Capacity-Achieving CPM Schemes

Abstract

The pragmatic approach to coded continuous-phase modulation (CPM) is proposed as a capacity-achieving lowcomplexity alternative to the serially-concatenated CPM (SC-CPM) coding scheme. In this paper, we first perform a selection of the best spectrally-efficient CPM modulations to be embedded into SC-CPM schemes. Then, we consider the pragmatic capacity (a.k.a. BICM capacity) of CPM modulations and optimize it through a careful design of the mapping between input bits and CPM waveforms. The so obtained schemes are cascaded with an outer serially-concatenated convolutional code to form a pragmatic coded-modulation system. The resulting schemes exhibit performance very close to the CPM capacity without requiring iterations between the outer decoder and the CPM demodulator. As a result, the receiver exhibits reduced complexity and increased flexibility due to the separation of the demodulation and decoding functions. Memoryless Channel Convolutional Convolutional decoder CPE SISO decoder and demapper demodulator Memoryless CPM channel SISO binary encoder modulator CPE P (y|x) CCPM x(t; b) y(t; b) Ĉ d d Π Π −1 Π M Fig. 2. Block diagram of a serially concatenated CPM co-decoder. The block labeled M maps blocks of m bits to M -ary CPM symbols.

Maximum Likelihood Timing Estimation for CPM Using Legendre Polynomials

“…As L decreases and/or h increases the phase transition no longer resembles a linear function and the approximation accuracy decreases. As further illustration, consider two alternative capacity achieving CPM schemes [10] with parameters M c = 4, 2RC, h = 1/8 and M c = 2, 4REC, h = 1/4. In this case, Figure 3 shows a close match to the MCRB for a large range of E s /N o values, with little difference between m = 2 and m = 4 at E s /N 0 ≤ 15dB.…”

“…For our purposes, we can approximate the S-curve using a known preamble sequence in (10). To this end, the approximation over N symbols can be expressed as…”

Wideband partial response CPM demodulation via multirate frequency transformations and decision feedback equalization

“…Subsequent to the MFT-ESA demodulation stage, a recursive prediction approach based on MA signal modeling of the estimated IF, together with decision feedback equalization, was presented to address the problem 6 Memory removal via decision feedback equalization: a symbol error probability of MFT-ESA approach for binary CPFSK with zero-forcing and MMSE decision feedback equalization to remove memory induced due to partial response signaling and b symbol error probability for multilevel CPFSK with zero-forcing and MMSE decision feedback equalization. In both cases, 3-REC CPM with parameters T b = 1s, f s = 50Hz, and f c = 12Hz was employed.…”

“…Gaussian Minimum Shift Keying (GMSK), a specific form of CPM, is the main ingredient in the Global System for Mobile communications (GSM) [2,3] used in GPS applications. Pragmatic CPM modulation schemes have recently been studied as capacity attaining low-complexity alternatives to serially concatenated CPM [6].…”

FDMA System with Space–Time Encoded CPM Signals

“…Each data stream is conveyed to one of M T CPM modulators. A rate 1/3 systematic recursive CE with four states and good distance properties [17] has been chosen. Its connection polynomials (in octal notation) are (7; 5; 3) 8 , where 7 8 represents the coefficients of the feedback polynomial [18].…”