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THE MODERN STATE ANALYSIS OF DIGITAL SIGNAL PROCESSING APPLYING DUE TO THE QUADRATURE DOWNCONVERSION INACCURATES COMPENSATION
AT THE ZERO-IF RECEIVERS
Elena R. Khasianova,
MTUCI, Moscow, Russia, ehasyanova@gmail.com
Keywords: quadrature downconverters, IQ-imbalance, blind source separation, statistical methods, maximum likelihood method, adaptive filtration, DC-offset.
The major compensation schemes of I/Q-imbalance and DC-offset errors arising due to the analog front-end non-idealities are reviewed and classified in the paper: maximum likelihood method, statistical and filtration algorithms. In addition, a mathematical model of a signal with two types of the I/Q imbalance introducing principle is revised: the two and the one path adding type.
The most effective of them are based on the information sequence estimation. There was intentionally not made emphasis on quadrature downconversion non-idealities compensation for OFDM systems, since the pilot signal information is most often used for this purpose wherein the compensation principle remains unaltered. The difference is in the signal structure based estimation.
The main article conclusion is despite the diversity of approaches, there is a need to develop a simplified type of compensation that is similar to the statistical method but has the less convergence time and more precise accuracy.
Information about author:
Elena R. Khasianova, PhD student, Moscow Technical University of Communications and Informatics (MTUCI), Moscow, Russia
Для цитирования:
Хасьянова Е.Р. Анализ современного состояния применения цифровой обработки сигналов для компенсации погрешностей квадратурного преобразования в радиоприемных устройствах с нулевой промежуточной частотой // T-Comm: Телекоммуникации и транспорт. 2017. Том 11. №11. С. 84-88.
For citation:
Khasianova E.R. (2017). The modern state analysis of digital signal processing applying due to the quadrature downconversion inaccurates compensation at the zero-if receivers. T-Comm, vol. 11, no.11, рр. 84-88.
T-Comm ^м 11. #11-2017
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1. introduction
Direct RF conversion receiver could be the ideal architecture due to the Software-Defined Radio design. However one of the best ana log-to digital converters (ADC) from the Analog Devices Inc. lias the maximum dynamic range 91.5 dB at the rale of 10 MS PS and 16 bits resolution (it's meant AD6726). The use of such ADCs in the mass radio equipment is not possible due to the high cost and significant energy consumption even assuming the further dynamic range and processing speed increasing. Therefore there is a radio frequency (RF) path between the antenna and the ADC, which in genera! ease includes a bandpass filter, low noise amplifier, and a frequency down converter. According to the world's leading manufacturers datasheets the quadrature mixers may introduce the imbalance 0.2-2% and 0.2-2° (in amplitude and phase, respectively). Thus, the reducing all conversion errors to an acceptable level seem to be impossible even with the use of modem inlegraled-circuit production technology. This is particularly noticeable w ith the using of high-order modulation such as QAM-16, -64, -128 or the OFDM technology. In the latter case the orthogonally failure can significantly degrades the reception quality. The other limiting factors may include the DC offset (DCO) and the carrier frequency offset (CFO). The CFO compensation problem generally relates to I he synchronization task. Therefore the main attention in the article is paid to the review of IQ-imbalance and DCO compensation methods.
2. Receiving signal mathematical model with allowance
for the quadrature downconvcrsion imperfections
Quadrature downconversion non-idealities compensation approach is determined by the way in which the imbalance is introduced into the model of the received signal. Publications analysis allows concluding that two types of imbalance models could be used during the simulation process: introduction of imbalance coefficients in either branches or its addition only to the quadrature branch (Fig. 1). The DC-offset component can be simulated as the addition of a constant level signal into the each branch of the receiving signal.
«v
Mis^-E
w
A<c>, \
R,(t) V')
-i
0
£ COS(ft.)
'R.mDC,' RQ(t)+DCQj
(2)
Here (1-g) is the amplitude imbalance level and <pr is the phase imbalance vaiue.
The differences between the imbalance models from the formula (1) and (2) in the context of the compensation coefficients using after of them estimation are in the scale coefficients and the phase rotation value.
