sukh 04560087 sukh

Signal Detection for the STFC-OFDM System over Time Selective Fading Channels

Jin-Tao Wang, Member, IEEE, Yu Zhang, Jun Wang, Jian Song, and Zhi-Xing Yang

Abstract —The key assumption in all space-time block

coded orthogonal frequency division multiplexing (OFDM) schemes is that the channel remains static within the whole codeword length. This will inevitably introduce an irreducible error floor, caused by the inter-transmit-antenna interference (ITAI), in the high signal-to-noise (SNR) region over the time selective fading channels. To mitigate the impact of ITAI, a novel signal detection scheme for four-transmit-antenna space-time-frequency coded OFDM system has been proposed in this paper. Through the theoretical analysis and computer simulations, it is proven that the proposed method can handle both slow and fast fading channels very effectively as well as efficiently, removing the error floor within the normal Doppler frequency range1.

Index Terms —Space-time block codes, orthogonal frequency division multiplexing (OFDM), transmit diversity, time selective fading, inter-transmit-antenna interference (ITAI).

I. INTRODUCTION Space-Time block coding scheme has been regarded as the

most effective approach of using the transmit diversity to combat the detrimental effects in the wireless fading channels and the implementation is relatively simple and cost-effective. Orthogonal designed space-time block codes (STBCs) proposed by Alamouti [1] and generalized by Tarokh, Jafarkhani, and Calderbank [2][3] can achieve full transmit diversity. Using the maximum-likelihood (ML) decoding algorithm, the transmitted symbols can be decoded separately, instead of jointly, which greatly facilitates the receiver design. Since the systems using orthogonal codes can’t achieve the full transmission rate with transmit antennas of more than two, the STBCs from quasi-orthogonal (QO) designs with full rate but partial transmit diversity were proposed [4]-[6]. With the quasi-orthogonal structure, the receiver has to perform the ML decoding by searching for the pair of symbols, which introduces certain computational complexity. Recently, the full diversity quasi-orthogonal designs have been proposed through the constellation rotation [7][8], and this potentially achieves the goal of full transmit diversity as well as full rate.

From literatures in this research area, it is easily to figure

1 This research was supported by “Multistandard integrated network

convergence for global mobile and broadcast technologies” (MING-T, FP6 STREP Contract Nr.045461).

Jin-Tao Wang, Jun Wang, and Zhi-Xing Yang are with the Department of Electronic Engineering, Tsinghua University, Beijing, 100084, China (e-mail: [email protected]).

Yu Zhang and Jian Song are with the Research Institute of Information Technology (RIIT), Tsinghua University, Beijing, 100084, China (e-mail: [email protected]).

out that the typical ML decoders in the most existing STBC schemes rely on the so-called “quasi-static channel” assumption which is very critical. It says: if an Tn -transmit-antenna STBC scheme with code matrix Tp n× is adopted, the channel remains static over the entire length of codeword, i.e.

spT , where sT is the symbol period and p is called decoding delay. Such assumption is valid in some cases but it may not hold anymore in mobile wireless channels. In this type of applications, the time-varying, multi-path (i.e., double selective) fading must be considered and the “quasi-static channel” assumption becomes invalid. Time selective fading will destroy the orthogonality or quasi-orthogonality property of the channel matrix and therefore, causes the so-called inter-transmit-antenna interference (ITAI). For example, with the four-antenna quasi-orthogonal schemes [4]-[6], the time-variation in the channel results in ITAI among all the symbols, so the pair-wise ML decoding method will be suboptimal. Due to the impact of ITAI, an irreducible error floor in the bit-error-rate (BER) curves will appear in the high signal-to-noise (SNR) region. Many schemes have been developed to mitigate the ITAI mentioned above [9]-[12].

