Partitioning for SA(B,C) for CPM signals

Continuous phase modulation (CPM) has been widely used in telecommunication and aeronautical telemetry system due to its high power and spectral efficiency. Non-coherent detection is a kind of feasible CPM detection method if there is large phase noise or residual carrier frequency offset. Near-optimal non-coherent sequence detection, which is based on Viterbi algorithm, has a performance close to that of maximum-likelihood sequence detection (MLSD). However, near-optimal non-coherent detection of CPM is very complicated to be implemented, and it is even more difficult to achieve a high speed due to feedback in the process of calculating branch metrics, add-compare-select (ACS), updating the beginning phase and phase reference symbol. In this paper, we first review near-optimal non-coherent detection of CPM, and then we present a high speed design of FPGA implementation for near-optimal non-coherent detection of a 64 state, 4-ary, length-3T raised cosine (3RC) CPM on Xilinx XC7VX690T device. In our scheme, the frequency pulse truncation is used to simplify the CPM detection. We propose a feedback processing in parallel for different states of CPM trellis to achieve a low latency. Furthermore, we develop a recursive implementation architecture for the process of updating the beginning phase. We achieve the CPM bit rate of 25Mbps for the on-chip processing clock of 100MHz. The results of simulation shows near-optimal non-coherent detection performs much better the coherent detection when residual carrier frequency offset or phase noise exists. It is found that the implementation can achieve a degradation in the Eb/N0 from computer simulation of as small as 0.3 dB for an average BER=10-5.

In order to understand the optimal parameter settings of spectrally efficient continuous phase modulation (CPM), we elaborate on our previous work on numerically optimized CPM. An empirical model is developed based on an expression for the effective bandwidth of CPM, an approximate expression for the smallest Euclidean distances of spectrally efficient CPM and observed properties of the numerically optimized phase pulses. We find that the optimized phase pulses, which resulted from a joint optimization of modulation index and phase pulse, share common properties for different alphabet sizes and different spectral efficiencies. These properties are described by three phase pulse parameters, and we show that they attain approximately equal values at the so-called saturation length. The model can predict the minimum Euclidean distance at the saturation length for a CPM system using an even-integer alphabet and jointly optimized modulation index and phase pulse, and it partly extends to less spectrally efficient CPM systems.

Joint source and channel (JSC) coding using combined trellis coded quantization (TCQ) and continuous phase modulation (CPM) is studied. The channel is assumed to be the additive white Gaussian noise (AWGN) channel. Analytical bounds on the channel distortion for jointly designed TCQ/CPM systems with maximum likelihood sequence detection (MLSD) are developed. For a memoryless uniform source, our upper bounds for the investigated TCQ/CPM systems are shown to be asymptotically tight for increasing channel signal-to-noise ratio (SNR) values. It is concluded that the minimum Euclidean distance of the CPM system alone is not enough to evaluate the performance of the combined TCQ/CPM systems. The number of the error events having the minimum Euclidean distance and the total distortion caused by those error events also affect the asymptotic performance of the investigated systems. This work provides an analysis tool to estimate the performance for a given combined TCQ/CPM system. The analysis method is very general, it may be applied to any trellis based JSC coding schemes.

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.

Continuous phase modulation (CPM) consists of a large family of signals that are especially suitable for wireless communication. CPM signals have not been represented by discrete points in signal space because the phase of the carrier is time-variant. However, in this paper we present a new method to represent the binary CPM signals by discrete points in signal space by utilizing the amplitude modulated pulse (AMP) representation of the CPM signals. We use this new signal space representation to compute the Euclidean distance for any CPM signal and we compare the performance of CPM signals with each other and with other modulation schemes.

The paper shows that some continuous phase modulation (CPM) schemes have some properties that allow a near optimum reception with very low complexity. The proposed reception method applies simultaneously three techniques for complexity reduction of CPM receivers, which have been previously object of separate analysis with additive white Gaussian noise (AWGN). These techniques are: first-quadrant metrics calculus on a F-dimensional Walsh space, derivation of the other quadrant metrics using a no loss derivation algorithm and finally the use of constrained complexity maximum likelihood sequence detection (MLSD) using the M-algorithm. The cumulative effect on total performance loss is negligible and no more than the sum of the partial losses due to the Walsh space and the M-algorithm, known to be negligible when observing the respective standalone rules for the complexity reduction limits.