Since only the position of the Q component oil the signal constellation will change with the use of the model (2), the model {1), which is used in further studies, is more appropriate to the practice. It assumes the appearance of a correlation between I and Q branches, which is a consequence of the amplitude inequality and orthogonally failure when performing a downconversion operation. However, it is preferable to carry out the correction of the distorted signal with compensating coefficients by assuming the model (2) from the implementation point of view, since it allows to reduce the number of operations of multiplication and addition twice (Fig, 2b).
k, P ----™ K0
a) b)
Fig. 1. Two case of IQ-imbalatice adding: a) the double branch and b) the single branch models; e„ g - amplitude imbalance coefficients;
Ai[>, - the value of the phase imbalance
In the first case the unbalanced signal in the matrix form could be represented as follows:
:r)cos(Aft) (l+i>in(Ap,)VR,(t) + DC, (1)
Here DC|, DCq are present the DC offset level in the caeh of the branches, cr is the amplitude imbalance value, A<pr is the phase imbalance error.
In the case of 1/Q-im balance adding only to the Q-branch, the receiving signal can he represented in a certain way:
t t tit,
a) b)
Fig. 2. The compensator's structure with the compensation coefficients using in a) the both paths; b) only in the Q path
3. Digital compensation methods overview
Amplitude-phase mismatch correction could not be necessary for each application and modulation type, since their values are not so large. There are several ways to correct the imbalance of quadrature components at the moment In a broad sense, they can be divided into non-data aiding schemes or "blind methods" and algorithms with the using of training data from the pilot signal. It should be noted, the imbalance estimation principle does not change from the estimation signal type: by the pilot signal or received data. For example, in work [I], a statistical method is used to estimate the l/Q imbalance of quadrature components over the OFDM signal training sequence.
The use of the "non-data aided" term is more preferable, since in the case of the "blind estimation" term there is confusion with equalizers based on the "blind source separation" principle.
N on-data aiding correction schemes are widely used as long as there is no a priori knowledge about the modulation type, pilotsignal or the test signal introduction in the case of them using. In general all Of the methods could be divided into the several types: maximum likelihood method, blind source separation method, filtration methods and the statistical estimation algorithms.
Maximum likelihood method
I/Q-imbalance estimation with the help of the maximum likelihood (ML) method has been extensively studied in the literature [2-4]. DC offset, I/Q-imbalance, and the carrier frequency offset are successfully evaluated with its application (Fig. 3,4).
■--no I/o imb comp
O—6SS L'Ü Im 11 comp. —*— stat 1*3 .mil comp. - *—r Ideal IAi Imb. comp. _ _„ no 1/Q lmb. romp. . , Ij. BSS I/O Imb. comp . jy . f^ itat I/O imb. comp. ^ Ideal VQ Imb. comp.
Fig. 6. BER of a linearly modulated 64 QAM system, l/Q imbalance of 0.5 dB and 5° in bolli Tx and Rx with/without a known of frequency offset in a multipath environment [9]
Filtration methods
Adaptive linear or non-linear filtration could be used due to the performing of the quadrature non-idealities correction. In the first case [10] the following equation system might be solved on the purpose of amplitude imbalance estimation:
v(«) = .v(n)+ vf {/:).*■*(»)
(8)
w(n + l) = w(i?)- M y(n)y(n)
Where y(n) is the output signal, x(n) is the input complex signal, x*(n) - complex conjugate of the input signal. BER curves estimation results for the QAM-64 signal with the weight step size M=0.000l is presented on the fig. 7 [11 ]■
Nonlinear filtering method is based on the Kalman filtration algorithm and the modified Tikhonov's least square method [12, 13] and is used to the simultaneous estimation of the CFO, 1/Q-imbalance, DCO and propagation delay time error. The effect of phase noise on the algorithm evaluation process is taken into account in contrast the above methods. An autoregressive phase noise model was used due to the simulation process. This estimation method has about the same accuracy as the blind source separation method, comparable computational complexity with a large number of evaluation parameters. However, some simplification, for example the separate evaluation of the error values, is needed to the practical application feasibility.
Fig. 7. g-imbalance estimation curves with the linear filtration algorithm. AWGN Eb/No=10 dB
Conclusion
The most popular classes of quadrature downconversion imperfections compensation methods were reviewed in the paper. Basically, their work is evaluated in AWGN channel in order not to be effective at modem wireless communication systems. However, it should be noted the investigations with the multipath and fading environments consideration are also existed. There was intentionally not made emphasis on quadrature downconversion non-idealities compensation for OFDM systems, since the pilot signal information is most often used for this purpose wherein the compensation principle remains unaltered. The difference is in the signal structure based estimation. Based on the overview, there is a need to develop a simplified type of compensation that is similar to the statistical method but has the less convergence time and more precise accuracy. Also the filtration effectiveness due to the 1/Q-imbalance problem under the noisy environment conditions is observed because of the relatively small values of them. The static DC-offset error could be compensated with the heip of the averaging. Alternatively, time varying DC-offset, which often is not taken into account, should be tracking using some sort of adaptive filtration.