Orthogonal frequency division multiplexing (OFDM) is one of the most competitive schemes for the digital broadband communication systems in the multi-path fading environments. It can effectively avoid the negative impact of the inter-symbol- interference (ISI) caused by the multi-path propagation. Multiple antenna technology can be employed in the OFDM systems to achieve the spatial diversity or increase the spectral efficiency [13]. Since OFDM offers the possibility of coding in both time and frequency dimensions, two methods, space-time coded OFDM (STC-OFDM) and space-frequency coded OFDM (SFC-OFDM), have therefore been introduced [14][15]. To improve the performance of OFDM system with four antennas in the double-selective channels, the space-time- frequency coded OFDM (STFC-OFDM) scheme has been proposed [16]. This scheme performs block coding in both time and frequency dimensions simultaneously assuming that the channel responses between adjacent OFDM frames and sub-carriers are approximately the same. So the channel assumption of STFC-OFDM is much more relaxed than that of either STC-OFDM or SFC-OFDM system [14][15]. However, if the channel condition changes very fast (from frame to frame), the STFC-OFDM scheme still suffers from ITAI, even though less significantly than that from STC-OFDM.

Contributed PaperManuscript received November 19, 2007 0098 3063/08/$20.00 © 2008 IEEE

J.-T. Wang et al.: Signal Detection for the STFC-OFDM System over Time Selective Fading Channels 283

Fig. 1. The diagram of the transmitter end in the four-antenna STFC-OFDM scheme.

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯−⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

With this practical concern, a simple zero-forcing (ZF) method to cancel ITAI based on the STFC-OFDM code structure is proposed in this paper and its performance is further evaluated through both theoretical analysis and computer simulations.

The rest of the paper is organized as follows. Section II describes the channel model with the time selective fading. After briefly reviewing the STFC-OFDM design in section III, a simple ITAI cancellation scheme for STFC-OFDM system is introduced in section IV. Section V gives the simulation results. We then conclude this paper in section VI.

Note: in the following, a complex conjugation, transposition and Hermitian operator are denoted as the superscript *, T, H, respectively.

II. CHANNEL MODEL WITH TIME SELECTIVE FADING Generally, a wireless frequency selective fading channel

can be modeled as a finite impulse response (FIR) filter with L taps. The received signal can be written as

1

0

( ) ( ) ( ) ( )L

i ii

r t h x t w tτ τ−

=

= − +∑ (1)

where iτ is the delay time and ( )ih τ is the complex fading coefficient for the i-th tap, ( )x t is the time domain transmitted signal, and ( )w t is the zero-mean, complex additive white Gaussian noise (AWGN). The fading coefficient of each tap is independently modeled as a zero-mean, complex Gaussian random variable. Let the power of each path be normalized by the power of the first path, i.e. 0( )h τ having the unit variance. The power value of the rest paths is denoted as Pi with i>0. Since the channel is time-varying, the relationship of the channel coefficient ( )h t at time st nT= and ( ) st n m T= + , where sT is symbol period, are definitely different yet can be described via a first-order auto-regressive (AR) model referring to [9],

( ) ( ) ( )mh n m h n n mα β+ = + + (2)

where *0E ( ) ( ) J (2 )m d sh n h n m mf Tα π⎡ ⎤= + =⎣ ⎦ . [ ]E is the

expectation operator, ( )0J is the zero-th order Bessel

function of the first kind, and df is the Doppler frequency.

( )nβ is another independent complex Gaussian random variable with zero mean and variance of

22

2

1 0

(1 ) 0m

i m

i

P iβ

ασ

α

⎧ − =⎪= ⎨− ≠⎪⎩

(3)

It has been proved in [17] that the first-order AR model provides a sufficiently accurate model for the time selective fading channels and we therefore, will adopt the AR model for analysis and simulations in the following.

III. REVIEW OF STFC-OFDM SCHEME To improve the performance of OFDM system with

multiple transmit antennas in the double-selective fading channels, a space-time-frequency coded OFDM (STFC-OFDM) scheme has been proposed [16]. In the following, we give a brief review on this scheme considering the multi-antenna OFDM system with four transmit antennas, one receive antenna and N sub-carriers. The diagram of four-antenna STFC-OFDM is shown in Fig. 1.

