ADVANCED ELECTROMAGNETICS, VOL. 5, NO. 3, NOVEMBER 2016
Baseband I/Q regeneration Method for Direct Conversion Receiver to nullify effect of I/Q mismatch Milind Shah, Sanjeev Gupta Dhirubhai Ambani Institute of Information and communication Technology, Gandhinagar, Gujarat-382007, INDIA E-mail:
[email protected]
Abstract Direct C onversion Receiver is t he c hoice o f t he t oday’s designer for low p ower co mpact wireless r eceiver. DCR is attractive d ue to lo w p ower, s mall s ize a nd h ighly monolithic i ntegratable s tructure, b ut d istortions a ffect its performance. I /Q mismatch i s the o ne o f t he major distortion which is responsible for performance degradation. In t his pa per, a novel method f or D irect Conversion Receiver is suggested, which makes it insensitive to the I/Q mismatch. H ere t he cl assical h omodyne ar chitecture is modified t o nu llify e ffect of I/Q mismatch. T he pr oposed method can b e i mplemented i n t he D igital Signal Processing (DSP) b ack-end section also. This feature makes i t accep table i n t he already d esigned/functioning classical homodyne architecture based receiver.
1. Introduction Direct C onversion R eceiver ( DCR) o ffer a l ow p ower an d very high level of integratable [1] solution for the design of wireless d evices. D ue t o s ingle mixer s tage, D CR e nables the implementation of the flexibility in the baseband digital signal processing, required by modern wireless communication s ystems. O ther t ypes o f r eceiver architectures require an image filter that can be designed in surface acoustic wave or bulk acoustic wave technology for which the level of the integration is very low [2]. However, the b aseband signals I (t) a nd Q (t) a t th e o utput o f this receiver can b e co rrupted b y d irect cu rrent ( dc) o ffset, inphase and quadrature (I/Q) mismatch, local oscillator (LO) leakage, and even order distortion [3-5]. This p aper d escribes th e I /Q mismatch p roblem i n DCRs. This distortion is mainly because of two reasons: (i) Local oscillator signal driving the mixers in I and Q branch are n ot i n q uadrature p hase i .e. 9 00 phase s hift, a nd ( ii) Difference in the transfer functions of I and Q branch due to production tolerance, which results in the uneven phase shift to I and Q branch signals. Gain error appears as a non unity scale factor in the amplitude, while phase imbalance corrupt one channel with a fraction of the d ata pulses in the other channel. W ireless d evices f or C ognitive R adio ( CR) applications are v ery sensitive to this problem [6]. Therefore, major effort has been put on the removal of this problem nowadays.
Several techniques are proposed in the literature to solve the I /Q mismatch p roblem. These ap proaches can b e classified i n two b road cat egories: ( i) D ata - aided approaches an d ( ii) B lind ap proaches. V arious d ata-aided techniques ar e d escribed i n [ 7]-[13]. These ap proaches ar e strongly s tandard d ependent because t hey r ely o n k nown pilot o r t raining s equences. As r eceived r eference symbols contain the impairments o f t ransmitter a nd r eceiver s ignal processing c hain, t hese methods ar e s uitable f or co mbined mitigation o f s everal i mpairment s ources. [ 7] an d [ 8] represent co mpensation o f I /Q mismatch with le ast square approach i n c ombination with frequency o ffset, while [9],[10] compensate with channel estimation. [11] represents compensation of frequency d ependent I /Q mismatch on t he transmitter side a nd [ 12],[13] bot h on t ransmitter a nd receiver side in MIMO systems. Various bl ind methods a re d escribed i n [ 14]-[19]. Blind methods rely on statistical properties of the influenced signal. [ 15] u ses t he statistical i ndependence b etween t he desired s ignal a