References
1. Puntsri K, (2015). A Very Simple Algorithm of Sequential IQ Imbalance and Carrier Frequency Offset Compensation in Coherent Optical OFDM. KKU Resj. 20(2), pp. 168-176,
2. Gil G;-T, (2005). Joint ML Estimation of Carrier Frequency, Channel, 1/Q Mismatch, and DC Offset in Communication Receivers. IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, vol. 54, no. I, pp. 338-349.
3. Gappmair W. and O. Koudelka. (2012). CRLB and low-complex algorithm for joint estimation of carrier frequency/phase and l/Q imbalance iti dircct conversion receivers. Proc, IEEE 8th Int. Symp. Cnmmun. Systems. Networks and Digital Signal Processing, Jul, 2012, pp. 1-5.
4. Gappmair W (2013), Low-Complexity Estimation of Carrier and Imbalance Parameters in Direct-Conversion Receivers, Advances in Electronics and Telecommunications. vol. 3, no. 5, December 2013, pp.32-38,
5. Valkama M. at al. (2005). Blind l/Q Signal Separation-Based Solutions for Receiver Sinnal Processing. EURASIP Journal on Applied Signal Processings no. 16, pp. 2708-2718.
6. Mai land M. at al. (2005). Blind IQ-imbalance Compensation Using Iterative Inversion for Arbitrary Direct Conversion Receivers. 1ST Mobile & Wireless Communication Summit, vol. 14.
7. Rykaczewski P. at al. (2006). Non-Data-Aided l/Q Imbalance Compensation Using Measured Receiver Front-End Signals, in Proc. IT"1 Annual IEEE Int'l Symp, On Personal Indoor and Mobile Radio Communications (PIMRC), Helsinki, Finland, pp. 1-5, Sept. 2006.
8. Peslryakov A.V. Poborchaya N.E. Khasianova E.R. (2016). Simplified distortion compensation algorithms to the QAM-signal observed against the background of additive noise. Electrosyyaz, no. 4, pp. 35-40.
Rykaczewski P., Jondral F. (2007). lilind l/Q Imbalance Compensation in Multipath Environments. Proc of IEEE International Symposium ISC AS 2007.
10. Anttila L. (2007). Blind Compensation of frequency-selective l/Q imbalances in quadrature radio receivers: circularity-based approach. Proc oflCASSP 2007.
I). Khasianova F..R. Sedov M.O. (2017). Experimental investigation of quadrature downconversion impairments estimation and compensation methods to the M-QAM signals. Proc: IEEE Int. Conf. On Systems of Signal Synchronization. Generating and Processing in Telecommunications (SINKHROINFO), Kazan, Russia. July 2017.
12. Poborchaya N.E. (2011). Random signal parameters estimation under the information gap conditions in the phase and synchronization purposes. LAP Lambert Academic Publishing. 100 p.
13. Pestryakov A.V., Poborchaya N.E., Kliasyanova E.R. (2015). Synthesis and analysis of the compensation on algorithm to the QAM signal distortion due to nonidealities of quadrat ure downconversion at AWGN and phase noise in the presence of quazidctcnninistlc bandpass interference. T-Comm, vol. 9, no. 3, pp. 82-85.
COMMUNICATIONS
АНАЛИЗ СОВРЕМЕННОГО СОСТОЯНИЯ ПРИМЕНЕНИЯ ЦИФРОВОЙ ОБРАБОТКИ СИГНАЛОВ ДЛЯ КОМПЕНСАЦИИ ПОГРЕШНОСТЕЙ КВАДРАТУРНОГО ПРЕОБРАЗОВАНИЯ В РАДИОПРИЕМНЫХ УСТРОЙСТВАХ С НУЛЕВОЙ ПРОМЕЖУТОЧНОЙ ЧАСТОТОЙ
Хасьянова Елена Равыловна, Московский Технический Университет Связи и Информатики, Москва, Россия,
ehasyanova@gmail.com
Дннотация
Рассмотрены и классифицированы основные схемы коррекции возникающих вследствие погрешностей аналогового ВЧ тракта разбаланса квадратурных составляющих и сдвига постоянной составляющей: метод максимального правдоподобия, статистические и фильтрационные методы. Кроме того, представлена математическая модель сигнала с учетом правила ввода в нее погрешностей квадратурного преобразования и принцип их компенсации в принимаемом сигнале.
