The Tight Bound for the Number of Pilots in Channel Estimation for OFDM Systems

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1 Counications an Network, 01, 4, htt://x.oi.org/10.436/cn Pubishe Onine May 01 (htt:// The Tight Boun or the Nuber o Piots in Channe Estiation or OFDM Systes Marya Iani *, Haireza Bakhshi Eectrica Engineering Deartent, Shahe University, Tehran, Iran Eai: * iani@shahe.ac.ir Receive February 4, 01; revise March 8, 01; accete Ari 0, 01 ABSTRACT Coherent etection in OFDM systes requires accurate channe state inoration (CSI) at the receiver. Channe estiation base on iot-sybo-assiste transissions rovies a reiabe way to obtain CSI. Use o iot sybos or channe estiation, introuces overhea an it is esirabe to kee the nuber o iot sybos as iniu as ossibe. This aer introuces a new tight boun or the nuber o iots in channe estiation using aative schee in OFDM systes. We cacuate the iniu nuber o necessary iots using two aroaches. The irst aroach or the nuber o iots is obtaine base on Doer requency shit estiation an the secon aroach is acquire base on channe ength estiation using secon orer statistics o receive signa. Finay we obtain the tight boun or the nuber o iots using attaine vaues. Keywors: Doer Frequency Shit; Secon Orer Statistics; Channe Estiation; Piot; OFDM 1. Introuction Orthogona requency ivision utiexing (OFDM) reresents a vai choice or a variety o wireess aications since it has been shown to outeror singe-carrier schees eseciay in high ata rate aications [1]. To correcty eouate the receive ata sybos, the channe estiation ays an iortant roe to the syste erorance greaty. The ost coon technique to obtain channe inoration is via iot aie channe estiation []. Piot sybos consue both ower an sectru an thus it is esirabe to kee the nuber o iot sybos as iniu as ossibe. Soe aroaches or reuction o iot overhea were roose in [3-5]. On the other han the sacing between iot sybos shou be sa enough to ake channe estiates reiabe. Aative resource aocation in orer to achieve a roer trae-o between utiize resources an quaity o channe estiates base on CSI is necessary. Soe authors iscusse the nuber o use iots in channe estiation an reresent soe ethos or reuction the in OFDM systes. Authors in [6] use eviation o corresoning signas as a araeter to reict the channe characteristics in the transitter en. They transit ixe ength o test signa to the channe whenever connection setu initiation takes ace. Then by using the resonse, nuber o iot signas to insert is eterine an corresoningy aene to the ata signa. Thus by vary- * Corresoning author. ing the nuber o iots eening uon the channe environent, it certainy iroves the channe estiation an reuction in nuber o iots use or channe estiation an eeback. The roose estiator in [7] eoys a seciic iot structure which consists o two tyes o iot sybos with ierent iot ensity. The cobination o intererence aeviation an iot rearrangeent not ony akes the channe estiation robust to the tie seectivity o the channe but aso reuces the nuber o iot subcarriers neee to estiate the channe. Authors in [8] eveo a etho to obtain the otia nuber o known iot sybos or iot-aie inear channe estiation in OFDM. They erive an exression or channe estiation error covariance ro which erorance easures can be nuericay evauate to obtain the otia nuber o iot sybos. In [9], the shortest reabe that attains a given ean square error in a sequence that uner-saes the channe sectru is oun. A high obie wireess channe is tie-variant ue to Doer requency shit. Then, the nuber o use iots in channe estiation eens on the Doer requency shit. So, we reresent a ower boun or the nuber o iots base on it. Aso, the nuber o use iots eens on the ength o channe. Thus, we evauate channe ength estiation robe or obtaining another ower boun or the nuber o iots. Finay the tight boun is obtaine. The reiner o this aer is structure as oows: in Section the syste oe is introuce. Bouns or Coyright 01 SciRes.

