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SYNTHESIS AND ANALYSIS OF THE COMPENSATION ALGORITHM TO THE QAM SIGNAL DISTORTION DUE TO NON-IDEALITIES OF QUADRATURE DOWNCONVERSION AT AWGN AND PHASE NOISE IN THE PRESENCE OF QUAZIDETERMINISTIC BANDPASS INTERFERENCE
Poborchaya Natal'ya Evgen'evna,
PhD in Technical Science, MTUCI, associate professor, Russia, Moscow, n.poborchaya@gmail.com
Pestryakov Alexandr Valentinovich,
Doctor of Technical Science, MTUCI, dean of the Radio and Broadcasting faculty, Russia, Moscow, a.v.pestryakov@mail.ru
Khasyanova Elena Ravylovna,
PhD student MTUCI, Russia, Moscow, ehasyanova@gmail.com
Direct conversion receivers with quadrature signal processing have become widely spread, especially in the mass radio equipment, for last ten years. However, despite the obvious advantages of such structures (its simplicity, absence of image receiving channels, excluding the difficult path of selectivity at the intermediate frequency), there are significant imperfections re-lated to the quadrature conversion errors. These imperfections are caused by I/Q-imbalance of the frequency downconverter and the LO signal leakage lead to time-varying DC-offset.
As the studies [1, 2, 3] have shown, these errors can significantly decrease the signal reception quality. In addition, the more complex signals are used in the system, the stronger this effect is. As far as the circuit solutions and the technological level of the modern component base [2] don't provide the necessary rates nowadays, literature observes a wide range of the error compensation methods with the digital signal processing. Review and classification of such algo-rithms are shown in [4]. More often proposed algorithms were received empirically or produced without the real interference. Frequently the developed algorithms don't include the comprehen-sive analysis checked by modeling in the channels close to the ideal. Moreover different types of errors as a rule are estimated and compensated separately.
Thereby the analysis of the possibility of the joint assessment and assigned error com-pen-sation is timely. Article observes the estimation of signal parameters with the quadrature am-plitude modulation (QAM) at the output of the quadrature downconverter for further distortion compensation not only in the presence of the white AWGN but with the quazideterministic bandpass interference, which appears as the result of the quasi-harmonic oscillation superposition, spread along frequency. The problem will be solved by the nonlinear filtering method [5, 6].
Keywords: QAM, nonlinear filtering method, amplitude and phase offset, Tikhonov's func-tional, AWGN.
For citation:
Poborchaya N.E., Pestryakov A.V., Khasyanova E.R. Synthesis and analysis of the compensation algorithm to the QAM signal distortion due to non-idealities of quadrature downconversion at AWGN and phase noise in the presence of quazideterministic bandpass interference. T-Comm. 2015. Vol. 9. No.3. Рр. 82-85.
82
■
Let us consider QAM signal z, = S,(X j . observed in the presence of the noise n and quazideterministic interference n :
y, - Z, + n, + n, , (1)
where f = \,m - discrete time, m - Tí, Tn - observation time.
At
At - sample time, x,=(a,. ■■■ a„ fl if, y, A<p, bcl bj -
vector of estimating parameters, («T»-transpose functional)
y, = (yi, A)' - M, = (Mi, M«)T• 'I = (n„ iJ, S,(») = (zb zic )T -non-linear vector-function describes quadrature signal components z.,,zk Í7,8]:
z* = r.A^giM-kT-r,)(/sin(^ + ) + Jbcos^ + Aft))+V (2)
z* = -kT-T,)(/„ cos(5t>- Jkr sin(4» + hct ■
k-1
Here (2) = Aa>l(M~t,)+<pl, (pf= <pm -- the signal
phase stipulated by the oscillators phases on the transmission and receiving side {<pa¡) and by the delay in the propagation channel
(r ), f - carrier frequency, j-. - signal delay appears at the work of the clock oscillator, ae>, - In■ Af, , Af, - frequency left after the removal of the carrier frequency, - basic im-
pulse signal amplitude and p - \ «tags» of the previous impulses at the moment of time i, y Atp - amplitude and phase offset, ¿, b. slowly changing «constant» components of the quadrature signal, JkT=(2r-\-jM)d - amplitude
of the information signal with discrete values, q,r- I: >/A7, 2d -distance between close amplitudes, (mt-\)T < Ati-t¡ < mtT,
T - symbol interval / (j ), ffl| =.\~ñ, rt = Zk.
T
git) =
sin(m/T) cos(/?-7f/7")
MÎT 1 -4 pWtf* Impulse response of the channel. Its frequency characteristics has the type of «raised cosine», p - slope coefficient, p e [0;1],
A - signal amplitude.
As the model of the bandpass interference the sum of the quaziharmonic is used:
ñk = £4* ms(mkA{¡ + xt ),
(3)
2. + " Phase noise-
= =0 , at ~ Gaussian
forming noise.
