EFFICIENT PILOT PATTERNS FOR CHANNEL ESTIMATION IN OFDM SYSTEMS OVER HF CHANNELS Ma Julia Ferniindez-Getino Garcia, JosC M. Piiez-Borrallo, Santiago Zazo Dpto. de Sefiales Sistemas y Radiocomunicaciones. E.T.S.I. Telecomunicaci6n Universidad Polittcnica de Madrid, 28040 Madrid, SPAIN E-mail:
[email protected],
[email protected]
Abstract - In this paper, the distribution of pilot
performed aided by pilot-symbols inserted in the time-frequency lattice determined by the OFDM system [3] [4]. Therefore, these Probe symbols are employed in this multicarrier scheme [2] as pilot symbols for frequency channel estimation; in Fig. 1, pilot symbols are marked in grey. This pilot pattern can be viewed as a particularization of a rectangular pattern in which frequency dimension is completely swept and pilot density is 33 %; results are shown in [21.
symbols in the time-frequency lattice of a multicarrier system for HF communications has been analysed. Pilot density of an OFDM modem based on the HFDL standard can be reduced, so data rate can be about 3600 bps. An hexagonal pilot pattern has been proposed and compared with rectangular geometries. Hexagonal distribution of the pilots is optimum in terms of sampling efficiency and it provides better performance in terms of BER.
Frequency
I. INTRODUCTION Communications over HF links is classically a very difficult task due to the deep fading and severe intersymbol interference that ionospheric propagation brings about. Presently, the International Civil Aviation Organization (ICAO) has developed a standard known as HFDL [ l ] for data communications in the HF range between ground stations and aircrafts based on single-carrier techniques. However, a multicarrier alternative has been recently proposed by the authors [2], which provides better performance from the points of view of interleaver length and Bit-Error Rate (BER). These advantages point out this multitone modem as a current state-of-the-art candidate for interactive applications like transmission of digital voice. Initially, this OFDM (Orthogonal Frequency Division Multiplexing) proposal [2] has been developed being constrained to the timing requirements imposed by the single-carrier standard. A TDM Data-Probe structure, with a 2:l ratio, where Probe sub-blocks are known symbols that the single-carrier receiver uses to track time variations. In the coherent OFDM version, channel estimation must be carried out to combat highly frequency selective Rayleigh fading channels and this can be
)be
Figure 1: Time-frequency structure with II‘DMconstrairIt If leaving this time constraint and spreading out symbols in all time-frequency grid, pilot density can be reduced significantly, and therefore, data rate can increase. Also, it must be considered that an hexagonal distribution of the pilots will provide better performance than rectangular geometries. This leads to the possibility of achieving a bitrate around 3600 bps, what means a great improvement compared with the 1800 bps of the HFDL standard. Different pilot densities have to be analysed, finding a trade-off between performance and data rate In section 11, pilots patterns considering twodimensional sampling are described. Section 111 presents the design of parameters for pilot distributions in this HF system. In section IV, simulation results in terms of BER are shown. Section V analyses the bitrates that can be achieved
Work partly supported by National Project TIC 98-0748
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depending on the design. Section VI discusses and concludes the paper.
Hexagonal distribution of pilots is optimum in terms of sampling efficiency and it provides better BER performance than rectangular ones. Fig. 2 depicts rectangular and hexagonal geometries.
11. PILOT DISTRIBUTIONS IN 2-D GRIDS The frequency response of the HF channel, which is highly frequency selective and Rayleigh fading, can be viewed as a two-dimensional, 2-D, stochastic signal (time and frequency) which is sampled at pilot positions. Channel attenuations in positions where a pilot is not transmitted will be estimated with the aid of channel knowledge at pilot positions. Pilot distribution in the time-frequency grid can be viewed in terms of 2-D sampling and each geometry is described defining two linearly independent vectors VI =(v11 , v ~ ~and ) ' v2 =(v12,v22)', where V = ( v1 VZ) is the sampling matrix that characterizes the pattern. Therefore, the locations of a doubly periodic set of samples in the in the (dl,d&plane or (time,frequency)-plane are:
dl = v11 n1 + v12 n2 = v21 121 + v22 n2
I
I
Figure 2: Pilot geometries in time-frequency lattice The sampling matrix for both geometries can be written as:
(1)
111. PARAMETERS DESIGN
d2
The design of pilot spacing in time and frequency domain is highly dependent on the system characteristics; therefore, these parameters must be chosen according to the constraints imposed by the application.
with vector notation can be written as:
d=Vn being:
In this multicarrier modem, the 3-Khz bandwidth is splitted into N=32 sub-carriers, so intercarrier spacing is Af = w/N = 93.75Hz . Binary data are
The most typical way of sampling a 2-D signal is with periodic rectangular sampling, where d-th dimension (d= { 1,2}) has qui-spaced samples with a certain period. N , denotes pilot spacing in time domain (it is related to coherence time) and N2 is pilot spacing in frequency domain (it is related to coherence bandwidth). However, periodic sampling can adopt various geometries.