nd its mirror im age f or f requency independent I/Q mismatch compensation in lo w-IF receiver by blind signal separation. In [16] a g radient descent search method i n t ime do main a nd a f requency do main a pproach based o n a s ingle-tap matrix i nversion for f requency dependent I /Q i mbalance c ompensation is pr esented. [ 17] provides ad vanced b lind s ource s eparation t echniques f or frequency i ndependent I /Q i mbalance co mpensation i n MIMO s ystems a nd [ 18] s hows t he s ame for t he frequency dependent cas e b y u sing h igher-order s tatistics in a n independent c omponent a nalysis. T he c ompensation of I /Q mismatch using pr operness pr operty of t he s ignal i s represented in [19]. Data-aided methods g ive fast c onvergence a nd good performance b ut a t t he c ost of high c omputational complexity. Blind m ethods a re standard i ndependent a nd therefore ar e m ore f lexible i n i ts u se, b ut n eed l onger convergence t imes an d s ometimes high i mplementation effort. As a s olution to th ese p roblems, a n a rchitectural approach has been adopted here to propose a simple solution for I /Q mismatch pr oblem. Here a n ovel method of I /Q regeneration i s proposed with s elf c alibration strategy to nullify I /Q mismatch p roblem. S elf c alibration method makes t his ap proach s tandard i ndependent an d s imple algorithm makes it f ast a nd computationally less c omplex. Comprehensive s imulated an d p ractically measured results
are p resented t o i ndicate t he effectiveness o f t he p roposed architecture.
[3]. N ext s ection, de scribes t he pr oposed m ethod of I /Q regeneration, which nullify the effect of I/Q mismatch.
2. Analysis of classical DCR 3. Analysis of proposed method
The p urpose of an R F d irect co nversion r eceiver i s t o demodulate a signal aRF(t) with car rier f requency fRF, complex e nvelope env(t) =I(t) + jQ(t), and a mplitude ARF using a s ignal aLO(t) generated b y a l ocal oscillator with frequency fLO = fRF and amplitude ALO. The two signals can be represented by the two complex waves. aRF(t) = ARF(I(t) + jQ(t))exp(j2πfRFt) aLO(t) = ALO exp(j2πfLOt).
Here, we introduce I /Q mismatch d istortion a nd t hen demonstrate the ability of proposed method to nullify effect of d istortion o n th e o utput o f th e r eceiver. I /Q mismatch i s introduced b y t aking different gain a nd phase for t he l ocal oscillator path-1 and path-2. In this case the local oscillator signal to mixer-1 and mixer-2 are
(1) (2)
vLO1(t) = ALO1 cos(2πfLOt+ϕ) vLO2(t) = ALO2 cos(2πfLOt+π/2 +ε)
The voltages vRF(t) and vLO(t) are obtained by taking the real part of Equation (1) and (2). vRF(t) = ARF(I(t)cos(2πfRFt) - Q(t)sin(2πfRFt)) vLO(t) = ALO cos(2πfLOt).
(3)
(8) (9)
where ϕ is the phase shift between transmitted carrier signal and locally generated carrier signal, while ε is phase shift introduced due to non- similarity in design and other factors. Therefore, the o utput o f low pass filters in the presence of I/Q mismatch are
(4)
I(t) a nd Q (t) re present t he inphase a nd q uadrature ( I/Q) signals. F igure 1 r epresents t he cl assical d irect co nversion receiver using quadrature down conversion, which performs the demodulation of vRF(t).
v1(t)= A1.cos(ϕ).I(t)+ A1.sin(ϕ).Q(t) (10) v2(t)= A2.cos(ε).I(t)+ A2.sin(ε).Q(t) (11) A system can be written using (10) and (11)
v1 (t ) I (t ) v (t ) = B Q(t ) (12) 2 with
A cos(φ ) B= 1 A2 cos(ε )
A1 sin(φ ) A2 sin(ε )
If w e s uppose that t he m atrix B is no nsingular, then we obtain Figure 1: Classical Direct Conversion Receiver
v (t ) I (t ) −1 1 Q(t ) = B v (t ) 2
As p er F ig.1, R F s ignal i nput t o mixer-1 a nd mixer-2 i s vRF(t). While, lo cal o scillator ( LO) s ignal to mixer-1 i s vLO1(t)= vLO(t) and to mixer-2 is vLO2(t)= ALO cos(2πfLOt+π/2).
