Continuous Phase Modulation Systems Research Articles

Modular Arithmetic CPM for SDR Platforms

This brief presents a new Continuous Phase Modulation (CPM) module for multi- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula> transmission based on modular arithmetic processing. It is well known that CPM systems are sensitive to changes in the modulation index, which is implied when fixed-point format is used in the hardware implementation. In this scenario, modular arithmetic allows a more accurate signal processing regarding SQNR performance. This proposal has been shown to improve performance compared to other state-of-the-art methods, even when the modulation indices do not have an exact representation in a given fixed-point format. Due to its highly reconfigurable architecture, this hardware block is suitable for Software Defined Radio (SDR) platforms. A complete digital architecture is also provided. Implementation results show that the new proposal have clear advantages in terms of hardware resources and operating frequency against other CPM transmitters in open-literature.

CPM Training Waveforms With Autocorrelation Sidelobes Close to Zero

Continuous phase modulation (CPM) plays an important role in wireless communications due to its constant envelope signal property and tight spectrum confinement capability. Although CPM has been studied for many years, CPM training waveforms having autocorrelations with zero sidelobes have not been reported before, to the best of our knowledge. Existing works on the CPM system design mostly assume that the channel fading coefficients are either perfectly known at the receiver or estimated using random CPM training waveforms. In this correspondence paper, we propose a novel class of CPM training waveforms displaying autocorrelation sidelobes close to zero. The key idea of our construction is to apply differential encoding to Golay complementary pair having perfect aperiodic autocorrelation sum properties.

Performance analysis of adaptive space-time coded systems with continuous phase modulation

In modern wireless communications, it is getting urgent to make a better trade-off between reliability and effectiveness in wireless systems. In fact, the use of coded cooperation (e.g. space time coding) in multiple input and multiple output (MIMO) system has drawn much attention for this purpose. However, it needs to be further investigated how to select the space time codes (STC) adaptively. On the other hand, continuous phase modulation (CPM) is a promising technology for its merits of power and spectrum efficiency. This study is to consider adaptive space time coded CPM systems. The criterion of adaptive switching is based on the Frobenius norm and the thresholds between STC schemes. Analysis and simulation are made to the proposed system in terms of frame error rate and data rate.

Coherent RAKE Receiver for CPM-Based Direct Sequence Spread Spectrum

Direct sequence spread spectrum (DSSS) using continuous phase modulation (CPM) inherits the techniques’ benefits, constant envelope, anti-interference, and spectral efficiency. To get diversity gains over a Rayleigh-fading multipath channel as in conventional direct sequence spread-spectrum binary phase shift keying (DSSS-BPSK) system, a new class of coherent RAKE receivers is proposed in this work. By introducing chip branch metric to the receiver scheme, despreading and data detection can be done meanwhile based on Maximum Likelihood Sequence Detection (MLSD). Compared to the conventional RAKE receiver which sums decision metrics symbol-by-symbol, the proposed DSSS-CPM RAKE receiver accumulates symbol branch metric increments over every phase state of multiple paths after chip phase synchronization. Numerical results show that DSSS-CPM using the synchronous despreading and demodulation algorithm has no performance loss compared to CPM system that employs MLSD algorithm under the same test conditions. Moreover, the proposed RAKE receiver outperforms conventional RAKE receiver and achieves a remarkable diversity gain of bit error rate (BER) under the Rayleigh-fading multipath channel.

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.

Advanced continuous phase modulation for high mobility communications

This paper focuses on the design of continuous phase-modulated systems and simplified receiver for high-mobility wireless communications. A class of spectrally efficient coded modulation systems is proposed and analyzed in terms of Euclidean distance and spectral efficiency. Moreover, the simplified detector based on mismatched receiver is designed to reduce the detection complexity exponentially for partial response systems. To deal with the fast time-varying channels without channel state information, a class of noncoherent detection algorithms for continuous phase modulation systems is developed to offer near-coherent performance. The proposed system is assessed over both the additive white Gaussian noise and fast-fading channels. Numerical and simulated results show that the proposed system offers not only high spectral efficiency but also near-optimum performance over fast time-varying scenarios.

