AN ITERATIVE FEEDBACK ALGORITHM FOR CORRECTING THE I/Q IMBALANCE IN DVB-S RECEIVERS

Transcription

1 AN ITATIV FDBACK ALGOITHM FO COCTING TH I/Q IMBALANC IN DVB- CIV lias Nemer and Ahmed aid Advanced Technology Office, Consumer lectronics Group, Intel Corporation 35 Plumeria Drive, an Jose, CA 9534 UA phone: + ( , fax: + ( ; enemer@ieeeorg ABTACT In digital video broadcast systems, such as those used in satellite and terrestrial transmission (DVB-, -T, an analog tuner is used at the user site to down-convert the signal and provide a first stage of demodulation that yields the baseband uadrature (I and Q components Due to imperfect analog demodulation and A/D mismatch, the uadratures will be off-balance in both phase and magnitude This in turn has a negative effect on the signal N, as well as on the operation of the internal loops in the receiver This paper describes a novel timedomain method for balancing the I and Q uadratures at the front end of the receiver The proposed solution consists of iterative feedback loops operating independently, and without apriori knowledge of the transmitted symbols imulation on the DVB- constellations - QPK, 8PK and 6QAM - shows the scheme is robust in severe channel impairments and yields a significant improvement of the cluster variance at the receiver output KY WOD I/Q imbalance Analog demodulation Introduction The demodulation in an imperfect analog tuner with uadrature imbalance may be modelled ] as shown in Figure : the usoids used for each uadrature branch may be viewed as non-orthogonal and un-eual in magnitude In addition, the analog filtering and A/D conversion may also introduce magnitude and phase errors between the uadratures The aggregate phase error is denoted as ϑ and the magnitude error asε It can be shown ] 7] that the corrupted uadratures (I and Q may be written in terms of the un-corrupted (hypothetical uadratures (I and Q and the magnitude imbalance (ε and the phase imbalance ( ϑ : cos I ' + ε I Q' ε Q cos For MPK modulations, the I/Q imbalance causes a warping of the (otherwise round constellation The effect is more pronounced for suare constellations such as the 6-QAM, and is less significant for the QPK case Figure : Tuner demodulation model In Figure below, the constellation at the input of the receiver is shown along with an ideal constellation for the case of 8PK and 6-QAM respectively The effect is more dramatic when other impairments, such as reflections and noise, are added to the channel imulation also shows that the convergence of the eualizer is negatively impacted by the I/Q imbalance and often yields a worsened constellation at the output of the receiver, as will be illustrated later Figure : ffect of I/Q imbalance on 8PK and 6-QAM In terrestrial broadcast systems utilizing multi-carrier OFDM modulation 3], a number of I/Q corrections schemes 6] 8] 9] have been proposed and can be applied in the freuency domain These schemes reuire either a calibration phase or apriori knowledge of the preamble symbols to estimate the imbalance before applying a correction In this paper, we propose a novel time-domain method for balancing the I/Q uadrature in a blind way (ie in a nondecision-aided manner and without apriori knowledge of

2 the transmitted symbols and prior to running any of the other loops in the receiver The correction can be applied at the receiver front end, after the analog demodulation and digital sampling (ie after the A/D on each of the I and Q branches in Figure, and thus does not reuire an accurate symbol timing estimation This method is particularly suitable for gle-carrier QAM receivers, such as those used in digital video broadcast by satellite ] 4] The paper is organized as follows: ection provides the derivation for the exact and the proposed solution to the I/Q estimation and correction ection 3 details the iterative feedback loops for the magnitude and phase correction imulation data and results are discussed in section 4 Blind Correction of the I/Q Imbalance xact olution to the I/Q Imbalance Theorem : Given a block of N data points representing M > symbols, the exact solution to the I/Q imbalance may be shown to be as follows: The phase imbalance is: ϑ ( I Q ] with I Q The magnitude imbalance is : ] ] ' ε with I ] ' + Q Proof : see appendix A ] An estimation and correction scheme based on the above derivations may be implemented in a block mode, where the statistical entities are estimated ug time averages over the total number of N samples, namely: ' ' ' ' I Q ] ( I n Q n ; I ] ( In ; Q ] ( Qn Once the imbalance is estimated, a correction may be applied to the uadratures, by a matrix inversion of : ~ cos I ε I ' ~ K Q + ε Q ' cos K ε cos ϑ ( ( Proposed olution To implement the above I/Q correction in a computationally-efficient way, the following are noted: The estimation problem may be divided into independent ones, whereby the magnitude and phase correction are done seuentially: the magnitude imbalance is estimated and corrected first, and then phase correction is done ug the magnitude-balanced uadratures For a real-time implementation, it is desirable to avoid divisions and minimize multiplications The above estimators may be reformulated ug energy differences instead of ratios and total energy instead of the product of individual uadrature energies For a power-independent scheme, the energy difference would have to be normalized by the total energy In practical receivers, the total energy may be assumed known apriori and is available from the automatic gain control (AGC loop, whose function is to maintain the input signal energy at a preset target An iterative approach is desirable ce it allows for continuous adjustment and does not reuire explicit summation and averaging over a large number of points Magnitude estimation ug energy differences Proposition : Assuming the total signal energy is known, the magnitude imbalance ε may be approximated by: ε ; ' ' { I ] Q ]} where represents the normalized energy difference between the uadratures Proof: The above approximation can be easily shown ce the total signal energy is given by (see appendix A: I' ] + Q' ] ( + ε and for small values ofε, it may be approximated as: ubstituting the expressions for, I ], Q ], ( 5, 6 in Appendix A into the above expression for yields the relation: ε Phase correction ug total energy normalization Proposition : Assuming there is no magnitude imbalance and the total signal energy is known, the phase imbalance may be approximated by: I' ] ϑ p ; p 3 Proof: This can be derived by considering the crosscorrelation between the uadratures ( 4 in Appendix A ince there is no magnitude imbalance, the crosscorrelation simplifies to I' ] ( ϑ The total energy in this case is, and assuming a small value of the phase imbalance ϑ, the above crosscorrelation becomes: I' ] ϑ /, from which the imbalance is deduced

