Sampling Phase Estimation in Underwater PPM Fractionally Sampled Equalization

Blind Fractionally Spaced Channel Equalization for Shallow Water PPM Digital Communications Links

“…Sampling Phase Sensitivity : The results shown in Figure 8 and Figure 9 have been obtained by averaging on three different sampling phase values, namely k0 = 0,1,6 as these latter result from the fourth order statistic based sampling phase estimation technique presented in [17]. While the MMNL based blind equalization scheme has reached convergence in all the Monte Carlo runs, in the CMA based blind equalization scheme, a significant convergence failure percentage has been observed, on average equal to about 7.5%.…”

“…In (7), r[n] = r(t)t=nTc/P denotes the samples obtained by fractional sampling the received signal r(t), and k0 ∈ double-struckN(P)=def{0,1,⋯,P − 1} indicates the fractional sampling phase, the blind estimation of which is discussed in [17]. It is worth noting that the equalized sequence truec^[n] estimates the samples of the transmitted M PPM chips bMPPM[n] only if the symbol timing has been already acquired, otherwise it simply furnishes an estimate of unsynchronized chips.…”

“…With the scheme described in [16], synchronization is restored by estimating the time derivative of the equalizer output modulus and then adjusting the timing offset in feedback mode through interpolation. However, equalization performance strictly depends on the initial phase the received fractionally sampled signal is locked to; to this regard, a blind sampling phase estimation technique has been presented in [17].…”

“…In detail, the modified Bussgang approach considers the introduction of an M -memory nonlinearity, never addressed before, in place of the classical zero-memory nonlinearity. Moreover, since another relevant issue in fractional sampling is the choice of the sampling phase, we resort to the mechanism described in [17] as part of the equalizer architecture. We remark that all the here presented matter are neither investigated nor mentioned in [17], which describes a sampling phase estimation technique here merely recalled, but not discussed or deepened at all.…”

“…Moreover, since another relevant issue in fractional sampling is the choice of the sampling phase, we resort to the mechanism described in [17] as part of the equalizer architecture. We remark that all the here presented matter are neither investigated nor mentioned in [17], which describes a sampling phase estimation technique here merely recalled, but not discussed or deepened at all. It is worth remarking that the use of PPM signals allows the described FSE scheme to be implemented in a blind fashion, while in OFDM based schemes certain known (pilot) symbols are exclusively used for channel estimation.…”