Modified Cramér-Rao Bounds for Continuous-Phase Modulated Signals

We consider the estimation of signal amplitude, time offset, and the parameters of a polynomial-phase signal from a continuous-phase modulated (CPM) signal that contains both unknown data symbols and known pilot symbols. Transformation of the polynomial-phase signal into an orthogonal basis allows us to derive the modified Cramér-Rao bounds (MCRB) for the problem of vector-parameter estimation in closed form. Numerical results demonstrate that the achievable estimation accuracy significantly depends on the burst structure and highlight the need for properly designed pilot sequences. Since our bounds are easy to evaluate, they can aid the design of pilot and burst configuration for CPM systems.

Encoding Performance of Orthogonal Space-Time Coded Continuous Phase Modulation System

The orthogonal space-time coded continuous phase modulation (OST-CPM) system shows attractive performance over fading MIMO channels. In this paper, the Chernoff bound on pair-wise error probability (PWEP) is studied for two transmit antennas over spatially correlated quasi-static Rayleigh-fading channel. The maximum likelihood sequence detection (MLSD) algorithm is applied to the OST-CPM system. Approximate bound for high signal-to-noise ratio (SNR) is derived to evaluate the encoding performance in correlated channel. The effects of correlation coefficient matrices on the coding performance are simulated. Both analytical and simulation results show that the coding performance of this system decreases as the fading coefficients between the antennas increases. And the penalty on the coding performance increases a lot in fully correlated channel. DOI: http://dx.doi.org/10.11591/telkomnika.v11i5.2469

Orthogonal-Like Space–Time-Coded CPM Systems With Fast Decoding for Three and Four Transmit Antennas

The Alamouti orthogonal space-time block code for two transmit antennas was designed primarily for QAM and PSK modulations, and we have previously generalized it for the continuous phase modulation (CPM), denoted as OST-CPM, by maintaining the orthogonality (for the fast ML decoding/demodulation) and the phase continuity of two signals from two transmit antennas. In this paper, we design orthogonal-like space-time coded CPM systems for three and four transmit antennas based on orthogonal and quasi-orthogonal space-time codes. Although the signals from transmit antennas in the proposed orthogonal-like space-time coded CPM systems are not orthogonal, the fast decoding/demodulation is maintained like the two transmit antenna case. Simulation results show that the performance of the proposed orthogonal-like space-time coded CPM systems for four transmit antennas is much better than that of the OST-CPM systems for two transmit antennas.

Performance analysis for convolutional coded CPM over rings

In this paper, we present upper bounds on the symbol error probability for convolutional encoded continuous phase modulation (CPM) over rings with maximum likelihood sequence detection (MLSD). Both coded CPM schemes with and without feedback from the CPM encoder to the ring convolutional encoder are considered. The bounds are based on the transfer function technique. The paper contribution is in the development of the analytical upper bound on the symbol error probability for the investigated system. The bound can be used as a tool to analyze and design ring convolutional encoded CPM systems.

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.

On Walsh Filtering Method for Decoding of CPM Signals

Walsh filtering has been used as a method to reduce receiver complexity in several coding and modulation systems, especially in continuous phase modulation systems. In this paper, we show that its lowpass filtering ability is poor and alias components arising from an adjacent channel can significantly degrade the maximum-likelihood decoding. Instead, a lowpass filtering method is more robust against adjacent channel interference and thus gives less decoding errors than the Walsh filtering method.

New lower bounds on symbol error probability for MLSD of CPM signals on AWGN channel

Symbol error probability bounds for maximum likelihood sequence detection (MLSD) of continuous phase modulation (CPM) signals are studied. The calculation of the upper bound is based on the transfer function technique, which has been generalised. A new method for constructing a lower bound for CPM systems is proposed. From numerical comparisons, it can be seen that the proposed algorithm can substantially improve the lower bound compared to previous approaches by considering the entire set of transmitted data sequences and not only the worst case. This generalised algorithm may be applied to any system that can be described as a finite-state machine.