QPSK modulated, so every sub-carrier, at non-pilot position, carries two bits of information. ReedSolomon block coding (63,45) is included, and therefore, code rate is -0.7 1.
Currently, most of pilot patterns proposed by existing OFDM systems are derived from periodic rectangular sampling. Basically, two distributions are found in the literature; the classical rectangular sampling [5] and a kind of a rectangular modified pattern, linearly increasing in frequency dimension. The last one has been adopted in DVB standard for scattered pilots [6]. We propose an hexagonal pilot pattern and compare it with the rectangular distribution. The most efficient sampling strategy of a 2-D signal is the hexagonal one, since, it requires 13.4 % fewer samples than rectangular sampling to represent the same signal with identical prediction error [7].
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A cyclic prefix (CP) is added to the OFDM-symbol to overcome the delay spread of the multipath channel. Since this CP is chosen to be longer than the maximum delay spread, inter-symbol interference is avoided. The
time
duration
yw
T, = (liAfX =
of
each
= 1 0 . 7sec ~ ,
sample
is
and the duration of
the whole OFDM-symbol, T, that includes the CP is given by: = Ts,OFDM
'cp
(4)
For ionospheric propagation, the standard channel can be modelled with Watterson model. Multipath amplitude fading with up to 2 Hz two-sided RMS
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Doppler spread and 2-path Rayleigh statistics are considered.
terms of BER. The target BER in this system is lo”, since this means a reasonable voice quality.
A trade-off has to be found, because, on one hand, pilots have to be placed close enough to guarantee a reliable channel’s frequency response estimation [8]; on the other hand, pilot density must be as low as possible because it reduces the data-rate.
Considering an HF channel with a delay spread z=0.25msec, a CP of 2 samples is added to guarantee that Cp>z and then, inter-symbol interference is eliminated. Since this channel is not highly frequency selective, = 4 is selected.
Interpolation will be carried out based on the
Four pilot symbols are employed to sample frequency dimension, that turns out to be not enough to have a reliable estimation of the frequency response of the channel. Results are shown in Fig. 3.
knowledge of 3(”,)pilots.
YN,
At every step, and
based on these pilots, p channel attenuations will be estimated, being:
1OD
p = N ( 2 N , +1)-3 (
h
2
)
That is, interpolation will be performed over a N x (2N, + 1) -grid; 2D interpolation has been carried out using an inverse distance method, where weights are determined with Green’s function. This grid contains 3 OFDM symbols in which pilots are included at certain frequency positions. The hexagonal pattern differs from the rectangular one in that alternate OFDM-symbols which include pilots are shifted
N
10.‘
1
..
,
.
,
.
. . . --..
I”
Since time variations of the channel are not very fast, N I could be reasonably long. This would provide a reduction in pilot density without degrading performance. However, a longer NI drives to a longer delay, that we cannot afford in a voice application. Interpolation delay, Td, is given by:
~
.
1
11
tt
positions in frequency dimension.
10
15 SNR [dBl
20
25
Figure 3: BER performance when N/N, = 4 and ~0.25msec
(6)
T, = 2 N ,
.
Considering N I = 3, Td < 70msec, what is admissible for interactive applications. Regarding pilot spacing in frequency domain,
It can be seen how the hexagonal distribution gives better results due to the fact of sampling frequency dimension at eight different frequency positions per estimation step, compared to only four different frequency positions for the rectangular geometry. In this case, T ~ 6 8 . 2msec, and, the bitrate attained is about 4000 bps. 1oo
(YN2)must be large enough to guarantee that the sampling theorem is fulfilled to have a good estimation in frequency domain. However, it must be kept as low as possible to reach the aim data-rate, about 3600 bps. It was considered = 4 - 8 , and
yN,
taking into account that NI was chosen to be 3, this means a pilot density of 4.16 % and 8.3 % respectively. In both cases, a 3600 bitrate is attained. 10-41
IV. COMPARISON IN PERFORMANCE The proposed hexagonal pilot pattern and the rectangular geometry have been both evaluated in
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10
15 SNR [dB]
20
25
Figure 4: BER performance when N/N2 = 8 and z=0.5msec
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The number of pilot symbols per OFDM-symbol, , can be increased from 4,as in the previous
yN,
case, to 8. In this case, the CCIR good channel, -0Smsec. is used. The time spreading effect of the channel will be overcomed with a CP of 3 samples. Now pilot density is 8.3 % and T ~ 7 msec. 0 Fig. 4 depicts performance results. Maintaining the previous pilot density, 8.3 %, a worse HF channel was considered. Now, frequency selectivity will be determined by -1 msec. A cyclic prefix of four samples is included in this case. Simulation results, in Fig. 5, are worse, as it would be expected; however, the hexagonal pattern reaches 10” at SNR=30 dB.