With
(5)
α α 2 B −1 = 1 β1 β 2
Output of low pass filter-1is v1(t) and of low pass filter-2 is v2(t), v1(t)= (ARFALO /2).I(t) v2(t)= (ARFALO /2).Q(t)
(13)
With (13) and the expression of the inverse of matrix B, the expressions of the I(t) and Q(t) signals are
(6) (7)
I(t) = α1(v1(t)) + α2(v2(t)) (14) Q(t) = β1(v1(t)) + β2(v2(t)) (15)
Analog to digital converter (ADC) converts v1(t) and v2(t) in digital d omain a nd th en a pplied to b ack-end d igital signal processing (DSP) section to extract the transmitted data bits. Extracting t he I (t) and Q(t) signal without d istortion is t he critical function of the receiver. I/Q mismatch greatly affect the f aithful r eproduction o f I (t) an d Q (t) s ignal at r eceiver
Equations (14) and (15) define the relation between I(t) and Q(t) signals, the two output voltages v1(t), v2(t) and the four real calibration constants (α1, α2, β1, β2). The c alibration of t he pr oposed method gives four real constants, which allow faithful I /Q r egeneration f rom 51
the t wo o utput voltages i n t he p resence o f I /Q mismatch. The four calibration constants can be calculated in two steps as follows.
receiver s ection. Receiver s ection d own co nverts t he received signal, low pass filtered the signal and then applied it to multiplier and adder block to regenerate I(t) and Q(t), and a t th e same time a pplied to c alibration a lgorithm to calculate calibration coefficients αi, βi.
1) An RF signal with known I(t) , Q(t) sequence (length of N symbols) is in jected a t in put o f th e d irect c onversion receiver. This input generates two o utput voltages that c an be used to write
I (1) α1 C. = α 2 I ( N ) Q(1) β1 C. = β 2 Q( N )
(16)
(17) Figure 2: Self-Calibration Method
v1 (1) v2 (1) with C = v1 ( N ) v2 ( N )
3.1. Properties of calibration constants
2) U sing t he d eterministic l east-square method, t he f our constants are calculated as
Analysis of properties of calibration constants is required to understand t he process o f I (t), Q (t) r egeneration p recisely. Define the five following vectors.
I (1) α1 T −1 T α = (C .C ) .C . 2 I ( N ) I (1) α1 −1 T T α = (C .C ) .C . 2 I ( N )
v (t ) (20) Vo = o1 vo 2 (t ) A . cos(φ ) A . sin(φ ) Gcos = 1 , Gsin = 1 A2 . cos(ε ) A2 . sin(ε ) α β α = 1 , β = 1 (22) α 2 β 2
(18)
(19)
After d etermining th ese f our r eal c oefficients, I /Q demodulation can take place using the t wo output voltages. There ar e t wo methods t o p erform t he cal ibration o f t he proposed system. 1) M ethod of pr ecalibration: T he pr oposed m ethod c an be calibrated d uring manufacture. A known I Q s equence is injected at the RF port for all the frequencies to be used and the coefficients of the calibration are recorded in memory. 2) Method of self-calibration: Here a self calibration method is pr esented with t he pr oposed m ethod i n F igure 2. Advantage o f th is method is that it is standard independent and activate during the power on of the device or during the ideal/ s tandby ti me d uration. F or e xplanation p urpose th e multiplier a nd ad der b locks ar e r epresented s eparately, b ut usually they are part of the DSP back-end. When t ransceiver en tered i n t he s elf cal ibration mode, switch S1 becomes open and switch S2 connected to terminal b. Thus antenna section is bypassed. DSP back-end section generates I (t) an d Q (t) s equences a nd ap plied t o Transmitter s ection. T ransmitter s ection modulates th e I (t) and Q(t) s equences and f requency up convert t he signal t o RF c arrier f requency. T his RF s ignal will b e a pplied to
(21)
The system de fined by (10) and (11) becomes the vectorial relation
Vo = I (t )Gcos + Q(t )Gsin
(23)
Equation ( 14) an d ( 15) can b e s een as t wo s calar p roducts. Using relation (23) and the two vectors defined by (22), we obtain
α v (t ) I (t ) = α • Vo = 1 • o1 α 2 vo 2 (t ) (24) 2
= ∑ α i voi (t ) i =1
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for tr aining p urpose ( i.e. utilized f or c omputation of constants αi and βi). Remaining data symbols will be utilized for calculation of BER. The s ymbol r ate u tilized is 5 Msamples/s.
