Dec 7, 2006 - Single-carrier block transmission (SCBT) has appeared to be an ... R T. P. H. H z K. N N N Ï. â. +. = h h h R X XR + I. X y. T. P. H. P N N. L. = S S.
Efficient Channel Estimation for MIMO Singlecarrier Block Transmission with Dual Cyclic Timeslot Structure
Dr. Xiqi Gao NCRL, Southeast University Nanjing 210096, China
Outline
¾ Introduction ¾ MIMO-SCBT with Dual Cyclic Timeslot Structure ¾ Channel Estimation and Pilot Design ¾ Fast Implementation ¾ Simulations ¾ Conclusions
2006-12-7
Dr. Xiqi Gao / NCRL
2
Introduction ¾ Single-carrier block transmission (SCBT) has appeared to be an alternative promising technique. ¾ The shortcomings of the OFDM in peak-to-average power ratio (PAPR) and sensitivity to frequency shifts can be avoided in the SCBT. ¾ In MIMO channels, the number of the channel parameters to be estimated increases in proportional to that of the transmit antennas and the receive antennas. ¾ It is important, challenging as well, to design accurate and efficient channel estimation schemes for real MIMO system. ¾ In this work, we investigate channel estimation for timeslot-structured SCBT over space-, time- and frequency-selective fading MIMO channels.
2006-12-7
Dr. Xiqi Gao / NCRL
3
MIMO-SCBT with Dual Cyclic Timeslot Structure ¾ In the SCBT system, the signal is transmitted block by block. –
Each block typically consists of a data sequence and a cyclic prefix or zero padded suffix.
¾ In this work, we consider the timeslot-structured SCBT –
The transmitted signal sequence is composed of one by one timeslots.
–
In each timeslot, there are several transmission blocks referred to as sub-timeslots.
¾ Dual cyclic timeslot structure –
There is a cyclic guard prior to each pilot segment, and there is also a "cyclic guard" G (and P) prior to each segment of D plus G (and P).
2006-12-7
Dr. Xiqi Gao / NCRL
4
MIMO-SCBT with Dual Cyclic Timeslot Structure Signal model for channel estimation ¾ The received signal for the k-th pilot segment after the removal of CP can be written as
y (k ) = (I N R ⊗ S)h(k ) + z (k ) ¾ To achieve optimal channel estimation in the whole timeslot, we needs to deal with the received pilot signals simultaneously.
y = Xh + z T T T T where y = [y (0), y (1),..., y ( K )] , X = I ( K +1) N R ⊗ S,
h = [hT (0), hT (1),..., hT ( K )]T , and z = [zT (0), zT (1),..., zT ( K )]T
2006-12-7
Dr. Xiqi Gao / NCRL
5
Channel Estimation and Pilot Design Channel estimation ¾ The linear MMSE solution of the channel vector is
hˆ = R h ( X H XR h + σ z2 I ( K +1) N R NT N P ) −1 X H y ¾
For a triply selective MIMO channel, it can be proved that the optimal pilots are related to the statistical CHI in eigen-mode.
¾ With the transmit antenna correlation unknown at the transmitter, the optimal pilots satisfy the orthogonal condition S H S = LP I N N . T
P
¾ With the optimal pilots, the channel estimation can be simplified to initial block-based LS channel estimation followed by space-time postprocessing.
hˆ ini = 2006-12-7
1 LP
X y, H
+ (Λ hˆ = UΛ
σ z2 LP
Dr. Xiqi Gao / NCRL
H hˆ I ( K +1) N R NT N P ) −1 U ini 6
Channel Estimation and Pilot Design Design of optimal pilot ¾ From the orthogonal condition, the training sequences transmitted from multiple antennas must have impulse-like auto correlation and zero cross correlation. ¾ In this work, the pilot sequence for each transmit antenna is derived by cyclically right shifting a single base sequence.
sn (l ) = a(((l − nN P )) LP ), S = circ{a}[I NT N P 0]T ¾ If the base sequence is cyclically orthogonal, then the S satisfy the orthogonal condition. jπ rl / L P ⎧⎪ e , a (l ) = ⎨ jπ rl ( l +1) / LP , ⎪⎩e 2
–
The Chu sequence:
–
The DFT-based sequence:
2006-12-7
for even LP , for odd LP .
} a = [a(0) a(1) " a(LP −1)] = vec{W N
Dr. Xiqi Gao / NCRL
7
Fast Implementation Initial channel estimation ¾ For any cyclic orthogonal pilot sequence, we have 1 [I NT N P 0]WLHP Λ aH WLP y m (k ) hˆ ini , m (k ) = LP
¾ With the Chu sequence and the DFT-based sequence as the base sequence, we have 1 [I NT N P 0]Ψ H WLHP PγH Φ H y m (k ) hˆ ini , m (k ) = LP 1 hˆ ini , m (k ) = [I NT N P 0]PαH (I Q ⊗ WNH )PβH Σ H (I Q ⊗ WN )Pα y m (k ) LP
¾ The implementation complexity can be reduced by half.
2006-12-7
Dr. Xiqi Gao / NCRL
8
Fast Implementation Space-time post-processing ¾ The space-time post-processing is related to eigen-decomposition of the channel correlation matrices. – This means that online estimation of the correlation matrices and online eigen-value decomposition (EVD) should be performed. – The eigen-matrix serves as the optimal de-correlation transform.
¾ To simplify the implementation, we replace the optimal decorrelation transform by the discrete cosine transform (DCT). – which can approximate the optimal performance and has fast implementation. p hˆ = (CIIK +1 ⊗ CIIN R ⊗ CIINT )T Λ st , p (CIIK +1 ⊗ CIIN R ⊗ CIINT )hˆ ini
2006-12-7
Dr. Xiqi Gao / NCRL
9
Simulations SIMULATION PARAMETERS -5
-24 LS CHE MMSE CHE-1 MMSE CHE-2 DCT CHE
-10
-26
V=250km/h -15 Normalized MSE (in dB)
-28
-20 -30 -25
-32
Tx antenna number
4
Rx antenna number
4
Transmit correlation factor
0 and 0.2
Receive correlation factor
0 and 0.5
Carrier frequency
3.5GHz
Symbol rate
1.28Msps
Velocity
250 and 3 km/h
Multi-path power profile
Exponentially distributed
Sub-timeslot number K
7
Guard Length LG
8
Pilot Length LP
32
User data length LD
312
-30 V=3km/h -34
-35
-40
0
2006-12-7
2
4
6
8 10 12 14 Average Received SNR (in dB)
16
18
-36 20 18.5 19 19.5
Dr. Xiqi Gao / NCRL
10
Conclusions ¾ Efficient channel estimation for the timeslot-structured SCBT over triply selective fading MIMO channels has been investigated. ¾ The condition on the optimal pilots has been derived, and a new design of the pilot sequences is suggested. ¾ With the optimal pilots, the channel estimation can be simplified to initial block-based LS channel estimation followed by space-time postprocessing. ¾ More efficient implementations for the initial channel estimation are obtained by using the structure of the pilot sequence. ¾ A DCT-based implementation for the space-time post-processing is developed to approximate the optimal solution with low implementation complexity. ¾ Simulation results have verified the performance of the proposed channel estimation.
Thank you for your attentions !
2006-12-7
Dr. Xiqi Gao / NCRL
11