R, = R , . r
(8)
where r is the code rate. Choosing N I and NZ parameters appropriately depending on the expected HF channel, a bitrate about 3600 bps can be obtained. In the following figure the information rates that can be reached are shown. The plane Rb=3600 is the reference point for the design, and, if parameters are carefully selected, this plane can be overpassed. Pilot density depending on both parameters is shown in Fig. 7.
1oo
t dlFh,
--
Rectangular Hexagonal
4000
1
p500
.., m
$3000
rn
..................
2500
2000 40
........................................
IO4
10
t
‘“’i I
t
1041
10
15
20
25
NN2 [sub-caniers]
Figure 6: Bitrate N / N , parameters.
30
SNR [dBl
Figure 5: BER performance when N / N , z= 1msec
=8
0-2
N I [OFDM-symbols]
depending
on
NI
and
and
Simulation results have proven that an hexagonal distribution of pilot symbols drives to better performance results when maintainig the same pilot density for both, rectangular and hexagonal, distributions.
. . . . ..>, 40..
. .
.’’
\
V. ACHIEVABLE BITRATES The aim of spreading pilot-symbols in the timefrequency lattice is achieving a better transmission throughput to reach a bit-rate of about 3600 bps, that it could make feasible transmitting voice. The channel rate, Rch, is given by:
Figure 7: Pilot densities for the system
if a generic M-PSK modulation is considered. The bitrate, Rb, of the system will be given then by,
In the scenarios analysed in the previous section, pilot densities of 4.16 % and 8.3 % were considered. For the first case, the R,h is about 5500 bps, what means that Rb is close to 4000 bps. When pilot density is 8.3 %, Rch decreases to about 5100 bps and Rb is around 3600 bps.
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[4]P. Hoeher, S. Kaiser, P. Robertson. “Twodimensional pilot-symbol-aided channel estimation by Wiener filtering”. Proceedings ICASSP’97, pp:1845-1848. Munich, Germany, April 1997.
If a worse HF channel had to be considered, N / N , would have to increase. In this situation, pilot density could be maintained if NI would increase, assuming a longer delay due to interpolation. A trade-off has to be found among all these parameters to guarantee a certain performance with the desired bitrate.
[5] Working document in the OFDM concept group. “Description of Telias OFDM based proposal”. ETSI STC SMG2#22. Bad Aibling, Germany. 12-16 May 1997.
VI. CONCLUSIONS
[6] U. Reimers. “Digital Video Broadcasting”. IEEE Communications Magazine, pp: 104-110. June 1998
Bitrates of about 3600 bps can be attained in multicarrier HF links, instead of the 1800 bps of the HFDL standard, and, it would be then feasible the possibility of transmitting voice through HF channels. This information rate can be reached if setting aside the time constraint imposed by HFDL and spreading Out pilot in timefrequency grid. With this spreading strategy, it was found that pilot density can be reduced significantly and, therefore, data rate can increase.
[7] D.E. Dudgeon and R.M. Mersereau. Multidimensional Digital Signal Processing. Prentice-Hall, NJ, 1984.
[8] M. Sandell. ‘‘Designand Analysis of Estimators for Multicarrier Modulation and Ultrasonic Imaging,,, Ph.D. thesis, Lulea univ. of Tech., Sweeden, 1996.
An analysis of the impact of different pilot densities in this communication system has been done. Pilot spacing in time and frequency domain must be chosen with a trade-off between density and performance. Interpolation delay must be taken into account, since, it can impede system interactivity; it shows up due to interpolation in time domain and it is determined by pilot spacing in this dimension.
Design strategies of pilot patterns have been also addressed. An hexagonal pattern has been proposed and compared with rectangular distributions. Hexagonal geometries provide better BER performance than the rectangular ones and they are optimum in terms of sampling efficiency.
REFERENCES [l] SARPS for HF Datalink, AMCP/S - WP 172, Rio de Janeiro, Brazil. January 1998 [2] S. Zazo, J.M. Piiez-Borrallo, M.J. FerniindezGetino Garcia, “High Frequency Data Link (HFDL) for Civil Aviation: A comparison between single and multitone voiceband modems”. IEEE Proc. of Veh. Tech. Con$, VTC’99, pp:2113-2118. Houston, USA. May 1999. [3] F. Tufvesson and T. Maseng. “ Pilot Assisted Channel Estimation for OFDM in Mobile Cellular Systems”. Proc. VTC’97, pp:16391643. Arizona, USA. May 97.
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