Most previous work that deals with channel tracking assumes that the number Kp of pilot subcarriers in each data OFDM symbol is at least as large as the number Kt of taps

In the IEEE 80211p standard the number Kp of pilot subcarriers is generally smaller than the number Kt of taps

The proposed algorithm is based on the following ideas

Sparsity While the number Kt of taps is larger than Kp the number Kmp of paths is often small and comparable to the number of pilot subcarriers Kp

Long-term vs short-term channel parameters Distinction between the long-term parameters 1048576 and the short-term time-varying amplitude vectors

Code-aided methods Utilizing the error-correcting properties of the LDPC code within a decision-feedback loop

Code-Aided EM Algorithm for Joint Channel Tracking and Decoding for Sparse Fast-Fading Multipath Channels

S Khalili O Simeone M Haimovich CWCSPR New Jersey Institute of Technology Newark NJ USA

Code Aided-EM Method

The transmitted frame contains OFDM symbols each consisting of K subcarriers

The first OFDM symbol contains only pilot subcarriers The following N OFDM symbols contain Kp pilot subcarriers

References

Conventional Approach

Introduction

Baseband equivalent discrete-time system model (a) transmitter (b) receiver

System Model

The channel corresponding to the nth OFDM symbol is defined by Kt taps

The channel taps are the result of the superposition of Kmp multipath components

Each path is characterized by a delay an average power and a complex amplitude that varies across the OFDM symbol

Due to the speed of the train the complex amplitudes are time-varying The complex amplitudes follow the standard Jakes model

The receiver and the transmitter move in the same direction and with the same known velocity

The Doppler frequency spread of the direct path is zero The time-domain channel vector

Channel estimation by utilizing the training OFDM symbol

The same channel estimate is used to perform coherent decoding of the subsequent N data OFDM symbols in the frame

Conventional approach assumes that the channel is time-invariant

Log Likelihood Ratios required for message passing

Effective noise variance to avoiding mismatch in the decoding metric

2

0( )1 SNR 1 (2 ( ) )

eff n D cpJ f K K n

[1] G Shafiullah A Gyasi-Agyei and P Wolfs ldquoSurvey of wireless communications applications in the railway industryrdquo in Proc Wireless Broadband and Ultra Wideband Communications (AusWireless 2007) pp 65-65 Aug 2007 [2] G Acosta and M-A Ingram ldquoModel development for the wideband expressway vehicle-to-vehicle 24 GHz channelrdquo in Proc IEEE WCNC vol 3 pp 1283-1288 Las Vegas NV Apr 2006[3] C Berger Z Wang J Huang and S Zhou ldquoApplication of compressive sensing to sparse channel estimationrdquo IEEE Commun Magazine vol 48 no 11 pp 164ndash174 Nov 2010[4] G J McLachlan and T Krishnan The EM algorithm and Extensions Wiley 1997

Code Aided-EM Method

Wireless communication networks are expected to play an increasingly prominent role in vehicular networks [1] [2] Wireless communication is currently being considered for use in railways services in order to provide control functionalities as well as passenger entertainment

Due to the high speed of the train wireless links between backbone nodes are subject to highly time-varying channelsCommon wireless standards such as IEEE 80211p prescribe a number of pilots that is significantly smaller than the total number of parameters to be estimated or tracked

A radio link subject to a fast-fading multipath channel within a train backbone network

1N

Channel Model

1

0

[ ] ( )mpK

n d n d dd

h m g m

0E (2 )n d n d D cpJ f K K

diag( )n n h G Γ α h

0 0

0 20

[ ] [ ]ˆ [ ] for 01 1| [ ] | 1

X k Y kH k k K

X k

0

1

20

20

20 0

2

ˆ| [ ] [ ] |exp

ˆPr( [ ] 0 | [ ] [ ])[ ] log log

ˆ ˆPr( [ ] 1| [ ] [ ]) | [ ] [ ] |exp

l

l

n

X eff nn nn

n n n

X eff n

Y k H k X

b k l Y k H kLLR k l

b k l Y k H k Y k H k X

S

S

Proposed Algorithm

Block diagram of the proposed algorithm

and G Γ h

nα

Estimation of Long-Term Channel Parameters

The channel taps Hn[k] are estimated using the MMSE criterion

( 1) ( )

( 1) 2

[ ] [ ]ˆ [ ]| [ ] | 1

ii n n

n in

X k Y kH k

X k

The long-term parameter in the ith iteration is estimated by calculating the empirical average of H ( )i

nH

( )( )( )

12 2

( ) ) )

0

dagger( (1

1 t

iiin n

Ni i inK K

nN

H H H

Γ F G H

The long-term matrix is estimated by using a CS-inspired method [3] The number of multipath components Kmp can be estimated by using the Minimum Description Length (MDL) or

Akaike Information Criterion principle

Joint Channel Tracking and Decoding

Maximum Likelihood (ML) detection

1 1

arg max | arg max E | n n

f f α αX X

X Y X Y X α α

The ML detection problem is efficiently solved by using the EM algorithm which converges to a local optimum by iterating between so called E- and M-steps [4]

1

( 1) ( 1)

1

1 ( 1)

1 0

E-step Calculate

| E log | |

E log [ ] | [ ] |

N

n

i j i j

N

N K i j

n n nn k

f

f Y k X k

α α

α

X X Y X α α Y X

α Y X

( ) ( 1)M-step Solve arg max |

i j i j

XX X X

The M-step in (16) is efficiently performed by using a message passing LDPC decoder

G

Simulations Results

QPSK modulation K = 64 Kp = 4 Kcp = 16 carrier frequency equal to 5 GHz 520 information bits B = 20 MHz = 350 kmh Kmp = 3

BPSK modulation K = 64Kp = 4 Kcp = 16 carrier frequency equal to 5 GHz 520 information bits B = 20 MHz = 350 kmh Kmp = 3

• Slide 1