Выявлено, что наиболее эффективными являются методы оценки, работающие по инфор-мационной последовательности и не зависящие от типа модуляции. Платой за универсальность является увеличение времени сходимости и вычислительной сложности. Акцент на компенсации разбаланса квадратурных составляющих и сдвига постоянной составляющей для OFDM систем не сделан намеренно, поскольку для этих целей зачастую используется информация, содержащаяся в пилот-сигнале, в то время как компенсационный принцип остается неизменным.
Результаты анализа показали, что большую эффективность при различных шумовых воздействиях и учете воздействия фазовых шумов имеют фильтрационные методы оценки. Кроме того, несмотря на кажущееся многообразие способов оценки I/Q-разба-ланса, существует необходимость в разработке метода, который будет иметь лучшие характеристики сходимости и точности по сравнению с действующими статистическими методами.
Ключевые слова: квадратурные преобразователи частоты, разбаланс квадратурных составляющих, слепое разделение источников, статистический метод, метод максимального правдоподобия, метод максимального правдоподобия, дрейф постоянной составляющей.
Литература
1. Puntsri K. A Very Simple Algorithm of Sequential IQ Imbalance and Carrier Frequency Offset Compen-sation in Coherent Optical OFDM // KKU Res.j. 2015; 20(2), pp. 168-176
2. Gil G.-T. Joint ML Estimation of Carrier Frequency, Channel, I/Q Mismatch, and DC Offset in Commu-nication Receivers // IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 54, NO. 1, JANUARY 2005, pp.338-349.
3. Gappmair W. and O. Koudelka, "CRLB and low-complex algorithm for joint estimation of carrier fre-quency/phase and I/Q imbalance in direct conversion receivers," in Proc. IEEE 8th Int. Symp. Commun. Systems, Networks and Digital Signal Processing, Jul. 2012, pp. I-5.
4. Gappmair W. Low-Complexity Estimation of Carrier and Imbalance Parameters in Direct-Conversion Receivers // Advances in Electronics and Telecommunications, Vol. 3, No. 5, December 2013, pp. 32-38.
5. Valkama M. at al. Blind I/Q Signal Separation-Based Solutions for Receiver Signal Processing // EURA-SIP Journal on Applied Signal Processing, №16, 2005, pp. 2708-2718.
6. Mailand M. at al. Blind IQ-imbalance Compensation Using Iterative Inversion for Arbitrary Direct Con-version Receivers // IST Mobile & Wireless Communication Summit, vol. 14, 2005.
7. Rykaczewski P. at al. Non-Data-Aided I/Q Imbalance Compensation Using Measured Receiver Front-End Signals, in Proc. 17th Annual IEEE Int'l Symp. On Personal Indoor and Mobile Radio Communications (PIMRC), Helsinki, Finland, pp. 1-5, Sept. 2006.
8. Пестряков А.В., Поборчая Н.Е., Хасьянова Е.Р. Упрощенные алгоритмы компенсации искажений КАМ-сигнала, наблюдаемого на фоне аддитивного шума // Электросвязь. 2016. №4. С. 35-40.
9. Rykaczewski P., Jondral F. Blind I/Q Imbalance Compensation in Multipath Environments // In Proc of IEEE International Symposium ISCAS 2007.
10. Anttila L. Blind Compensation of frequency-selective I/Q imbalances in quadrature radio receivers: circularity-based approach // In Proc of ICASSP 2007.
11. Khasianova E.R. Sedov M.O. Experimental investigation of quadrature downconversion impairments estimation and compensation methods to the M-QAM signals // in Proc. IEEE Int. Conf. On Systems of Signal Synchronization, Generating and Processing in Telecommunications (SINKHRO-INFO), Kazan, Russia, July 2017.
12. Поборчая Н.Е. Оценка параметров случайного сигнала при неполной информации в задачах фазовой и тактовой синхронизации. LAP Lambert Academic Publishing, 2011, 100 с.
13. Pestryakov A.V., Poborchaya N.E., Khasyanova E.R. Synthesis and analysis of the compensation on algorithm to the QAM signal distortion due to nonidealities of quadrature downconversion at AWGN and phase noise in the presence of quazideterministic bandpass interference // T-Comm: Телекоммуникациии и транспорт, 2015. Т. 9. № 3. С. 82-85.
T-Comm Том 11. #11-2017
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