2 M. IMANI, H. BAKHSHI 147 nuber o use iots in channe estiation are resente in Section 3. Soe siuation resuts are given in Section 4 an inay Section 5 concues the aer.. OFDM Syste Moe The basic buiing bock or OFDM transceiver is shown in Figure 1. In an OFDM transitter, at the nth sybo tie, K ata sybos Xnk,, k 0,1,,, K 1, are converte into tie-oain signas using the inverse ast Fourier transor (FFT). A cycic reix (CP) is inserte to reserve the orthogonaity between the subcarriers an to eiinate the intererence between the ajacent OFDM sybos. At the receiver, the CP is reove beore the FFT rocess. Assuing the iea synchronization at the receiver, the receive sybo o the k th subcarrier at the n th sybo tie can be reresente by: z, Xn, khn, k Znk, Y n k where H[n,k] is the requency resonse o the channe at the k th subcarrier an the n th sybo tie, an Z[n,k] is the backgroun noise, which can be aroxiate as zero-ean aitive white Gaussian noise (AWGN) with variance [10]. 3. Bouns or the Nuber o Piots We stuy the nuber o use iots or channe estiation in OFDM systes, an achieve the bouns or it. Here, we reca that unnecessary overhea is not esirabe in ters o the resource aocation or the iot signas. An aroriate iot istribution is necessary using aative iot aocation base on obtaine bouns The First Lower Boun or the Nuber o Use Piots in OFDM Systes For roer channe estiation, it is necessary to sae channe accoring to the Nyquist theore. The araeters o use in this section are iste in Tabe 1. Let us enote the sacing between iot sybos in the tie oain by N t an in the requency oain by N. The saing theore states that [11]: 1 1 Nt an N () T F s where an enote axiu Doer requency shit an axiu eay resectivey. T s e- Figure 1. Baseban OFDM transceiver. (1) Tabe 1. The ist o use araeters in Section 3.1. Paraeter N t N Seciication Piot sacing in the tie oain Piot sacing in the requency oain Maxiu Doer requency shit Maxiu eay OFDM sybo uration T s F Carrier sacing The nuber o iot tones N N s K The nuber o OFDM sybos The nuber o subcarriers notes the OFDM sybo uration an the carrier sacing, F, is the sacing in the requency oain. As iustrate in Figure, the transitter sens iot sybos scattere in the tie an requency oains in a reguar attern. Assuing that ower sectru ensity (PSD) o channe is base on jakes sectru [1], can be estiate as oows: 1 1 J0 rt n (3) π where J 0 is the 0 th orer Besse unction o the irst kin an rt n enotes the correation unction in the tie oain. Aso can be estiate with soe aroaches such as [13]. The N iot tones are uniory inserte into OFDM bock. N is cacuate as oows: N K Ns N N t where Ns is the nuber o OFDM sybos in the tie oain. Using Equations () an (4), the irst ower boun or the nuber o use iots is obtaine as oows: N 4KN T F s s 3.. The Secon Lower Boun or the Nuber o Use Piots in OFDM Systes We assue that channe iuse resonse is as oows: hn, n 0,1,, L hn 0, otherwise where L is the ength o channe. Authors in [14] roose an agorith or estiation o the channe ength without the nee o iots base on the secon-orer statistics o the receive signa. Here, we reresent a terse escrition o it. Assuing an arbitrary ositive integer N (N > L), we ay construct an (N + 1) 1 autocorreation vector or the receive signa such that: r (4) (5) (6) N 1 Coyright 01 SciRes.