β v (t ) Q(t ) = β • Vo = 1 • o1 β 2 vo 2 (t ) (25) 2
= ∑ β i voi (t ). i =1
BER Versus Phase Error
-1
10
Proposed Method Classical DCR
By using the expression of the vector Vo defined by (20) and replacing it in (24), we can deduce the following relation for the I channel: BER
I (t ) = I (t )α • Gcos + Q(t )α • Gsin
-2
10
-3
10
(26) -4
10
By id entification, we c an write th e f ollowing r elations for the I channel:
α • Gsin = 0 α • Gcos = 1.
-5
10
0
5
15
10
20
25
Phase Error
(27)
Figure 3: BER versus Phase Error (degree) (28)
In the same way, for the Q channel we obtain
β • Gcos = 0
β • Gsin = 1.
(29) (30)
Equations (27)-(30) show that the calibration procedure allows the following: 1) S eparation b etween t he I (t) a nd Q (t) s ignals [ with ( 27) and (29)]: The geometric property is that the vectors α and β are, respectively, perpendicular to the vectors Gsin and Gcos. 2) Normalization of vector α and β [with (28) and (30)]: This p roperty a llows th e n ormalization o f I(t) a nd Q (t) signals b y c ompensating t he a mplitude Ai of t he r eceived signal, i.e. if A i is low, the norms of vector α and β are high and vice versa.
4. Results
Figure 4: QPSK constellation for classical DCR
This s ection p resents t he s imulation r esults a s well practically measured r esults. T he s imulation r esults a re presented i n F igure 3 - 5. MATLAB is u tilized f or th e simulation purpose. Fig. 3 presents the effect of phase error between I(t) and Q(t) on the BER. Here the performance of classical D CR a nd p roposed method ar e t ested i n t he presence o f p hase er ror. C lassical D CR ar chitecture ca n maintain its performance during low value of phase error i.e. upto 3 o-4o degree. W hile proposed method can maintain i ts performance u pto s ufficient l arge a mount of ph ase-shift. This indicates that the proposed method is insensitive to the phase s hift e rror. S imulated constellation d iagram for th e classical DCR and proposed method is presented in Figure 4 and 5 . C onstellation d iagrams a lso d emonstrate t hat th e proposed method is insensitive to the I/Q mismatch. The t est-bench utilized f or ex perimental measurement i s s hown i n F igure 6. H ere an R F s ignal at 2.4GHz w ith Q PSK modulation i s pr ovided. O ut of t he entire d ata s equence, first s ixteen s ymbols will b e u tilized
Figure 5: QPSK constellation for Proposed Method
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The s ignal generator g enerates t he l ocal o scillator signal at 2 .4GHz an d t he L O p ower i s 0 dBm. T he v ector signal generator g enerates t he Q PSK-modulated s ignal at 2.4GHz an d t he R F p ower i s t uned as p er t he r equirement. Both t he signals a re s ynchronized. O ne more s ignal generator i s utilized t o g enerate an i nterfering s ignal o r Additive W hite G aussian N oise ( AWGN) s ignal. T he desired R F s ignal a nd i nterfering RF signal ar e ad ded with an in-phase power combiner and applied to the RF input port of C lassical Direct C onversion R eceiver ( DCR). T he t wo down c onverted l ow-pass filtered o utput v oltages o f D CR are sampled by 16-bit Data Acquisition Module and apply to the a lgorithm, written i n M ATLAB, for c omputation o f coefficients αi , βi. On the base of the computed value of αi and βi demodulation of received sampled signal is done and then the received bits are compared with transmitted bits for computation of BER. A large number of data sequences are demodulated t o e stimate B ER. T he m easured r esults ar e presented in Figure 7 and 8.
