Time-varying channel estimation and symbol detection for OFDM systems using superimposed training
which we will refer to as pilot sample over the entire slot t 2 [1 L þ tp, tp þ L 1]. The channel coefficients h(tp) are then estimated using the pilot sample, treating Htpstp þ vtp as an additive noise sequence. Motivated by the method in [3], we propose a novel channel estimator that is completely impervious to the unknown data by distorting the transmitted block sp with the distortion components
H. Zhang and X. Dai The problem of superimposed training (ST) based time-varying channel estimation and symbol detection for the OFDM system is addressed. Unlike the conventional approach, the effects of the unknown data on channel estimation are fully cancelled. The performance of the proposed approach is shown to significantly outperform existing methods based on ST.
Introduction: In recent years, a promising approach for channel estimation, superimposed training (ST) based channel estimation, has attracted attention owing to its potential transmission efficiency [1, 2]. However, one of the primary disadvantages of the method is that the estimated performance is severely degraded by the unknown transmitted data, which acts as additive noise. Reference [3] proposed a so-called data-dependent superimposed training (DDST) scheme to cancel the effects on estimation results due to the unknown data by introducing certain data distortion prior to adding pilot symbols. However, it is only suitable for the linearly time-invariant (LTI) case. Motivated by the method in [3], we propose a novel timedomain channel estimator in estimating linearly time-varying (LTV) OFDM channels, wherein the interference owing to the unknown data sequence will be fully cancelled by distorting certain data slots. Further, at the receiver, a data-reconstruction based iterative symbol detector is carried out to compensate for the introduced distortion. Proposed ST solution: Consider an OFDM system with K subcarriers operating over time-varying frequency-selective channels. Before going further, we first split K time intervals into P equispaced time slots of Q periods (let Q > 2L with L being the maximum channel order). Then, we make the following assumptions: (A1) channel coefficient varies in a linear model that has a constant slope within one slot. The time index can thus be expressed as t ¼ pQ þ q(p 2 [0, P 1], q 2 [0,Q 1]). To simplify channel estimation, a known impulse train c(t) ¼ c(t)d(t tp) with tp ¼ pQ þ Q=2 is added to the pth (p 2 [0, P 1]) slotted data stream sp ¼ [s(pQ þ 0), . . . , s(pQ þ Q 1)]T to produce the transmitted data, i.e. xp ¼ ½xðpQ þ 0Þ; . . . ; xðpQ þ Q 1ÞT ¼ sp þ cp
p 2 ½0; P 1 ð1Þ
where 2
3T
cp ¼ 4|fflfflfflffl{zfflfflfflffl} 0; . . . ; 0; cðtp Þ; 0; . . . ; 05 |fflfflfflffl{zfflfflfflffl} Q=21
Q=21
Owing to the evidence L > > > < hðt ^ p Þ þ tDh^ p p 2 ½0; P 1 and t 2 Q2 ; K Q2 ^ ¼ hðtÞ > hðt ^ P1 Þ t 2 K Q2 ; K 1 > > > > : þ t K þ Q2 Dh^ P1 ð7Þ PK1
Under the constraint of constant training power (1=N) t¼0 j c (t) j2 ¼ sc, the mean square error (MSE) can be derived using (5)–(7) as L1 2 Ls P LPsv ^ MSE ¼ E ð8Þ hðtÞ hðtÞ ¼ v ¼ Qsc Ksc l¼0 Clearly, the MSE on channel estimation is independent of the unknown data signals, unlike that in existing ST based schemes [1, 2]. Symbol detection: After the channel has been estimated, the knownpilot effects should be first cancelled using an operation yp ¼ yp hˆ p cp where hˆ p is the estimated CIR in pth time slot. Owing to the proposed data distortion (4), it is straightforward to show that the corresponding distortion on received signals is gp ¼ Jyp. Along with the fast Fourier transform (FFT) performed at the receiver, gp will be equally spread over all frequency bins, and thus give rise to an error floor on symbol detection. Therefore, we perform the following data reconstruction based iterative symbol detector to compensate for the performance degradation of symbol error rate (SER) owing to the distortion gp: 1. Perform the banded LMMSE equaliser adopted in [4] to derive the T ˆ (I) detected data symbol sˆ (I) ¼ [sˆ (I) 0 , ..., s P1] . 