Soft-output demodulator in space-time-coded continuous phase modulation

Space-time coding has shown great promise for digital transmission in wireless communication links, especially when the channel response is known at the receiver. Space time coding combined with continuous phase modulation (CPM) can offer better tradeoffs in bandwidth and power efficiency. Because of the memory inherent in CPM, channel estimation is often harder than for linear modulations. We present an adaptive soft algorithm that performs joint channel estimation and data detection for space-time CPM systems. Properly designed pilot symbols are inserted at the very beginning to give good initial estimates of the channels. This soft receiver is further applied to the interleaved space-time CPM system to yield better performance with moderate complexity through iterative processing. Simulation results show that the receiver can often achieve near-coherent performance in quasistatic fading as well as in time-varying fading.

Serially concatenated continuous phase modulation with iterative decoding

Serially concatenated and interleaved continuous phase modulation (CPM) with iterative decoding is investigated. An a posteriori probability (APP) algorithm for CPM is developed based on the classic APP algorithm for channel codes. The system is analyzed through upper bounds on the average bit error probability. For coded and interleaved minimum shift keying, the weight spectrum is computed, resulting in a transfer function bound. This is cumbersome for a general CPM system; instead, only the most significant error events contributing to the weight spectrum are identified. Simulations show that, firstly, these events give a satisfactory view of system performance when equal outer codes are used, and secondly, that remarkably good performance can be obtained for some simple systems. Finally, power spectral densities and bandwidths are computed, allowing for a bandwidth/performanee comparison of different combinations.

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.

Performance of binary CPM schemes in frequency selective fading channels with pilot symbol assisted detection

Signals transmitted over a land mobile radio channel are very often subjected to frequency selective fading. A detection technique is proposed for continuous phase modulation (CPM) operating in such an environment. The technique uses embedded pilot symbols for channel impulse response estimation. The estimated channel response is updated from symbol to symbol and is used during the sequence detection of the CPM signal. Unlike pilot symbol assisted linear modulation, the pilot symbols in this CPM system are divided into two groups. The first group of pilot symbols is data-dependent and is used to force the modulator to return periodically to a known system state. The second group is not data-dependent and is used to specify a known waveform emanating from the periodic known state, for the purpose of channel estimation. The proper pilot symbol encoding rules, as well as the structure of the companion channel estimator, are presented. It is shown that CPM schemes employing this detection technique exhibit no irreducible error floor even in the presence of fast fading and large delay spread. The modem actually performs better in a heavily frequency selective fading environment, due to the implicit diversity effect provided by the channel. The difference in energy efficiency between frequency selective and flat fading can be as large as 5 dB at a 10-3 bit error rate and 8 dB at a 10-4 error rate. These results suggest that the proposed technique is very suitable for use in a system which employs diversity.

Pilot symbol-assisted detection of CPM schemes operating in fast fading channels

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.

Joint evaluation of time and frequency selective fading effects in CPM systems with LDI detection

AbstractLimiter ‐ discriminator ‐ integrator (LDI) detection of binary full and partial response continuous‐phase modulation (CPM) in a channel characterised by Rayleigh fading, time and frequency selectivity, is investigated. An analytical approach able to take into account the presence of any number of delayed paths in the channel is presented. The narrowband bandpass filter effects and the role of the post‐detection integration time and other system parameters are evaluated. The numerical results show that full‐response schemes perform better than partial‐response modulation formats as regards the error floor due to the Doppler effect or the presence of a delayed version of the received signal.

On the spectral efficiency of CPM systems over real channel in the presence of adjacent channel and cochannel interference: a comparison between partial and full response systems

In all the new radio systems to be designed-for example, local radio networks or portable communication systems-a crucial point is determination of the actual spectral efficiency obtainable. To this end, the fundamental role played by adjacent and cochannel interference must be considered. The computer program implemented allows general analysis of continuous phase modulation (CPM) systems with limiter-discriminator detection and symbol-by-symbol regeneration, the combined effects of intersymbol interference, noise, and adjacent channel or cochannel interference have been tested to give the design criteria of the transmission system. To emphasize the role played by interference, an ideal multipath-free channel has been considered: with reference to a binary case, Gaussian minimum-shift keying (GMSK) systems have been investigated and compared with full-response CPM systems to obtain a suitable tradeoff between spectral efficiency (connected to channel spacing at radio frequency) and signal-to-noise ratio with fixed bit-error probability. The numerical results presented emphasize the performance obtainable with full- and partial-response techniques for varying system parameters such as phase deviation index, receiver filter bandwidth, and spectral efficiency.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>