3 3 Iterative Feedback Algorithm 3 Magnitude correction An iterative feedback scheme for estimating and correcting the magnitude imbalance as given in is shown in Figure 3 below At each iteration instance n, the uadrature values of I and Q are suared and then averaged ug an auto-regressive filter H (z The output of each the filters is an approximation of the long term energies of the I and Q uadratures respectively These energies are subtracted and the result normalized by the total energy factor, /, assumed to be computed s apriori Figure 3 : Feedback loop for the magnitude correction The resulting difference is the energy error and is accumulated ug a first order integrator The integrated error is simply the estimate of the magnitude imbalanceε ; from this entity, two terms are generated: ε and + ε, and are used to correct the next incoming samples on the I and Q branches respectively This scheme is run at the sampling rate, assumed to be to 4 samples per symbol 3 Phase correction An iterative feedback scheme for estimating and correcting the phase imbalance as given in 3 is shown in Figure 4 below At each iteration instance n, the uadrature values of I and Q are multiplied and then filtered ug a first order auto-regressive filter H (z This smoothed cross-correlation is then normalized by the total energy factor, / The result is the phase error s and is accumulated ug a first order integrator The integrated error is simply the estimate of the phase imbalance, ϑ ; from this value, the inverse of the phase imbalance matrix (denoted by A in u can be ϑ generated as : A cos ( ϑ cos cos Figure 4 : Feedback loop for phase correction The trigonometric ratios needed for the inverse matrix may be generated from a look-up table, indexed by ϑ The phase of the next incoming samples on the I and Q ~ " branches is then corrected as: I I ~ A ] " Q Q 4 imulation esults A first-generation DVB- transmitter/receiver system ug QPK, 8PK and 6-QAM modulation according to the specifications in ] 4] is simulated ug Matlab The symbol rate is set to 3 Msymb/s and an oversampling of 4 samples per symbol is used A baseband channel model is assumed and impairments added These encompass I/Q imbalance, with ε 5; ϑ 5deg ; up to 4 micro-reflections at 36, 55, 85, and 55 nsec according to the echo path profile in 5] ; and additive noise at various levels of b N A simple receiver model consisting of an AGC, an eualizer and a carrier recovery phase-lock loop is modelled as shown in Figure 5 Baseband (I + j Q Baseband Channel AGC I / Q balancing Nyuist Filter Nyuist Filter I-Q Imbalance eflections AWGN F F Carrier PLL I / Q Mapping Avg difference random QAM licer F B Figure 5 : Transmit / receive model Transmitter Cluster N oft eceiver The graphs in Figure 6 below show the convergence of the loops, namely the values of the magnitude and phase imbalances As can be seen, the magnitude estimate converges to the correct value in about 6, samples (5, symbols and the phase estimate in about 3 times this interval It is noted here that the loops are enabled