BER
Figure 8 p resents t he s ensitivity measurement o f t he receiver. S ensitivity is t he minimum R F i nput p ower required t o e nsure re quired B ER. If re quired B ER i s assumed to 10-3, t hen t he measured sensitivity of proposed method is -62.5 dBm, while that of c lassical DCR is -60.8 dBm. 10
0
10
-1
10
-2
10
-3
Sensitivity Chart
-4
10
Measured Proposed Method Simulated Proposed Method Simulated Classical DCR Measured Classical DCR
-5
10
-6
10 -70
-69
-68
-67
-66
-65
-64
RF Power of Modulated Signal (dBm)
-63
-62
-61
Figure 8: BER versus RF power of signal
5. Conclusions In t his p aper a n ovel m ethod i s p resented t o r emove I /Q mismatch di stortion. H ere p roposed m ethod i s pr esented with its principle of operation and self-calibration technique. Self c alibration te chnique adapts c alibration c onstants during th e li fe o f t he s ystem, r ejects th e d istortion a nd regenerate t he I /Q signals w ith m inimum n umber of error. Proposed m ethod with s elf c alibration doe s n ot r equired high co mputational co mplexity a nd can b e eas ily implemented i n D SP b ack-end s ection. T his r esults in to a cost ef fective upgrading s olution. T his feature makes t he proposed method very attractive. Experiments a re pe rformed on t he pr oposed D CR with Q PSK s ignal t o va lidate t he p resented t heory. Measured r esults ar e s upporting o ur claims. W ith r eference to theoretical BER, proposed method with self calibration is implemented with t he i mplementation l oss of 0. 8dB. The sensitivity a chieved with pr oposed method i s -62.5 dB m a t BER = 10-3. The sensitivity of the proposed method can be improved with h elp o f LNA, which is not u tilized in t he proposed test bench. As proposed method is very effective in I /Q mismatch r emoval, a D CR with t his r obust, no e xtra hardware, d istortion r emoval a bility will b e a g ood contender f or C ognitive R adio R eceiver. H ere proposed method is tested for only QPSK modulation scheme, but in later it c an be tested for other complex modulation scheme, as well proposed method can be expanded to deal with other distortions present in the direct conversion receiver.
Figure 6: Test-bench utilized for experimental measurement of BER Figure 7 p resents t he co mparison o f t he p erformance o f classical DCR with our proposed method in static condition with AWGN. H ere co mparison h as b een d one with t he theoretical B ER for Q PSK s ystem with simulated a nd measured B ER o f cl assical D CR ar chitecture an d p roposed method. A t B ER = 10 -3, th e i mplementation lo ss for proposed D CR a rchitecture is e qual t o 0. 8dB, w hile for classical DCR it is approximately 2dB. 10
-2
BER
10
BER Versus SNR
-1
10
10
-3
Theoretical probability of Error Simulated Proposed Method Simulated Classical DCR Measured Proposed Method Measured Classical DCR
References
-4
0
1
2
3
4 Eb/No (dB)
5
6
7
8
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Figure 7: BER versus SNR
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