Non-linearity Correction of ADCs in Software Radio Systems

Transcription

1 on-linearity Correction of ADC in Software Radio Sytem Luca De Vito,2, Linu Michaeli 3, Sergio Rauano Deartment of Engineering, Univerity of Sannio, Piazza Roma, 82, Benevento, Italy Ph.: , Fax: {devito, htt://leim.ing.uniannio.it 2 Teley telecommunication SA, Benevento Reearch Laboratory, via dei Sanniti, 828, San Giorgio del Sannio (B), Italy Ph.: , Fax: , htt:// 3 Deartment of Electronic and Telecommunication, Technical Univerity of Košice, Park Komenkého 3, SK-42 Košice, Slovak Reublic, linu.michaeli@tuke.k Abtract - The aer reent the reult of the exerimental validation of a method for digital comenation of ADC non-linearity error. Firt, the theory underlying the method i briefly decribed. Then, the comenation method ha been validated both on inuoidal ignal and on 3 rd generation mobile telecommunication ignal, comliant to 3GPP ecification. I. Introduction In meaurement and control ytem, in which high-frequency ignal are involved, both fat amling and roceing and high accuracy are required. Thee requirement are articularly relevant in many alication related to ignal intercetion and verification, uch a electronic urveillance ytem, military communication, emitter interceting and interference identification. Thi kind of alication, in fact, i often realized by uing oftware radio receiver []. A oftware radio i a radio ytem whoe channel modulation waveform are defined in oftware [2]. That i, the ignal to be tranmitted are generated a digital waveform and then converted from digital to analog at bae band or intermediate frequency (IF) via a wideband digital-to-analog-converter (DAC). Then, they are oibly uconverted from IF to RF and tranmitted. The receiver, imilarly, emloy a wideband analog-to-digital-converter (ADC) that cature all the channel of the oftware radio node. The receiver, then, extract, downconvert and demodulate the channel waveform uing oftware running on a general uroe roceor or a Digital Signal Proceor (DSP) [2]. In thee ytem the ADC characteritic lay an imortant role in the definition of the quality of the communication. The receiver, in articular, require both a high amling rate and a large dynamic range, becaue (i) the wideband IF ignal hould be amled at a frequency high enough to include all the required channel, and (ii) the uriou free dynamic range (SFDR) hould be high enough to enure that ome uriou ectral comonent with high amlitude do not hide the ueful ignal. In thi cenario, in order to imrove the receiver erformance, the identification of internal nonlinearity error of the ADC and the develoment of method for their correction in real-time could achieve a coniderable SFDR increae. Several aer dealing with the real-time correction of ADC non-linearitie can be found in literature. The mot art of them achieve a dynamic comenation of non-linearity error by uing a hae-lane [3] or tate-ace [4] aroach. In thee cae, the difference between the actual and the ideal code i collected in a look-u table (LUT), a a two-dimenional function of the current outut code, and either the loe of the ignal or the reviou code. Thi aroach require, however, a large amount of memory [5] in order to build u the LUT. Moreover, ome roblem arie with (i) the election of the tye and number of the calibration ignal [6], and (ii) the comenation of mall non-linearitie, whoe value are maller than the quantization te. An alternative aroach to non-linearity reduction uing bayeian filtering ha been rooed in [7,8], teted in imulation and imlemented on a DSP board equied with a low frequency, high reolution ADC [9]. In order to rove the caability of the method in more realitic condition, a tet lan on a high frequency, low reolution ADC ha been carried out. The exerimental tet have been divided in three hae. Firt, ome tet have been carried out on a converter by uing ine-wave ignal to identify the caability of the method of comenating the intrinic nonlinearity of the ADC, which i below the LSB [9]. A econd grou of tet ha been