2. Reconstruct the received signals of each slot, i.e.yˆ (I) p p 2 [0, P 1], using sˆ (I) and previously estimated CIR hˆ (t) from (7). 3. Replace the distorted elements gp by Jyˆ (I) p . 4. Go back to 1 with the results obtained in 3. This completes the Ith iteration. 5. To continue iterations, repeat 2–4 with I I þ 1. Notice that the proposed reconstruction based scheme depends crucially on the ratio of distorted signals over one OFDM symbol size. Since the data distortion increases with P, P should be constrained under the condition (2L 1)P=K 15% (based on experiment study). Numerical results: In our simulations, the transmitted sequence is chosen to be QPSK signals with symbol rate fs ¼ 1M baud and OFDM symbol-size is K ¼ 2048. We set L ¼ 6, with each tap being simulated by Jake’s model, and divided the time-varying channel into P ¼ 8 equispaced slots. The Doppler spreads fd ¼ 100 Hz is considered in this simulation. For comparison, we also simulated the estimation method in [5], wherein 12.5% bandwidth is occupied by pilot symbols. As shown in Figs. 1 and 2, our proposed scheme achieves a considerable
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gain compared with both the conventional ST based method and the method in [5] in terms of MSE and SER against SNR, respectively. Fig. 2 also indicates that 1 dB gain in SNR is achieved using the proposed iterative symbol detection scheme in the first iteration.
Conclusions: We have presented a novel time-domain estimator for fast time-varying OFDM channels. The interference on channel estimation due to the unknown data is fully cancelled by distorting certain data slots. Furthermore, the SER performance degradation owing to the introduced distortion is guaranteed with the proposed iterative reconstruction based detection method. Acknowledgment: This work is supported by the Joint Foundation of the National Science Foundation of China (NSFC) and Guangdong Province U0635003. # The Institution of Engineering and Technology 2007 27 May 2007 Electronics Letters online no: 20071400 doi: 10.1049/el:20071400 H. Zhang and X. Dai (Department of Electronic Engineering & Communication Engineering, Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China) E-mail:
[email protected] References
Fig. 1 MSE against SNR Power allocated for pilot symbols is 5% of total transmitted power. Normalised Doppler frequency Nfd ¼ Kfd=Pfs ’ 0.2, with Npfd ¼ Nfd=P ¼ 0.025 in each slot
1 Zhou, G.T., Viberg, M., and Mckelvey, T.: ‘A first-order statistical method for channel estimation’, IEEE Commun. Lett., 2003, 10, (3), pp. 57–60 2 Tugnait, J.K., and Luo, W.L.: ‘On channel estimation using superimposed training and first-order statistics’, IEEE Commun. Lett., 2003, 7, (9), pp. 413–415 3 Ghogho, M., Mclernon, D., Hernandez, E.A., and Swami, A.: ‘Channel estimation and symbol detection for block transmission using datadependent superimposed training’, IEEE Signal Process. Lett., 2005, 12, (3), pp. 226–229 4 Tang, Z., Cannizzaro, R.C., Leus, G., and Banelli, P.: ‘Pilot-assisted timevarying channel estimation for OFDM systems’, IEEE Trans. Signal Process., 2007, 55, (5), pp. 2226–2238 5 Yasamin, M., and Donald, C.: ‘ICI mitigation for pilot-aided mobile OFDM systems’, IEEE Trans. Wirel. Commun., 2005, 4, (2), pp. 765–774
Fig. 2 Bit error rate with different training schemes
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