M-ary Continuous Phase Modulation Research Articles

A Timing False Lock Detector for M-ary Partial-Response CPM

We consider a timing false lock detector for continuous phase modulation (CPM), which is needed for M-ary partial-response CPM schemes. Our approach maintains a running count of successive, simple, short-term false lock decisions, rather than conducting a single, long-term decision. Using a Markov chain model, we show that our scheme can provide accurate and rapid synchronization for capacity-approaching CPMs that operate at very low signal-to-noise ratios.

Pre-Equalization for Continuous Phase Modulation

In this paper, a channel precoding technique is proposed for M-ary continuous phase modulation (CPM) for multipath downlink channels. The proposed pre-equalizer, based on the approximation of CPM signals by complex exponential functions, applies modulo-arithmetic operations to ensure the stability as in Tomlinson-Harashima method. Spectrally efficient precoded signals are obtained with small envelope variations by employing a transmit antenna selection technique. Because the equalization functions are transferred to the base station, the complexity in the mobile terminals is reduced significantly. The simulation results depict the power spectral density of the transmitted signals and the bit-error rate. An upper bound on the error performance is computed and the relation between the number of transmit antennas and the spectral efficiency is derived.

MMSE-Optimal Approximation of Continuous-Phase Modulated Signal as Superposition of Linearly Modulated Pulses

The optimal linear modulation approximation of any M-ary continuous-phase modulated (CPM) signal under the minimum mean-square error (MMSE) criterion is presented in this paper. With the introduction of the MMSE signal component, an M-ary CPM signal is exactly represented as the superposition of a finite number of MMSE incremental pulses, resulting in the novel switched linear modulation CPM signal models. Then, the MMSE incremental pulse is further decomposed into a finite number of MMSE pulse-amplitude modulated (PAM) pulses, so that an M-ary CPM signal is alternatively expressed as the superposition of a finite number of MMSE PAM components, similar to the Laurent representation. Advantageously, these MMSE PAM components are mutually independent for any modulation index. The optimal CPM signal approximation using lower order MMSE incremental pulses, or alternatively, using a small number of MMSE PAM pulses, is also made possible, since the approximation error is minimized in the MMSE sense. Finally, examples of the MMSE-optimal CPM signal approximation and its comparison with the Laurent approximation approach are given using raised-cosine frequency-pulse CPM schemes.

M-CPM with MRC diversity in Rician-, Hoyt-, and Nakagami-fading channels

An equation is derived for the bit error probability (BEP) of M-ary continuous phase modulation (CPM) with differential phase detection (DPD) and maximal ratio combining (MRC) in various fading channels. As an example, the BEP of Gaussian minimum shift keying with B/sub g/T=0.5 is computed. In the case of a Rician channel, the Doppler frequency shift is also taken into account. As an example, the BEP of M-ary continuous phase frequency shift keying with M=2, 4, 8 and f/sub Dm/T=0.04 is computed.

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.

Noncoherent sequence detection of CPM

Schemes in which noncoherent sequence detection based on the Viterbi algorithm are proposed for linearly modulated signals transmitted over additive white Gaussian noise channels, have recently been proposed by the authors. These schemes are attractive because their performance closely approaches that of coherent receivers with acceptable complexity, and they avoid the drawbacks of phase-locked loops. The authors extend these results to M-ary continuous phase modulation (CPM) signals.

Coded continuous phase modulation using ring convolutional codes

Rate 1/2 convolutional codes over the ring of integers modulo M are combined with M-ary continuous phase modulation (CPM) schemes whose modulation indices are of the form h=1/M. An M-ary CPM scheme with h=1/M can be modeled by a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is linear over the ring of integers modulo M. The fact that the convolutional code and the CPE are over the same algebra allows the state of the CPE to be fed back and used by the convolutional encoder. A modified Euclidean distance function that substantially simplifies the search for good codes has been derived and used to find new codes. Numerical results show that this approach consistently improves the performance as compared to coded schemes using binary convolutional codes with the same decoding complexity.

Decomposition of M-ary CPM signals into PAM waveforms

It is widely known that minimum shift keying (MSK) may be seen as a PAM signaling scheme and that the same is true, albeit approximately, with MSK-like modulations. It is also known (perhaps not so widely) that any binary continuous phase-modulated (CPM) signal may be exactly decomposed into the sum of a few PAM waveforms. In this paper we show that this property extends to multilevel CPM signaling. Features of a PAM decomposition are discussed as a function of the alphabet size, the modulation index, and the frequency response of the system. It is found that, especially with signaling schemes with a long memory, the decomposition has so many terms that it becomes unmanageable. For these cases an approximation is proposed with a limited number of terms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A simple derivation of the power spectrum of full-response CPM and some of its properties

Using a new representation for continuous-phase modulated (CPM) signals, it is shown how a closed-form expression for the power spectral density of full-response M-ary CPM with modulation index J/M can be obtained by straightforward computations. This result is used to provide an explanation of the fact that this power spectral density depends only on J and not on M. >