2 Ideal quantizer x onlinearity k Actual ADC Figure. ADC model, ued for deriving the correction method. realized with ine-wave ignal by introducing a elf-built analog nonlinearity affecting few code but with an amlitude of everal LSB and conidering the ADC a ideal [9]. Finally, an exerimental hae ha been carried out with a new analog non-linearity, which occuie the whole full cale range of the ADC. During thi hae ine wave and Univeral Mobile Telecommunication Sytem (UMTS) ignal, baed on the Wideband Code Diviion Multile Acce (W-CDMA) technique, have been ued. The firt two hae already howed a relevant SFDR increae [9]. In the aer the reult of the lat hae are reented. The method ha been firt validated on imulated W-CDMA ignal. Then, it ha been verified on a tet bench coniting of a PC data acquiition board equied with an 8-bit GS/ A/D converter. In order to conider the ADC a an ideal one, a elf-built analog ditortion circuit, whoe non-linearity i much greater than the intrinic non-linearity of the ADC, ha been ued. In the next Section the method i briefly recalled, then the reult obtained by the imulation hae are given. Finally, the reult of the characterization hae uing actual ignal are reented. II. The method For the coe of the reent work, the effect of the non-linearity on an actual ADC ha been modelled a a ditorting channel in which the outut of an ideal quantizer x i maed to the actual outut k (Fig.) [8]. In thi cae, an etimation of the original code x can be obtained by the following formula [8]: 2 x= x ˆ = E{ x k} = x ( x k), () where E{} i the exected value oerator, i the number of bit of the converter, (k) and (x) are the robabilitie of the actual code k and the ideal one x, reectively. (x k) i the conditional robability of x, given k. The conditional robability (x k) i obtained by mean of the Baye theorem, a follow: ( k x) ( x) ( k) 2 x= ( k x) ( x) ( x k) = =. (2) ( x) ( k x) If dither i alied, in order to reduce quantization noie and mall cale non-linearity error, an etimate of the ideal code x can be found by over-amling, alying a Bayeian filter and uing a moothing window of length 2L + to remove the dithering: L ( k[ i + j] x[ i + j] ) ( x[ i + j] ) ( k[ i j] ) 2 xˆ [] i = xe[ i + j] = x[] i. (3) 2L + j= L 2L + j= L x[] i = + L In thi cae a imle rectangular moothing window ha been choen [8]. The matrix containing (k x) conditional robabilitie can be evaluated in a calibration hae tarting

3 from the code tranition level a hown in [7]. Sine wave hitogram tet rocedure, reorted in [], ha been ued for etimating code tranition level. III. Simulation reult A imulation tudy ha been carried out in MATLAB language on W-CDMA ignal, according to the block cheme reorted in Fig. 2. A W-CDMA ignal i generated in comliance with 3GPP ecification [] at an IF frequency of.32 MHz and double reciion amle. Then, it i quantized uing both an 8-bit ideal ADC model and an 8-bit actual ADC model, with a imle nonlinearity 4 code wide and 6 code high, having the IL hown in Fig. 3. After the quantization, the method for the non-linearity correction ha been alied and the SFDR referred to the carrier frequency ha been evaluated, a in []. Fig. 4 how the Power Sectral Denity (PSD) of the ignal before and after the non-linearity correction, reectively. It can be noted a relevant imrovement of more than 2 db in the SFDR, referred to the carrier frequency. Actual ADC model W-CDMA ignal generation Ideal quantization on-linearity Baye correction algorithm on-linearity arameter evaluation Ideal ADC model Ideal quantization Figure 2. Block cheme of the rocedure adoted for the imulation tet. IV. Exerimental reult The tet bench conit of a develoment ytem comoed of a PC baed on a Pentium IV,7 GHz CPU and a Signatec PDA data acquiition board, equied with a GS/ 8-bit flah ADC. A it can be een in Fig. 5, ignal are generated by an Agilent E4438C vector ignal generator, then, ent to a elf-built analog board which i ued for corruting the ignal with a known non-linearity. An electrical cheme of thi circuit i given in Fig. 5 in enlarged view. Data are collected by the PC and corrected. In a firt hae, ome exerimental tet have been conducted uing a 5 MHz ine-wave ignal. The ignal ha been acquired uing a 25 MS/ amling frequency. The integral non-linearity (IL) ha been evaluated by mean of the ine-wave hitogram tet rocedure []. From the IL diagram of Fig.6a the IL introduced by the non-linearity circuit can be clearly oberved. Fig. 6b how the reult of the correction method. In articular, a reduction in the econd harmonic of 28.8 db can be oberved, while the SIAD increae i equal to db. IL [LSB] Code Figure 3. IL of the non-linearity model. Power Sectral Denity [db/hz] Before correction After correction Frequenza [MHz] Figure 4. PSD of a W-CDMA ignal before and after the correction.

