Equalization algorithms in the frequency domain for continuous phase modulations

Double Turbo Equalization of Continuous Phase Modulation with Frequency Domain Processing

“…After the removal of the prefix and low-pass filtering with a two-sided bandwidth of 1/T s Hertz, the discrete symbols are obtained by sampling the filter output every T s seconds as in [9] such that the additive noise is still white and there is no aliasing. The corresponding discrete-time signal is…”

“…The advantages of frequency domain processing and iterative information exchange are combined in [9], where a turbo linear equalizer (TLE) is presented in which a SISO block-form FDE (BFDE) is followed by the SISO CPM demodulator and channel decoder modules. Here, the soft CPM signal information to start the subsequent equalization iterations are computed from the code bit probabilities obtained from the back-end channel decoder.…”

“…Moreover, because the proposed FDE operates on blocks of information, it still involves matrix inversions which result in an increased computational cost. For this reason, we propose herein a soft-information-aided FDE for CPM which overcomes the disadvantages of that in [9] and which is used in a doubly-iterative joint CPM equalization and demodulation architecture similar to the one in [5], so as to achieve a better error performance with lower computational complexity compared to the methods in both [5] and [9] .…”

“…Then, these two soft outputs are employed in a doubly-iterative information exchange where the CPM demodulator is coupled with both the front-end FDE and the back-end decoder. Because the CPM signal probabilities are not computed from the code bit probabilities, the error bursts of [9] due to the modulation memory are not encountered, which results in a significant performance improvement. Moreover, because its implementation does not involve any matrix inversion, the proposed SISO FDE is computationally less complex than the equalizers in [5] and [9].…”

“…Because the CPM signal probabilities are not computed from the code bit probabilities, the error bursts of [9] due to the modulation memory are not encountered, which results in a significant performance improvement. Moreover, because its implementation does not involve any matrix inversion, the proposed SISO FDE is computationally less complex than the equalizers in [5] and [9]. The doublyiterative CPM receiver with the FDE is also more feasible in attaining faster convergence to low bit-error rates (BERs) because the number of equalization iterations are decreased by performing several demodulation/decoding iterations per each equalization iteration to improve the equalizer a priori information.…”