Continuous phase modulation (CPM) is a very attractive digital modulation scheme, with constant envelope feature and high efficiency in meeting the power and bandwidth requirements. CPM signals with pairs of input sequences that differ in an infinite number of positions and map into pairs of transmitted signals with finite Euclidean distance (ED) are called catastrophic. In the CPM scheme, data sequences that have the catastrophic property are called the catastrophic sequences; they are periodic difference data patterns. The catastrophic sequences are usually with shorter length of the merger. The corresponding minimum normalized squared ED (MNSED) is smaller and below the distance bound. Two important CPM schemes, viz., LREC and LRC schemes, are known to be catastrophic for most cases; they have poor overall power and bandwidth performance. In the literatures, it has been shown that the probability of generating such catastrophic sequences are negligible, therefore, the asymptotic error performance (AEP) of those well-known catastrophic CPM schemes evaluated with the corresponding MNSED, over AWGN channels, might be too negative or pessimistic. To deal with this problem in AWGN channel, this paper presents a new split-merged MNSED and provide criteria to explore which conventional catastrophic CPM scheme could increase the length of mergers with split-merged non-periodic events, effectively. For comparison, we investigate the exact power and bandwidth performance for LREC and LRC CPM for the same bandwidth occupancy. Computer simulation results verify that the AEP evaluating with the split-merged MNSED could achieve up to 3dB gain over the conventional approach.

A physical-layer network coding (PNC) scheme is developed using serially concatenated continuous phase modulation (SCCPM) with symbol interleavers in a two-way relay channel (TWRC), i.e., SCCPM-PNC. The decoding structure of the relay is designed and the corresponding soft input soft output (SISO) iterative decoding algorithm is discussed. Simulation results show that the proposed SCCPM-PNC scheme performs good performance in bit error rate (BER) and considerable improvements can be achieved by increasing the interleaver size and number of iterations.

In this letter, a physical-layer network coding (PNC) scheme based on continuous phase modulation (CPM) signal using the titled-phase model, i.e., TIP-CPM-PNC, is presented, and the combined titled-phase state trellis for the superimposed CPM signal in TIP-CPM-PNC is discussed. Simulation results show that the proposed scheme with low decoding complexity can achieve the same error performance as CPM-PNC using the traditional-phase model.

We consider space time block coded-continuous phase modulation (STBC-CPM), which has the advantages of both STBC and CPM at the same time. A weak point of STBC-CPM is that the normalized spectral efficiency (NSE) is limited by the orthogonality of the STBC and CPM parameters. The purpose of this study is to improve the NSE of STBC-CPM. The NSE depends on the transmission rate (TR), the bit error rate (BER) and the occupied bandwidth (OBW). First, to improve the TR, we adapt quasi orthogonal-STBC (QO-STBC) for four transmit antennas and quasi-group orthogonal Toeplitz code (Q-GOTC) for eight transmit antennas, at the expense of the orthogonality. Second, to evaluate the BER, we derive a BER approximation of STBC-CPM with non-orthogonal STBC (NO-STBC). The theoretical analysis and simulation results show that the NSE can be improved by using QO-STBC and Q-GOTC. Third, the OBW depends on CPM parameters, therefore, the tradeoff between the NSE and the CPM parameters is considered. A computer simulation provides a candidate set of CPM parameters which have better NSE. Finally, the adaptation of non-orthogonal STBC to STBC-CPM can be viewed as a generalization of the study by Silvester et al., because orthogonal STBC can be thought of as a special case of non-orthogonal STBC. Also, the adaptation of Q-GOTC to CPM can be viewed as a generalization of our previous letter, because linear modulation scheme can be thought of as a special case of non-linear modulation.

Conventional CPM signals employ information sequence with time-unlimited phase shaping pulse (PSP) to achieve power and bandwidth efficient transmission. On the contrary, information sequence using time-limited PSP was believed to produce power-wasting data-independent discrete spectral lines in CPM spectra, and was suggested to be avoided. In this paper, we revisit this problem and adopt the time-limited PSP to replace the one with time-unlimited, it turns out to have an alternative solution to the CPM scheme. We first modify the spectral computing formula for the CPM with time-limited PSP (or CPM-TL) from conventional CPM formula and show that the discrete spectral lines appeared in the power density spectrum of CPM-TL signals can be diminished or become negligible by appropriately choosing PSP. We also show that this class of CPM can use any real number modulation index (h) and the resultant trellis structure of CPM guarantees the maximum constraint length allowed by the number of states in the MLSD receiver. Finally, the energy-bandwidth performance of CPM using time-limited PSP is investigated and compared with conventional CPM with time-unlimited PSP. From numerical results we show that, under the same number of states in the MLSD receiver and bandwidth occupancy, this subclass of CPM could outperform the conventional CPM up to 6dB coding gain, for h<1, in many cases.

In this paper, a low-complexity symbol-spaced turbo frequency domain equalization (FDE) algorithm based on Laurent decomposition is proposed for precoded binary continuous phase modulation (CPM) with modulation index h=1/2. At the transmitter, a precoder is utilized to eliminate the inherent memory of the CPM signal. At the receiver, a matched filter based on Laurent decomposition is utilized to make the detection symbol-spaced. As a result, the symbol-spaced iteration can be taken between the equalizer and the decoder directly without a CPM demodulator, and we derive a symbol-spaced soft interference cancellation frequency domain equalization (SSIC-FDE) algorithm for binary CPM with h=1/2. A new data block structure for FDE of partial response CPM is also presented. The computational complexity analysis and simulations show that this approach provides a complexity reduction and an impressive performance improvement over previously proposed turbo FDE algorithm for binary CPM with h=1/2 in multi-path fading channels.

Continuous phase modulation (CPM) is a non-linear modulation technique whose power and bandwidth efficiency make it an attractive choice for mobile communication systems. Current research has focused on devising encoding rules for using CPM over multiple-input multiple-output (MIMO) systems in order to obtain the improved bit error rate (BER) and high data rates promised by MIMO technology. In this paper, optimal and suboptimal non-coherent receivers for a class of CPM signals called orthogonal space-time CPM (OST-CPM) are derived under a quasi-static fading channel assumption. The performance of these receivers is characterized and shown to achieve the same diversity order as that of the corresponding optimal coherent receiver.

This letter develops an efficient CPM demodulator which provides soft outputs for use in coded CPM. The proposed algorithm offers reduced-complexity soft output detection in which the number of matched filters and trellis states is appreciably reduced. The complexity reduction is achieved by approximating the CPM signal using the Laurent representation. A simulation study of iterative decoding of serially concatenated CPM with an outer code was performed. The performance degradation of the proposed algorithm relative to optimal full complexity generation of soft outputs was found to be small.

This paper shows the method of theoretical analysis for the bit error probability of the trellis-coded partial response continuous phase modulation (TCM-PR-CPM) over the correlated Rician fast frequency nonselective fading channel. In the analysis, the fading correlation of the channel and the effect due to finite interleaver are taken into account. By applying the method to the rate 1/2 (7, 2) trellis code with the raised cosine pulse of length 2 (2RC) partial response signaling, we show that the tighter upper bounds of the bit error rate are obtained than those in the preceding report.