Error probability for a discriminator detector with decisionfeedback for continuous phase modulation

A discriminator detector using decision feedback for continuous phase modulation (CPM) is proposed. Different thresholds are employed in the hard decision device owing to the memory in the CPM signal. This leads to an improved performance, especially for high signal/noise ratios. Parameters such as bandwidth of the IF filter, sampling time and integration time are optimised     

Multiple differential detection of continuous phase modulationsignals

A sequence estimation algorithm for the differential detection of the continuous phase modulation (CPM) signals, yielding significant gains in BER performance and with considerable resistivity to fading, is introduced. These advantages, along with the reduced hardware complexity, low cost, and fast synchronization which characterize the differential detector, make the proposed receiver useful for land mobile radio and mobile-satellite communications. The new receiver is based on multiple differential detection. The multiple differential detection strategy provides the decoder with more information regarding the transmitted data and applies a noise decorrelation process on the received signal, useful to the sequence estimation. The algorithm is derived in a general form, and can be applied on any CPM scheme, with any degree of complexity. The authors have evaluated the receiver for two of the most popular CPM schemes, the tamed frequency modulation (TFM) and Gaussian minimum-shift keying (GMSK) (with B₁ T=0.25), in the presence of additive white Gaussian noise (AWGN) and Rician fading. The BER performance evaluation results indicated significant gains and considerable reduction of error floors. In AWGN improvements close to 9 dB have been verified     

On decision-feedback detection of differential space-time modulation in continuous fading

We show that linear prediction (LP)-based decision-feedback detection (DFD) for nondiagonal differential space-time modulation (DSTM) may suffer from a severe performance degradation in continuously fading channels. DSTM constellations that incur no degradation in LP-DFD are identified as those with a diagonal generator. To cater to other constellations, we propose a low-complexity DFD scheme by inserting decision-feedback symbols into the metric of multiple-symbol differential detection.     

M-ary FSK with limiter discriminator integrator detection and DPSK with differential phase detection in a Rician Fading channel

We derive an expression for the error probability of M-ary differential phase shift keying with differential phase detection and of M-ary frequency shift keying with limiter discriminator integrator detection which is valid for Rician. Rayleigh and Gaussian channels.     

Reduced state sequence detection of full response continuous phase modulation

A reduced state sequence detector (RSSD) which combines decision feedback with Viterbi decoding is proposed for M-ary full response continuous phase modulation. The detector is analysed with minimum Euclidean distances and by simulations of the symbol error probability. It is shown that M-ary full response CPM schemes can be optimally decoded by a decoder with only two states when the modulation index is relatively small (>     

Serially concatenated continuous phase modulation with reduced iterative demodulation and detection

A reduced state Soft Input Soft Output （SISO） a posteriori probability algorithm for Serially 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 performance degradation is little with proper reduction scheme.     

Multiuser detection for continuous phase modulation over Rayleigh fading channels

We study multiuser (MU) continuous phase modulation (CPM) over Rayleigh fading channels with a receiver antenna array. An optimum symbol-by-symbol MU detector is derived and its practical implementation with reduced-complexity is considered. According to the numerical results, the MU detector performs very close to a system free of interference by other users, when each user has more than one receiving antenna. For three receiving antennas, this difference is less than 0.25 dB, 0.4 dB, and 0.6 dB for two, three and four users, respectively. Moreover, the proposed system is bandwidth efficient as CPM is a bandwidth efficient modulation scheme, and the MU system only uses the single user CPM bandwidth.     

Nonlinear continuous phase modulation

A class of nonlinear CPM signals is introduced by extending nonlinear CPFSK signals to other forms of frequency pulses. The distance results and spectral properties of nonlinear CPM signals are reported. Bit error probabilities of nonlinear CPM signals are simulated in presence of adjacent channel interference     

Generalized APP detection of continuous phase modulation over unknown ISI channels

Techniques for computing soft information in the presence of unknown intersymbol interference are presented, with a particular focus on iterative detection of serially concatenated continuous phase modulation. The techniques are centered around the recursive least-squares algorithm, thus enabling unsupervised detection. In particular, we employ bidirectional estimation.     

Generalized nonlinear continuous phase modulation

A class of generalized nonlinear full-response CPM signals is constructed by extending the known ordinary nonlinear CPM signals. Numerical results presented at different numbers of states indicate that generalized nonlinear CPM signals achieve higher minimum Euclidean distances than ordinary nonlinear CPM signals     

Multi-h phase codes for continuous phase modulation

The best multi-h phase codes which produce the highest minimum Euclidean distance are reported at preselected numbers of states. 2-h, 3-h and 4-h signals are considered in the code search. Numerical results are presented separately for binary full-response and partial-response signals, with a rectangular and a raised cosine baseband pulse.<>     

Joint data detection and channel estimation for coded and uncoded continuous phase modulation signals