4 simultaneously, though in principle, the phase loop would only start proper operation once the magnitude imbalance has been corrected, which explains its later convergence psilon stimate Output after eualization without I-Q balancing Cluster N 45 db x 5 Phi estimate (rad Input at the receiver with I-Q imbalance, AWGN (b/no5db, and multi-paths (4 echoes Output after I-Q balancing and eualization Cluster N 97 db x 5 Impairments : AWGN + reflections + IQ imbalance Time (samples Figure 6 : magnitude and phase imbalance estimation The constellation of the soft symbols at the eualizer output is shown in the next 4 figures for 8PK, QPK and 6QAM In each figure, the graphs on the right illustrate the difference between eualization only and eualization following an I/Q balancing ug the proposed algorithm Figure 7 illustrates the case of 8PK with added channel impairments consisting of I/Q imbalance ( ε 5; ϑ 5 deg and multipaths ( echoes at 55 and 85 nsec Figure 8 : 8PK with and without I/Q balancing The case of QPK with combined AWGN ( b N db, reflections (4 echoes at 36, 55, 85 and 55 nsec and I/Q imbalance ( ε 5; ϑ 5 deg is shown in Figure 9 The I/Q balancing in this case results in a 5 db improvement in cluster N Output after eualization without I-Q balancing Cluster N 5 db Output after eualization without I-Q balancing Cluster N 58 db Input at the receiver with I-Q imbalance, AWGN (b/no and multi-paths (4 echoes Cluster N 5 db Output after I-Q balancing and eualization Figure 9 : QPK with and without I/Q balancing Input at the receiver with I-Q imbalance and multi-paths ( echoes Output after I-Q balancing and eualization Cluster N 36 db Figure 7 : 8PK with and without I/Q balancing The effect is uite pronounced in this case with the I/Q balancing resulting in a db improvement of the cluster N The same constellation is shown in figure 8, but with a different set of impairments, namely I/Q imbalance, multipaths (4 echoes at 36, 55, 85 and 55 nsec and AWGN (at b N 5dB The case illustrates how the eualizer cannot properly converge when I/Q imbalance is present The net effect of I/Q balancing is a 5 db improvement in cluster N Finally, the case of a 6QAM with I/Q imbalance and multipaths ( echoes at 55 and 85 nsec is shown in Figure The improvement in N is uite significant as eualization alone removes the effects of the echoes but not the I/Q imbalance 5 Conclusion This paper described a novel scheme for a blind estimation and correction of the I/Q imbalance in QAM receivers used in DVB systems The algorithm consists of iterative feedback loops operating independently, with no division and a reduced number of multiplications imulation on the constellations used in the first generation DVB- system ] 4], namely QPK, 8PK and 6 QAM shows the scheme is robust in severe

5 channel impairments and yields a significant improvement of the cluster N at the receiver output Output after eualization without I-Q balancing Cluster N 58 db The energy simplifies to ' I ] ( + ε cos + or simply: ' I ] ( + ε 5 ' similarly: Q ] ( ε 6 Input at the receiver with I-Q imbalance and multi-paths ( echoes Output after I-Q balancing and eualization Cluster N > 45 db Figure : 6 QAM with and without I/Q balancing Appendix A: Proof of Theorem First observe that for the un-corrupted uadratures of a suare M-QAM signal, the following three conditions hold: a I Q] b I c I ] Q ] + Q ] Namely, the uadratures are orthogonal, have eual energy on average, and the total signal energy is twice the energy of one uadrature From The cross correlation between the impaired uadratures is: I ( + ε ( ε cos + I Q ] Q ( + ε ( ε cos + L cross terms L The cross terms cancel, ce I Q], thus: I' ] ( + ε ( ε cos I + Q ] Ug trigonometric identity, the above simplifies to: I' ] ( ε ( + ε ( ϑ 4 Now consider the individual energies of the corrupted uadratures, ie I' ], Q' ] : I ( + ε cos + Q ( + ε ' ] I ϑ ϑ I Q ( + ε cos ince I Q] and I ] Q ] Ug the euations developed so far, The phase imbalance can be determined from the ratio : I Q ] ( ε ( + ε ( I ] Q ] ( ε ( + ε Thus : ϑ ( ϑ ( ϑ The magnitude imbalance is derived from the ratio : Q eferences ' I ] ( + ε ' ] ( ε ; thus ε + ] A/8 Modulation and coding reuirements for digital TV applications over satellite ATC tandard July 999 ] M Buchholz, A chuchert, Hasholzner, ffect of tuner I Q imbalance on multicarrier-modulation systems, Proc of the Conf on Devices, Circuits, and ystems, March Vol, pp T65/ T65/6 3] N Digital Video Broadcasting Framing structure, Channel Modulation for Digital Terrestrial Television TI V4-4] N 3 4 Digital Video Broadcasting (DVB Framing structure, channel coding and modulation for / GHz satellite services TI V ] N Digital Video Broadcasting (DVB atellite Master Antenna Television (MATV distribution systems TI V ] Fouladifard et al A new techniue for estimation and compensation of I Q imbalance in OFDM receivers I International Conference on Communications ystems Vol, pp 4-8 7] C Liu Impact of I Q imbalance on QPK-OFDM- QAM Detection I Transactions on Consumer lectronics, Vol 44, issue 3, Aug 998 pp ] A chuchert and Hasholzmer A novel IQ imbalance compensation scheme for the reception of OFDM signals I Transactions on Consumer lectronics, Vol 47, issue 3, Aug pp ] J Tubbax Compensation of I Q imbalance in OFDM systems I International Conference on Communications 3 Vol 5, pp Note: the algorithm presented in this paper is based on a patent filed by Intel Corporation (app # /746,55