In 1986, Laurent showed that binary continuous phase modulated (CPM) signals can be decomposed into pulse amplitude modulated (PAM) waveforms. This result, later extended to multilevel CPM signals by Mengali and Morelli, has attracted much attention, especially for the design of simplified receivers. The paper proceeds from the premise that the decomposition into PAM waveforms is not unique, and follows a systemtheory approach that leads to a natural formulation. First, the CPM modulator is represented by a nonlinear part (encoder) followed by a linear part (bank of PAM modulators).The two parts are then rearranged with the aim of obtaining real-valued continuous PAM waveforms and to reduce their number. Several classes of decompositions arise with this approach, each of which admits an infinite number of different decompositions of the same CPM signal, among which the Laurent and MengaliMorelli results appear as special cases. Throughout the paper, a systematic use is made of the Kronecker product, which appears to be the natural tool for dealing with CPM decompositions and for expressing results in a very simple form.

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.

Continuous phase modulation (CPM) is known for its attractive spectral properties. Furthermore, CPM has the property that the modulation signal maintains a constant envelope, so CPM is effective for satellite communications. Recently, generalized nonlinear CPM (GNCPM), which can achieve a larger minimum Euclidean distance than ordinary CPM, was introduced. In this paper, we propose a convolutional coded GNCPM to improve the bit error rate (BER) performance of uncoded GNCPM without expanding bandwidth. Combination CPM with convolutional coding causes an increased number of phase trajectory patterns which can cause the bandwidth expansion. Therefore, in our proposed model, to control the bandwidth, we pay attention to the phase trajectory pattern which is already owned by uncoded GNCPM and change the modulation index appropriately, depending on the input symbols, to keep the number of phase trajectory patterns the same as in uncoded GNCPM. First, we consider the most suitable assignment of the modulation index which can increase the Euclidean distances without bandwidth expansion. Next, we theoretically derive the upper bound on the error event probability of the proposed model in additive white Gaussian noise (AWGN). The performance of the proposed convolutional GNCPM, obtained by computer simulation, shows that the proposed model can improve BER performance without bandwidth expansion. © 1998 Scripta Technica. Electron Comm Jpn Pt 1, 81(8): 42–50, 1998

The complexity of the multiple-symbol detection structures for partial response continuous phase modulation (CPM) signals goes exponentially with the length of the pulse shaping filter and the observation length as well. Simple no coherent trellis receivers for partial response CPM signals are proposed in this paper. Parallel to the simple coherent detectors, where CPM signals are approximately represented by a sum of Phase Amplitude Modulation waveforms, Laurent decomposition is applied to reduce the complexity. The proposed no coherent receiver is structured with only fixed K matched filters in the front-end and a processor which uses Viterbi algorithm with a 2N-1 states trellis to perform the sequence estimation. It is attractive because the structure does not involve any matrix calculations. The good error performance is confirmed by simulation results.

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.

It is known that space-time coding (STC) technology can improve the performance of MIMO continuous phase modulation (CPM) communication system, but it also leads to high receiver complexity. It is also known that any M-ary CPM signal can be exactly decomposed into a sum of time-offset pulse amplitude-modulated (PAM) waveforms based on the extended Laurent decomposition. In this paper, we develop a simplified detection algorithm using the CPM's PAM decomposition for the full response STC-CPM system which adopts space-time trellis coding. Analysis and simulation results show that this algorithm efficiently reduces the computation complexity with a very small degradation in error performance compared with the conventional maximum likelihood sequence detection.

Continuous phase modulation (CPM) with noncoherent detection over a one-symbol interval is discussed. In order to obtain good performance with this simple demodulation strategy, the phase function of the modulation scheme has to be designed properly. An approach to shaping the purchase function to achieve noncoherent orthogonal performance for various values of the modulation index (h) is presented. Using the Gram-Schmidt orthogonality procedure, an entire family of orthogonal phase functions for h>or=0.68 is derived. All CPM schemes with these phase functions produce the same performance as noncoherent orthogonal signaling. For h=1 the phase function reduces to that of the FSK phase function. It is shown that there are CPM schemes that give the same SNR performance as noncoherent orthogonal FSK but have some spectral advantages over the FSK modulation format. >

In this paper a general soft-based synchronization technique for continuous phase modulations (CPM) is presented. In particular two soft carrier phase estimation algorithms are derived, being the phase the parameter that shows the lower implementation complexity. These algorithms exploit the trellis structure inherent in the modulator of CPM signals and make use of a symbol-based BCJR, developed in an ad-hoc way for an uncoded CPM signal. The algorithms are blind and are designed to work with all CPM family. Simulation results for the soft carrier phase estimation are presented in terms of Root Mean Square Estimation Error (RMSEE). The modified Cramer-Rao bound (MCRB) is also shown for reference. RMSEE of soft recovery approach is very close to MCRB for all the examined formats.

The detection of convolutional codes over rings suitable for continuous phase modulation (CPM) are presented based on the Rimoldi's Decomposition of CPM. Because the ring convolutional codes are on the same ring as the inner codes of CPM, We can use reduced state sequence detection (RSSD) to analyze and detect the overall encoder. Numerical result shows the detection complexity of this RSSD is significantly reduced with a very small degradation in error performance.