Yu.A. Bryukhanov – Dr.Sc.(Eng.), Professor, Head of Department of Infocommunications and Radiophysics,

P.G. Demidov Yaroslavl State University

Е-mail: bruhanov@uniyar.ac.ru

Yu.A. Lukashevich – Electronic Engineer,

Department of Infocommunications and Radiophysics, P.G. Demidov Yaroslavl State University

Е-mail: dcslab@uniyar.ac.ru

The effect of quantization errors on the distortion and noise immunity of receiving signals with amplitude pulse modulation for an arbitrary number of bits is studied for different methods of coding and approximation of numbers. A nonlinear quantization model is used, which allows one to calculate processes for an arbitrary number of quantization levels. To isolate the modulating signal, a synchronous quadrature amplitude detector was used. The envelopes of radio pulses are calculated: non-quantized and quantized for different methods of approximating numbers represented in direct and additional codes. The dependences of the mean-square error of the envelope on the number of discharges during signal quantization are presented. The calculations of the probability of errors of reception of non-quantized and quantized signals are performed. It is shown that the probability of erroneous reception of signals is affected not only by the number of digits, but also by the size of the alphabet. This is due to the fact that in the process of quantization of part of the symbols of the alphabet, the number of levels of quantization of the signal decreases.

Studies on the effect of quantization on distortion of radio signals are of particular importance, since at present in radio receivers, analog pre-detector signal processing is replaced by digital, and functions of the physical level previously performed by hardware methods (filtering, modulation/demodulation, spectrum conversion, signal amplification, etc.) gradually give way to software-configurable (Software Defined Radio – SDR) and cognitive (Cognitive Radio – CR) methods. The purpose of the work is to study the effect of quantization errors on distortions and noise immunity of receiving signals with amplitude pulse modulation for an arbitrary number of bits R, for different methods of encoding and approximating numbers. A nonlinear quantization model is used. To isolate the modulating signal at the output of the quantizer, a synchronous quadrature amplitude detector was used.

The envelopes of non-quantized A and quantized Y (n) radio pulses are calculated and presented for different methods of approximating numbers represented in direct and additional codes. Due to quantization, the pulse envelope becomes unstable. When using the direct code with truncation, envelope dips occur and with an increase in the number of digits from 4 to 8, the range of dips decreases from 3.95 to 0.30% compared to A. In the additional code with truncation, there are envelope pulsations with respect to A and with an increase in the number of discharges in the same range, their amplitude decreases from 5.4 to 0.3%, respectively. The distortion of the modulating signal was quantified using the standard error σ. With an increase in the number of digits R from 4 to 8, when using the direct code with truncation, the error σ decreases from 8.92 to 0.63%, and in the additional code with truncation from 6.15 to 0.45%. The calculations of the probability of receiving errors of non-quantized and quantized with the number of bits R Î {4; 6; 8} signals. It is shown that the probability of erroneous reception of signals is affected not only by the number of digits, but also by the size of the alphabet M, for example, at R = 4, the probability of error without quantization is P = 10−5 with an increase in M from 2 to 8, the average probability of error increases by 1, 35 times. This is due to the fact that when M = 8, during the quantization of part of the symbols of the alphabet, the number of quantization levels decreases, and with it the effective number of digits becomes less than 4, while the symbol energy (and with it the average energy of the quantized symbol) decreases, and relative quantization errors increase. The results can be used in the design of message transmission systems with digital signal processing.

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