Frequency-Domain Channel Estimation for Single- Carrier Transmission in Fast Fading Channels

Transcription

1 Wireless Signal Processing & Networking Workshop Advanced Wireless Technologies University 18 February, 2013 Frequency-Domain Channel Estimation for Single- Carrier Transmission in Fast Fading Channels Tetsuya Yamamoto Department of Communications Engineering, Graduate School of Engineering, Tohoku University

2 Outline Introduction Transmission System Model Frequency-Domain Channel Estimation Schemes Simulation Results Conclusion 2

3 Channel gain Introduction Broadband single-carrier (SC) transmissions must deal with inter-symbol interference (ISI) arising from the severe frequency-selectivity of the channel. Frequency-domain equalization (FDE) [A, B] is simple, but effective to combat frequency-selective fading channel. Transmitted signal spectrum FDE weight f Frequency Received signal spectrum Equalized signal spectrum f FDE f [A] D. Falconer, et. al., Frequency domain equalization for single-carrier broadband wireless systems, IEEE Commun. Mag., Apr [B] F. Adachi, et. al., Introduction of frequency-domain signal processing to broadband single-carrier transmissions in a wireless channel, IEICE Trans. Commun., Sept

4 Introduction SC-FDE is a block transmission and DFT is used at the receiver. Cyclic prefix (CP) is often inserted in front of each data block.» to avoid the inter-block interference (IBI)» to make the received signal to be a circular convolution of the transmit signal block and the channel impulse response CP-SC Direct path Delayed path CP Data CP Data CP Data CP Data DFT Time FDE 4

5 Introduction Instead of CP insertion, a known training sequence () insertion [C, D] can be used. Identical is used for all blocks. The in the previous block acts as the CP in the present block. -SC Data Data Data Data DFT Time FDE The can be utilized for channel estimation.» No pilot block is needed unlike CP-SC transmission. CP-SC CP Pilot CP Data CP Pilot CP Data -SC Data Data Data Data [C] L. Deneire, et. al., Training sequence versus cyclic prefix - a new look on single carrier communication, IEEE Commun. Lett., July, [D] F. Adachi, et. al., Capacity and BER performance considerations on single-carrier frequency-domain equalization, Proc. ICICS 2011, Dec

6 Introduction Conventional channel estimation for -SC transmission [E, F] of 2L-symbol length, which is constructed from a of L-symbol length, is used.» Interference from the data block can be avoided. L: Channel length» The channel can be estimated in frequency-domain by exploiting the circular property of the. Transmission efficiency reduces. We introduce frequency-domain channel estimation schemes which require a of L-symbol length. Conv. CE L symbols Data Data Data Data Prop. CE L symbols Data Data Data Data Channel estimation Time Channel estimation [E] J. Coon, et. al., Channel and noise variance estimation and tracking algorithms for unique-word based single-carrier systems, IEEE Trans. Wireless Commun., June [F] Y. Hou et. al., Improvement on the channel estimation of pilot cyclic prefixed single carrier (PCP-SC) system, IEEE Signal Processing Lett., Aug Time 6

7 Data modulation + N c +N g - point DFT FDE N c +N g - point IDFT Data demodulation Transmission System Model Transmitter and receiver structure Channel estimates Data Received data Block structure is identical for all blocks. Data symbols (0) Data symbols (1) Data symbols (n) N c symbols DFT block N g ( L)symbols Time can be viewed as a CP of an N c +N g -symbol block.» The received signal is decomposed into N c +N g orthogonal frequency components by applying (N c +N g )-point DFT.» Simple one-tap FDE can be applied as in CP-SC. 7

8 -Based Frequency-Domain Channel Estimation - Basic concept - based frequency-domain channel estimation Obtaining the instantaneous channel estimate using N g -symbol.» The received having cyclic property is constructed for the frequency-domain channel estimation. (1) Add Data (n) Data (n) L-1 symbols N g symbols Time Cyclic property of is constructed. The received is decomposed into N g orthogonal frequency components by applying N g -point DFT. (3) Instantaneous frequency-domain channel estimation Instantaneous channel estimates (2) N g -point DFT 0 1 q N g -1 Frequency 8

9 -Based Frequency-Domain Channel Estimation - Basic concept - based frequency-domain channel estimation Delay time-domain windowing technique [G] is used for interpolation. Instantaneous ˆ N ( ) c N n g H q, q 0 ~ N g 1 channel estimates N g N g -symbol only has the frequency components at k=q(n c +N g )/N g, q=0~n g q N g -1 (1) N g -point IDFT Frequency Impulse response ˆ h ( ), 0 ~ N g 1 (2) Zero padding 0 N g -1 Delay time Channel estimates (3) N c +N g -point DFT ~ g H N 1 0 ~ h ( )exp j2k N N c +N g channel gains are obtained for performing FDE by interpolation with DFT/IDFT. c N g 01 k N c +N g -1 Frequency [G] J. J. de Beek, et. al., On channel estimation in OFDM systems, Proc. VTC, July

10 -Based Frequency-Domain Channel Estimation Channel estimation accuracy is poor due to the interference from the data block. Add Data (n) Data (n) L-1 symbols N g symbols We consider three schemes to obtain the improved channel estimate. I. Simple averaging and iterative channel estimation II. III. Recursive least square (RLS) algorithm based channel estimation RLS-based channel estimation with polynomial prediction 10