3 148 M. IMANI, H. BAKHSHI where Figure. Piot sybos in the OFDM signas. N1 0 1 N T r (7) 1 L yny n (8) M n 0 M enotes the sae size. Assue that the axiu ag N satisies that N > L. A thresho can be estabishe as oows: M 0 M ζ in ( 1) N N ( N 1), M where 0 1 is the araeter to be chosen an is enotes as the start-terina-coeicients-to-channegain ratio, which is reate to the etectabe start an terina channe coeicients, such that: 0 hl L h 0 (9) h (10) The stes o roose agorith or channe ength estiation in [14] are as oows: Ste 1: Choose axiu ag N an sae size M. Set the thresho ζ accoring to Equation (9). Ste : Coute r N 1 as given by Equation (7). Set N. Ste 3: Coute ζ. Deterine ˆL 1 i 1 with the thresho 1 ζ. Otherwise, ecreent by 1 an reo Ste 3 unti 0. Ste 4: I 0, set ˆL 0. Where ˆL is estiate channe ength. To contro the etectabiity, (high etec- tabiity) an 0.1 (ow etectabiity) are chosen. The erorance o resente channe ength estiation etho is not sensitive to the vaues o the araeter θ an is robust over a kins o consteations such as BPSK an QPSK. The oowing theore states that, with knowing ength o channe, we can have a boun or the nuber o iots. Theore: assuing equi-sace an equa ower iot tones with the nuber o iot tones, N, greater than or equa to the channe ength, iies: 1) The covariance atrix o the channe estiation error, Σ, is a iagona atrix. ) I atrix Σ is iagona, the MSEs o channe reiction are ientica or a subcarriers. 3) Increasing the nuber o iot tones greater than channe ength wi not enhance the erorance o the channe reictor. The roo o this theore is given in [15]. Then, we have: Lˆ (11) N 3.3. Aative Agorith or Piot-Aie Channe Estiation Base on Tight Boun We renae right han o inequaities (5) an (11), as oows: a 4 KN T F, b Lˆ (1) Then s s B in a, b, B ax a, b 1 B N B 1 (13) Thus, we have a tight boun or the nuber o necessary iots or channe estiation in OFDM systes as oows: (14) The receiver, ater cacuating the tight boun or the nuber o iots, ees these vaues back to the OFDM transitter such that these vaues wi be use in the next transission erio. By exoiting CSI, The roose syste iniizes the iot overhea whie aintaining esire channe estiation accuracy. In other wors, receiver by consieration the tight boun or the nuber o necessary iots an environent conitions, ecie that how any iots shou be use or channe estiation. Figure 3 iustrates roose aative agorith or iot aie channe estiation in the OFDM systes. 4. Siuation Resuts In this section, we evauate the erorance o roose aative agorith or channe estiation. Siuation araeters are shown in Tabe. BER vs. SNR curves with L 8, 1 are shown in Coyright 01 SciRes.

4 M. IMANI, H. BAKHSHI 149 Tabe. Siuation araeters. PARAMETER VALUE Nuber o tota subcarriers K 18 Cycic reix ength N 16 g Banwith OFDM sybo uration Carrier requency Mouation Ts 1 MHz 18s GHz 16QAM Channe tye Jakes Rayeigh aing [1] Tye o estiation Sae size Chosen araeter Start-terina-coeicient-to-channe-gain ratio Least square M Figure 5. Perorance iroveent using aative resource aocation base on the irst ower boun or the nuber o iots, N 4KN T F. Channe estiation using ixe s s iots is ieente in = 50 Hz. Figure 3. Proose OFDM syste with aative schee or nuber o use iots L=8 L=1 Figure 6. Perorance iroveent using aative resource aocation base on the irst ower boun or the nuber o iots, N 4KN T F. Channe estiation using ixe s s iots is ieente in = 150 Hz. BER SNR Figure 4. BER vs. SNR with L = 8, 1. Figure 4. The aative iot syste base on the irst ower boun is coare to ixe iot syste in Figures 5 an 6 in 50, 150 Hz resectivey. The ixe nuber o iots is cacuate accoring to the average situation o the environent an the nuber o aative iots is equa to a 4KN T F. s s Figure 7. BER erorance o the OFDM syste with ixe iots an aative iots base on obtaine tight boun with N = B 1 an N = B. Coyright 01 SciRes.

