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AN EFFICIENT USE OF DAC DYNAMIC RANGE IN FREQUENCY-SELECTIVE CHANNEL SIMULATOR
Gerasimov A.B.,
Yaroslavl State University, Russia, Yaroslavl, [email protected]
Solovyev D.M.,
Yaroslavl State University, Russia, Yaroslavl, [email protected]
Demidov P.G.,
Yaroslavl State University, Russia, Yaroslavl
Keywords: ehannel simulators, signal processing, DAC dynamic range.
Development of new communication systems includes an experimental testing and debugging of preproduction models. Channel simulators are widely used tools for testing systems in conditions which are very close to real-world radio channel [1]. Today's level of technologies allows to develop fully digital channel simulators, based, for example, on field programmable gate arrays (FPGA) [2]. Common problem for the fixed point arithmetic devices is choosing scale parameters. On the one hand we have to avoid overflow, but on the other hand we have to provide maximum ratio between signal and quantization noise. This paper presents the solution for the specified problem in case of hardware digital multipath fading channel simulator design.
This work was supported by the project №1060 within the government task for scientific research of the YarSU. The presented technique of parameter scaling for digital frequency-selective fading channel simulator provides maximally efficient use of dynamic range of signal processing for a specified level of distortions of channel statistical characteristics. The feature of presented technique is the division of scaling process into several stages, which provides minimal level of distortions of channel characteristics due to simulator parameters truncation. An effective use of DAC dynamic range of digital fading channel simulator permits to use external amplifiers with the lower gain to provide specified output signal power.
For citation:
Gerasimov A.B., Solovyev D.M., Demidov P.G. An efficient use of DAC dynamic range In frequency-selective channel simulator // T-Comm. 2015. No.1. Рр. 90-92.
A method for implementing digital multipath channel simulator
Equation for complex envelope of radio signal which has passed through multipath fading channel can be written as [2]:
(1)
where <? (?) is complex envelope of band limited radio signal with bandwidth B at transmitter's side; T-\jB is sample time; g((f) is a set of weight coefficients, which can be expressed as [3]:
(2)
where h(t,r) is channel's complex pulse response.
According to the equation (I), multipath fading channel can be modeled as tapped delay line {see fig. I).
m
¿o(')JL ä(')JL SM
[xi —KX) —HX) N—-rm<)
m t
S
Fig. I. Structural model of multipath fading channel
In most popular statistical models coefficients ¿({r) are
represented as complex stationary uncorrelated random processes with real and imaginary parts which are uncorrelated Gaussian random processes with zero mean, equal variance and power spectrum density (PSD) S(o)), which is defined by channel's Doppler spectrum [4], Variances of real and imaginary parts of random processes gt(r) are given by:
i Tp(kT)
<J. ----- !
(3)
where jr;(r) denotes delay power profile, which is key characteristic of multipath channel [3].
Parameter scaling technique for digital signal simulator
Random processes ¿((/) are commonly generated in accordance with the functional diagram, shown at fig. 2.
Doppler LPF
WGN fiW
generator
irm+Ji
WGN Doppler LPF NsM n>(!)
generator
Fig, 2. Functional diagram of random process gk(t) generation:
WGN - white Gaussian noise; f).(t) m '/,(0 — rea' normal processes with a unit SD and PSD 5{rt>); rj(t) — complex normal random process
The efficiency of dynamic range usage for digital representation of WGN improves with the increase of standard deviation (SD) of generated random numbers. At the same time it causes the increase of probability of dynamic range overflow, which leads to distribution function distortions. SD for generating WGN samples should be chosen for a specified overflow probability P.
Normally distributed random numbers deviate from its mean value not greater than x with probability, equal to
erf{xnJ(4?.o'))~ where erf(x) is error function [5]. Let a WGN representation range be normalized to I. Then the probability of WGN overflow will be equal to P, if SD of WGN is defined by the following expression:
(T =
S&f-l(P)
(4)
where erf '(.v) - inverse error function.
In the following SD of normal process should be kept unchanged, when it passes through Doppler LPF. Commonly Doppler LPF is realized as FIR filter with a impulse response h\m\ {/)ie[0,M)) [3]. Than SD will remain constant, when normal process passes through FIR filter, if the following condition is provided:
(S)
An efficient use of DAC dynamic range of fading channel simulator is also provided by appropriate normalization of random processes g^/)- If a simulator input signal has a constant envelope and covers a whole simulator input range, then real and imaginary parts of output signal complex envelope will be normal processes with the equal SD, given by formula:
tf-i
In this case output signal envelope will follow Rayleigh distribution with parameter Jler [3]. The probability of the overflows of output signal complex envelope samples will be
7TT
equal to P, if real and imaginary parts of complex normal processes g^/) are normalized in the following way:
(6)
2V-I nP
V t-0
level of distortions of channel characteristics due to simulator parameters truncation. An effective use of DAC dynamic range of digital fading channel simulator permits to use external amplifiers with the lower gain to provide specified output signal power.
References
Scaling parameters for complex normal random processes, applied to multipliers at outputs of tapped delay line, should be evaluated in accordance with expressions (4) and (6) for efficient use of DAC dynamic range.
Conclusion
The presented technique of parameter scaling for digital frequency-selective fading channel simulator provides maximally efficient use of dynamic range of signal processing for a specified level of distortions of channel statistical characteristics. The feature of presented technique is the division of scaling process into several stages, which provides minimal
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T-Comm #1-2015