The performance of decision‐directed approach for joint data detection and channel estimation for continuous phase modulation (CPM) signal is limited because of an inevitable decision delay, which results in a trade‐off between data detection and channel estimation. In this paper, a novel hard output demodulation that solves the conflict requirement on the decision delay by predicting the channel coefficients over a given observation interval through a Kalman filter is proposed for uncoded CPM signal. The prediction guarantees high channel tracking capability and meanwhile maintains the accuracy of data detection. The proposed hard output demodulator is further extended to design a soft‐input soft‐output demodulator for serially concatenated CPM signal, which allows iterative processing. The convergence behavior of the proposed iterative receiver is presented. Simulation results show that the proposed demodulators provide improved performance in terms of bit error rate over some existing algorithms. Copyright © 2014 John Wiley & Sons, Ltd.     

Block encoding with continuous phase modulation

Block encoding is considered to increase the minimum distance of CPM signals. Codes are constructed to prevent merging events with low Euclidean distances. Numerical results presented with full response, partial response and trellis coded CPM signals indicate that block coding can significantly increase the minimum distance of the signals. Nonlinear block codes are also considered     

Partial response continuous phase chirp modulation

A class of chirp modulation called partial response continuous phase chirp modulation is introduced by extending the length of the baseband pulse for more than one interval. Partial response chirp signals are constructed at finite numbers of states. Numerical results show that partial response chirp signals perform significantly better and they also have better spectral variations than the known chirp signals     

Neural net-based continuous phase modulation receivers

The authors propose feedforward neural networks (NNs) as receivers for partial-response continuous-phase-modulation (CPM) systems. Their approach is to replace the entire receiver structure, excluding timing recovery, with a neural net unit whose inputs are time samples of the incoming baseband signals, and whose outputs are the decoded symbols. Simulation results for coherent and incoherent NN-based receivers are presented, and their performance is compared with that of the optimum maximum-likelihood receiver. The performance of NN-based receivers at large SNR is analyzed     

Efficient estimation of continuous phase modulation with unknowncarrier phase

An efficient algorithm is presented for the estimation of continuous phase modulation (CPM) sequences over the Gaussian channel with unknown carrier phase. It operates on the excess phase trellis like the Viterbi algorithm, except that it is not a maximum-likelihood (ML) estimator. Its decision metric for survivor selection at each node is chosen so that it achieves the node error event probability of coherent ML estimation in the limit as the carrier phase remains constant over a long interval, so that the observation interval for forming the metric can be made large. It is shown for the case of minimum-shift-keying (MSK) that the bit-error probability (BEP) of perfectly coherent ML estimation is attained     

Catastrophic continuous phase modulation schemes and theirnoncatastrophic equivalents

Continuous phase modulation (CPM) schemes are bandwidth and energy efficient constant-envelope modulation schemes that can be viewed as a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is of convolutional type. It is observed that CPM schemes can be catastrophic in the sense that pairs of input sequences that differ in an infinite number of positions can be mapped into pairs of signals with finite Euclidean distance. This can happen in spite of the fact that the CPE is never catastrophic when considered as a stand alone convolutional encoder. The necessary and sufficient condition for a general CPM scheme to be catastrophic is given. Each member of the two major families of CPM schemes, namely the LREC and the LRC, has been classified as a catastrophic or noncatastrophic scheme. For the catastrophic schemes, the probability that a catastrophic event occurs is determined. A canonical precoder which transforms each scheme of both families into an equivalent noncatastrophic scheme is derived. The equivalent noncatastrophic scheme has the same number of states as the original one. Moreover, it has the property that if two input sequences differ in the ith position, the corresponding output signals have nonzero Euclidean distance in the ith interval     

Maximum-likelihood differential detection of uncoded and trelliscoded amplitude phase modulation over AWGN and fading channels-metricsand performance

This paper derives metrics for maximum-likelihood differential detection of uncoded and trellis coded MPSK and QAM transmitted over Rayleigh and Rician fading channels. Receiver structures based on these metrics are proposed and their error probability performance analyzed and/or simulated. The results represent a generalization of the notion of multiple symbol differential detection, previously introduced by the authors for MPSK over an AWGN, to the fading channel and other modulations. For the coded cases, ideal interleaving/deinterleaving is assumed and furthermore the presence or absence of channel state information. An interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly-varying phase error (the other extreme to the slowly-varying phase error case normally assumed for differential detection), under certain practical assumptions, it is shown that the optimum receiver is of the limiter-discriminator type     

A quasi-optimum receiver for continuous phase modulation

A simple receiver structure for any continuous phase modulation (CPM) scheme is introduced. Its front end is just the ordinary linear receiver followed by a subinterval sampler, eliminating the need for the standard analog matched filters. Its design is based on the decomposition of the CPM signal in the Walsh signal space. This brings the hardware requirement to a minimum, and near-optimum performance can be easily obtained