3. rt = const, Aft / 0 = const, A ft - const = const . ht l = const, bs, = const ■
4 Symbol sequence lt, Jt is known.
5. Amplitude A and waveform of the signal g(f) is unknown.
6. Amplitudes au,-~-api at time of the observation are independent of time, au = at,k = TTp ■
7. Frequency band [fmh; where interference i| can appear, is known.
On terms of screening y j - \ ■the estimation ofthc X
vector X should be found- At patterning the algorithm one signal reading per information symbol will be taken, i.e. At - T.
Solution.
Signal delay r was searched separately according to the assigned algorithm [9].
list i mat ion vcctor of the random signal parameters is searched by the modified least square method in the functional form by Tikhonov
= mm
¡i
(4)
(IHIp-"Hq-'" Euclidean nonn with the weight p-1 h o 1 j in conformity with (1), (2) ft (3), [10,11]:
X, = X, i + LK f(y, - S {X, ,)>, i= 1 :n,
(4a)
% = 7, X sin( A/i + xk + A tp,), where a - amplitudes, x, - random initial phases of the separate quaziharmonic ripple with the normal distribution at the interval ,t], ak =2nfk. frequency fk belongs to the interval
[i" j ; Fm ]■ According to the formula (3) the interference of the
demodulation got the amplitude and phase distortion as the desired signal.
The problem will be solved the following conditions:
1. |i( - fixed process with the unknown distribution,
Q = ) = , - noise observation covariance matrix, is known, =0,.,> i*jf E ~ mean value operator, [, , -
identity matrix with the size 2x2.
where K; = PD' ^D. PDf , +Q) , P = r, , + WW'cr:,
I = P - D, ,Kinitial conditions:r0. X() - from prior data.
St/(X■) = zk, f, =(l X/J, the form of the matrix D,., depends on the order of the laylor decomposition of the function S,(Xr) watch equation at the point X,.,, L=(0(^„ l(„.6Mp.i;).
Using of least square method allows solving the fallaciously assigned problem (by Adamar within the unknown noise distribution. The received algorithm is asymptotic optimal within the RMS-minimum criterion. [ 11].
As the revised problem is incorrect at this assigned (the current system is underdetermined: the length of the observation vector y is less than the length of the vector of the estimated
parameters x. (dynamic system)), the estimations (4a) at the end the works of the algorithm should be recalculated with the LS method the following way. Let us form the phase evaluation vector ^ = + i = /=1717 -implementation number then B = A ,X ■ Here
= <Pj Aft-),
■n-fow - ^ Kj -
T-Comm Vol.9. #3-2015
7ТЛ
Table 1
MSE estimating the signal parameters. Average interference bandwidth
&Flt=F„-FMln= 50 kHz, io= 21 dB
Signal-noise ratio, dB Signal- noise+interference ratio, dB 37(31) 27(21) 17(11)
21 (20.5) 19.8 (17.6) 15 (10)
cko. 0.02 0.023 0.03
ckOp (degrees) 1.03 1.08 1.34
cko v {Hz) 3.37 4.14 7.52
ckohi 0.005 0.005 0.0061
ckoK 0.0031 0.0038 0.0073
ckoy 0.0072 0.0077 0.0075
cko^ (degree) 0.27 0.29 0.44
Table 2
MSE estimating the signal parameters . Average interference bandwidth
= 500kHz, q0= 21 dB
Wg = - F
Sknai-noise ratio. dB Signal-noise+ interference ratio, dB 37(31) 21 (20.5) 27(21) 17(11)
19.8 (17.6) 15 (10)
cko. 0.02 0.02 0.37
ckoi} (degrees) 1.05 1.1 1.4
cko¥ (Hz) 4.14 4.7 7.9
ckobc 0.0059 0.0051 0,0062
ckoi3 0.0042 0.0041 0,0072
ckof 0.0063 0.0063 0.0077
cko Stf (degree) 0.23 0.26 0.43
Fig. 3 illustrates simulation error probability on symbol from the signal-noise ratio at receiving the QAM-64 signal with the help of the correlators for two cases: volume of the processed screening aa=500 and m=IOOO for = 21 dB, picture 4 - for
q0=27dB.
in ' 00
<
m=10oo
20 S 30 3D 4
m^500
\\
m= 1000
AF„ = SmkHz,q„ = 21 JB
b) AFn - 50 it//;. q„ = 2] JB
a) AF„ = 500 kHz, qa = 21 dB
h) AF„ - 50*//;, q, = 27 dB
Fig. 3. Error probability on symbol
Fig. 4. Error probability on symbol
Analysis of the practical application shows that using the processor TMS320C6400 with the perfomance 8800 MIPS, algorithm of the nonlinear filtering (4) estimates the signal distortion for 128 microsecond, if T = 0.25 microsecond at the volume of the processed screening m = 500 and 255 usee at m = 1000, Though the procedure (4a) takes 125 psec at m = 500 and 250 Usee at m = 1000.
Conclusions. Computing experiment showed that the reception of the QAM signal at the presence of the bandpass interference is satisfactory at signal-interference ratio q0 — 27 dB. At
<7fl = 21 dB it's advisable to compensate the interference in order to increase the quality of the reception. Synthesized algorithm (4a) may be realized in the real time the delay in time received by the assessment recalculation procedure (46) is minor.
References
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