5 150 M. IMANI, H. BAKHSHI Figures 5 an 6 iustrate that aative iot iroves erorance o OFDM syste eseciay uner high Doer requency shit. Figure 7 shows the bit error rate (BER) erorance o the OFDM syste with ixe iots an aative iots with N B1 an N B. Proxiity o curves or N B1 an N B eonstrates that resente boun in Section 3 is reay tight. 5. Concusion In this aer, we rive a new tight boun or the nuber o use iots in channe estiation or OFDM systes. This boun is e back to the transitter aativey to irove the syste erorance with ow iot overhea coare to the conventiona schees. REFERENCES [1] J. A. C. Bingha, Muticarrier Mouation or Data Transission: An Iea Whose Tie Has Coe, Counications Magazine, Vo. 8, No. 5, 1990, oi: / [] O. Eors, M. Sane, J. J. Van e Beek, S. K. Wison an P. O. Borjesson, OFDM Channe Estiation by Singuar Vaue Decoosition, IEEE Transactions on Counications, Vo. 46, No. 7, 1998, oi: / [3] G. Tauböck an F. Hawatsch, A Coresse Sensing Technique or OFDM Channe Estiation in Mobie Environents: Exoiting Channe Sarsity or Reucing Piots, IEEE Internationa Conerence on Acoustics, Seech an Signa Processing, Las Vegas, 31 March-4 Ari 008, [4] S. Bae, Y. Jang, S. Shin, Z. Chengshi an K. Kwak, Two Dientiona Estiations with Reuce Piot Arrangeents or OFDM Systes, Avance Counication Technoogy Internationa Conerence, Phoenix Park, February 009, [5] M. Chang an T. D. Hsieh, Detection o OFDM Signas in Fast-Varying Channes with Low-Density Piot Sybos, IEEE Transactions on Vehicuar Technoogy, Vo. 57, No., 008, oi: /tvt [6] J. Byng an N. P. Natarajan, Aative Piot Utiization or OFDM Channe Estiation in a Tie Varying Channe, IEEE 10th Annua Wireess an Microwave Technoogy Conerence, Cearwater, 0-1 Ari 009, [7] S. Lee, K. Kwak, J. Ki an D. Hong, Channe Estiation Aroach with Variabe Piot Density to Mitigate Intererence over Tie-Seective Ceuar OFDM Systes, IEEE Transaction on Wireess Counications, Vo. 7, No. 7, 008, [8] S. Ohno, E. Manasseh an M. Nakaoto, How Many Known Sybos Are Require or Linear Channe Estiation in OFDM? IEEE Internationa Conerence on Acoustics, Seech an Signa Processing, Prague, -7 May 011, [9] C. Oberi, M. C. Estea an M. Ríos, On Using Transission Overhea Eicienty or Channe Estiation in OFDM, IEEE Transactions on Counications, Vo. 58, No., 010, oi: /tcomm [10] J. W. Choi an Y. H. Lee, Otiu Piot Pattern or Channe Estiation in OFDM Systes, IEEE Transactions on Counications, Vo. 4, No. 5, 005, [11] P. Hoeher, S. Kaiser an P. Robertson, Two-Diensiona Piot-Sybo-Aie Channe Estiation by Wiener Fitering, IEEE Internationa Conerence on Acoustics, Seech an Signa Processing, Munich, 1-4 Ari 1997, [1] W. C. Jakes, Microwave Mobie Counications, Wiey, New York, [13] S. A. Husen, S. Baggen an A. Fiii, Bin Estiation o Maxiu Deay Srea in OFDM Systes, IEEE 64th Conerence on Vehicuar Technoogy, Montrea, 5-8 Seteber 006, [14] X. Wang, H. C. Wu, S. Y. Chang, Y. Wu an J. Y. Chouinar, Anaysis an Agorith or Non-Piot-Aie Channe Length Estiation in Wireess Counications, IEEE Conerence on Goba Teecounications, New Oreans, 30 Noveber-4 Deceber 008, [15] M. Karai, A. Oat an N. C. Beauieu, Piot Sybo Assiste Aative Mouation or OFDM Systes with Ierect Channe State Inoration, IEEE Conerence on Goba Teecounications, Miai, 6-10 Deceber 010, Coyright 01 SciRes.