11 -Based Frequency-Domain Channel Estimation I. Simple averaging and iterative channel estimation Improved channel estimate is obtained by simply averaging the instantaneous channel estimates over several (N B ) blocks. N 1 ~ B ~ Nc N g Y ( q) H q N g n0 U( q) Received having the cyclic property (q=0~n g -1) Frequency-domain representation for Instantaneous channel estimate At the iteration stage, both the estimated data blocks and the s are used. ~ H N 1 B Y n0 N 1 B n0 { Sˆ Sˆ } 2 * k-th frequency component of n-th received signal block (k=0~n c +N g -1) k-th frequency component of the transmit symbol replica block Tracking ability is a problem in a fast fading environment. The channel gains are assumed to stay constant over N B blocks. 11

12 -Based Frequency-Domain Channel Estimation II. RLS algorithm based channel estimation The interference to from the data block is canceled by utilizing the channel estimates of the previous block. (1) Cancel (2) Add Data (n) Data (n) (1) Cancel Channel estimates are obtained based on RLS algorithm. ~ H ~ N N * ( n1) c g Y ( q) U ( q) Z q N g N N 2 ( n1) c g U ( q) q N g ( n1) ( n1) Z / otherwise Updates at the n-th block Z Z ( n1) ( n1) Y Sˆ { Sˆ 2 } * Time N if k c N N g It is benefit of sequential channel estimation. Replica of the interference from the data block is generated by pre-equalization using previous channel estimates. g q, q 0 ~ N g 1 Y ~ (n) (q): Received having the cyclic property (q=0~n g -1) U(q): Frequency-domain representation for Y (n) (k): Frequency-domain received signal block (k=0~n c +N g -1) (n) Ŝ (k) : Frequency-domain symbol replica block Forgetting factor(0<<1) 12

13 -Based Frequency-Domain Channel Estimation III. RLS-CE with polynomial prediction RLS algorithm based channel estimation (RLS-CE) Replica of the interference from the data block is generated by preequalization using previous channel estimates.» The tracking ability against a very fast fading is limited. RLS-CE The previous channel estimates may be old at the present block in very fast fading channels. Interference cancellation from the data block does not work effectively. ~ ( 1) H n Utilized for pre-equalization n-m B n-1 n Block RLS-CE RLS-CE ~ ( 1) H n Actual channel ~ H n ) ( ( k ) n-m B n-1 n Block 13

14 -Based Frequency-Domain Channel Estimation III. RLS-CE with polynomial prediction RLS algorithm based channel estimation (RLS-CE) Replica of the interference from the data block is generated by preequalization using previous channel estimates.» The tracking ability against a very fast fading is limited. Polynomial prediction is introduced. Predicted channel gains are utilized for the replica generation. RLS-CE with polynomial prediction n-m B RLS-CE ~ ( nm ) H B n-1 RLS-CE ~ ( 1) H n ˆ ( ) H n Polynomial prediction n RLS-CE ~ H n ) Utilized for pre-equalization ( ( k ) Polynomial prediction using M B past channel estimates are applied. Block Actual channel n-m B n-1 n Block 14

15 Average BER Simulation Result I. Simple averaging and iterative channel estimation Normalized Doppler frequency f D T s vs Average BER N B =32, I=1 N B =16, I=2 N B =8, I=3 Data modulation QPSK Data symbol block length N c =64 length N g =16 Chu sequence [H] Fading type Frequency-selective Rayleigh Power delay profile L=16 path uniform power delay profile Equalization MMSE-FDE 10 3 QPSK Ideal channel estimation N c 64, N g =16 L=16-path uniform E b /N 0 =14dB Tracking ability against the fading variations tends to be lost as N B increases. With the increase in the number I of iterations, smaller N B can be used and tracking ability is improved. Normalized Doppler frequency, f D T s Travelling speed (km/h) 10MHz signal bandwidth at the carrier frequency 2GHz is assumed. 15

16 Average BER Simulation Results II&II. RLS-CE & RLS-CE with prediction Normalized Doppler frequency f D T s vs Average BER Simple averaging (N B =8, I=3) RLS-CE RLS-CE w/ prediction RLS-CE Forgetting factor is optimized for each f D T s. RLS-CE with polynomial prediction Second-order polynomial is used. Forgetting factor and the number M B of blocks to be used for the prediction are optimized for each f D T s QPSK N c 64, N g =16 L=16-path uniform E b /N 0 =14dB Ideal CE 10 4 RLS-CE provides better BER performance than simple averaging in a fast fading channels. RLS-CE with polynomial prediction further improves the BER performance in very fast fading channels. Normalized Doppler frequency, f D T s Travelling speed (km/h) 10MHz signal bandwidth at the carrier frequency 2GHz is assumed. 16

17 Conclusion We presented frequency-domain channel estimation schemes suitable for -SC block transmission with FDE. The received having cyclic property is constructed to perform frequency-domain channel estimation with a of L-symbol length. Improved channel estimate is obtained by» Simple averaging and iterative channel estimation» RLS-based channel estimation» RLS-based channel estimation with polynomial prediction RLS-CE with polynomial prediction has the best tracking ability against fast fading channel. achieves a BER performance close to the perfect channel estimation case even in a fast fading environment. 17

18 Thank you very much for your kind attention. 18