4 on-linearity board Agilent E4438C Vector Signal Generator PC Signatec PDA Data Acquiition Board Figure 5. Tet etu for the correction method. Then, a econd hae of tet ha been carried out uing W-CDMA ignal comliant to the 3GPP tandard []. Signal coming from a ingle Dedicated Phyical Channel have been generated at a 5 MHz IF and acquired with a 25 MS/ amling frequency. In Fig. 7 the PSD of the ignal before correction i reorted in grey colour, while for the PSD of the ignal after the correction i hown in black. The grah are reorted in db referred to the higher harmonic comonent. How it can be een, the effect of the non-linearity i well comenated and the SFDR i increaed from 4.88 db to 36.8 db. V. Concluion The exerimental validation of a method for digital comenation of high frequency, low reolution ADC non-linearity error ha been reented. In articular the comenation method ha been validated on 3 rd generation mobile telecommunication ignal, comliant to 3GPP ecification and a SFDR increae of more than 2 db ha been achieved both on imulated and on actual W-CDMA ignal. Further work i directed to exerimental invetigation uing different telecommunication ignal and to the integration of thi method with ome ecific meaurement method for 3G ytem. IL [LSB] a) b) Amlitude [db] before correction after correction Code Frequency [MHz] Figure 6. (a) IL introduced by the non-linearity board, and (b) the reult of the correction method for a inuoidal tet ignal.

5 Amlitude [db] before correction after correction Frequency [MHz] Figure 7. Power ectral denity of a W-CDMA ignal before and after the correction. Reference [] Pentek web ite: [2] J. Mitola III, Software radio cognitive radio, IEEE Communication Magazine, vol. 33, o. 5, , 995. [3] T. A. Rebold, F. H. Iron, A hae lane aroach to the comenation of high-eed analog-todigital converter, Proc. of IEEE Int. Sym. on Circuit and Sytem, Philadelhia, PA, USA, , 987. [4] F. H. Iron, D. M. Hummel, S. P. Kennedy, Imroved comenation for analog-to-digital converter, IEEE Tran. on Circuit and Sytem, vol. 38, o. 8, , 99. [5] H. Lundin, M. Skoglund, P. Händel, Minimal total harmonic ditortion ot-correction of ADC, Proc. of 8th International Workho on ADC Modelling and Teting, Perugia, Italy,.3-6, 23. [6] C. L. Monteiro, P. Araia, A. C. Serra, Dual tone analyi for hae-lane coverage in ADC metrological characterization, Proc of 2th IEEE Intr. and Mea. Tech. Conference, Vail, CO, USA, , 23. [7] P. Daonte, R. Holcer, L. Horniak, L. Michaeli, Uing the interolation method for noie haing A/D converter, Proc. of 6th Workho on ADC Modelling and Teting, Liboa, Portugal,.34-37, 2. [8] P.Daonte, R. Holcer, L. Horniak, L. Michaeli, S. Rauano, Uing an interolation method for noie haing in A/D converter, Proc. of 4th IEE ADDA 7th IMEKO TC-4 Workho on ADC Modelling and Teting, Prague, Czech Re.,. 47-5, 22. [9] L. De Vito, L. Michaeli, S. Rauano, Real-time imlementation of a method for ADC nonlinearity reduction, aer acceted for ublication on Meaurement Journal. [] IEEE 24 Standard for Terminology and tet method for analog-to-digital converter, 2. [] 3rd Generation Partnerhi Program. Technical Secification Grou Radio Acce etwork. Univeral Mobile Telecommunication Sytem (UMTS); Sreading and modulation (FDD), 3GPP TS 25.23, v5.2., 22.