Serial digital QAM-modem based on complex band-pass IIR filters with LF-prototypes of Bessel

Abstract

The article is devoted to the development and implementation of algorithms for the single-channel sequential quadrature amplitude modulation and demodulation based on digital complex band-pass IIR filters with LF-prototypes of Bessel. The use of complex IIR filters of Bessel allows to obtain orthogonal carrier signals which are close in shape to symmetric signals with practical non-overlapping spectra. The procedure for calculating the 4th-order digital low-pass Bessel filter using the generalized bilinear transformation method, which is used in the theory of digital signal processing to convert a continuous-time system into a discrete-time system, is considered. The variants of implementing the digital complex bandpass filters with a sequential structure using the complex delay method are considered, which allows to obtain the block diagrams of complex bandpass filters without additional calculations and to realize the restructuring of the central frequency without changing the frequency response shape by changing only two coefficients in complex delays. The procedure for obtaining of the expression of the impulse response of digital complex band-pass IIR filters of Bessel is considered. With the help of circuit modeling, the amplitude-frequency response and impulse response of such filter are determined. If the IIR filters are used in the modulator, the pulse characteristics of which are infinite and asymmetric, then it is necessary to use digital complex FIR filters consistent with the truncated pulse characteristic in the demodulator. But as an exception, the Bessel digital IIR filter has a phase-frequency response similar in shape closely to the linear one and, accordingly, a pulse response close to the symmetric one. In this case, the same recursive complex Bessel filters, similar to the filter in the modulator, can be used as matched filters in the demodulator. Therefore, the serial block diagram of the modem contains the same complex band-pass IIR filters with LF-prototypes of Bessel. The choice of the central frequency of the channel digital complex bandpass IIR filter is carried out by setting two coefficients. The results of circuit modeling of the data transmission system with the quadrature amplitude modulation (QAM-16) in the Microcap environment are presented, confirming the operability of the proposed option.