letter, we supplement the derivation in Laurent's paper by mathematically proving that combining binary continuous phase modulation (CPM) signals in different bit durations results in the decomposed CPM expression consisting of a set of continuous amplitude-modulated pulse functions.

Cyclic spectral analysis of continuous-phase modulated signals

Continuous-phase modulated (CPM) signals play a prominent role in modern communication systems due to their desirable constant-modulus property and the ability to control their power and bandwidth efficiencies. Popular CPM signals include the classical minimum-shift keyed (MSK) signal, the LREC family of signals also known as continuous-phase frequency-shift-keyed (CPFSK) signals, and Gaussian MSK, which is used in state-of-the-art GSM and PCS mobile communication systems. CPM signals, like virtually all man-made communication signals, are known to exhibit cyclostationarity, which implies that their probabilistic parameters, such as mean, second moment, and higher order cumulants, are almost-periodic functions of time. A novel representation of CPM signals as a sum of PAM signals is presented for both integer and noninteger modulation index cases. Then, the Nth-order cyclostationarity properties of binary CPM signals are derived in terms of Nth-order temporal and spectral moment and cumulant functions. Moreover, the case of M-ary CPM signals is briefly addressed. The results are illustrated with simulations involving MSK, LREC, and GMSK signals.

Blind self-noise-free frequency detectors for a subclass of MSK-type signals

Frequency offset due to Doppler shift and/or oscillator instabilities degrade the receiver performance. A family of frequency detectors for frequency offset estimation and compensation in digital receivers is introduced. The proposed detectors are best suited for frequency offset compensation of a subclass of binary continuous phase modulation with h=1/2 that includes modulation schemes with nonnegative frequency pulses. For the considered modulation schemes, the modulation-induced self-noise term is absent from the variance of the frequency estimate. The estimator is nondata- and nontiming-aided and its estimation range is either half or a quarter of the bit rate (R). With larger frequency offsets, the estimators that have a /spl plusmn/R/2 estimation range introduce a frequency ambiguity of R that is of no relevance to the performance of a differential detection based receiver.