Assume ( , )X k l is the frequency domain input symbol sequence, where k is the sub-carrier number with 0 1k N≤ ≤ − , and l is the OFDM frame number. ( , )eX m l and ( , )oX m l are the half length vectors denoting the even and odd component vectors of ( , )X k l with 0 / 2 1m N≤ ≤ − . The STFC-OFDM scheme performs block coding in both time and frequency dimensions simultaneously and from the analysis in [16], the equivalent transmitted codeword is given by

* *

* *

* *

* *

(2 , ) (2 1, ) (2 , 1) (2 1, 1)(2 1, ) (2 , ) (2 1, 1) (2 , 1)(2 , 1) (2 1, 1) (2 , ) (2 1, )

(2 1, 1) (2 , 1) (2 1, ) (2 , )

X m l X m l X m l X m lX m l X m l X m l X m lX m l X m l X m l X m l

X m l X m l X m l X m l

⎡ ⎤+ + + +⎢ ⎥+ − + + − +⎢ ⎥=⎢ ⎥+ + + − − +⎢ ⎥

+ + − + − +⎢ ⎥⎣ ⎦

S

(0 / 2 1)m N≤ ≤ − (4) Each column of S denotes the transmitted signals for

different antennas. It is easy to prove that the STFC-OFDM scheme satisfies the design criterion of the quasi-orthogonal space-time block code for OFDM systems with four transmit antennas [16].

284 IEEE Transactions on Consumer Electronics, Vol. 54, No. 2, MAY 2008

1, 2, 3, 4,* * * **

2, 1, 4, 3,* * * **

3, 1 4, 1 1, 1 2, 11

4, 1 3, 11

(2 ) (2 ) (2 ) (2 ) (2 )(2 1) (2 1) (2 1) (2 1)(2 1)

(2 ) (2 ) (2 ) (2 )(2 )(2 1) (2 1)(2 1)

l l l l l

l l l ll

l l l ll

l ll

R m H m H m H m H mH m H m H m H mR mH m H m H m H mR m

H m H m HR m+ + + ++

+ ++

⎡ ⎤⎢ ⎥ − + + − + ++⎢ ⎥ =⎢ ⎥ − −⎢ ⎥

+ − + −+⎢ ⎥⎣ ⎦

**

**1

2, 1 1, 1 1

(2 )(2 , )(2 1)(2 1, )

(2 )(2 , 1)(2 1) (2 1) (2 1, 1) (2 1)

l

l

l

l l l

W mX m lW mX m lW mX m l

m H m X m l W m+

+ + +

⎡ ⎤⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥ ++ ⎢ ⎥⎢ ⎥⎢ ⎥ + ⎢ ⎥⎢ ⎥⎢ ⎥ + ⎢ ⎥⎢ ⎥⎢ ⎥

+ + + +⎢ ⎥ +⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

(0 / 2 1)m N≤ ≤ − (6)

1 1 2* ** *

1 2 1* *

1 2 2**

2 1 2

(2 , ) (2(2 , )( ) 0 ( ) ( )0 ( ) ( ) ( )(2 1, ) (2 1, )( ) ( ) ( ) 0 (2 , 1)(2 , 1)( ) ( ) 0 ( ) (2 1, 1)

(2 1, 1)

lX m l X m lg m a m a m

g m a m a mX m l X m la m a m g m X m lX m la m a m g m X m l

X m l

η∧

∧

∧

∧

⎡ ⎤⎢ ⎥ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥−+ +⎢ ⎥ ⎢ ⎥⎢ ⎥= +⎢ ⎥ ⎢ ⎥⎢ ⎥− +⎢ ⎥+ ⎢ ⎥⎢ ⎥⎢ ⎥ + +⎢ ⎥⎣ ⎦ ⎣ ⎦⎢ ⎥+ +⎣ ⎦

*

*1

1

)(2 1)

(2 )(2 1)

l

l

l

mm

mm

η

ηη

+

+

⎡ ⎤⎢ ⎥+⎢ ⎥⎢ ⎥⎢ ⎥

+⎢ ⎥⎣ ⎦

(0 / 2 1)m N≤ ≤ − (10)

where, 2 2 2 2

1 1, 2, 3, 1 4, 1( ) (2 ) (2 ) (2 ) (2 )l l l lg m H m H m H m H m+ += + + + , 2 2 2 2

2 3, 4, 1, 1 2, 1( ) (2 ) (2 ) (2 ) (2 )l l l lg m H m H m H m H m+ += + + + , * * * *

1 1, 3, 2, 4, 1, 1 3, 1 2, 1 4, 1( ) (2 ) (2 ) (2 ) (2 ) (2 ) (2 ) (2 ) (2 )l l l l l l l la m H m H m H m H m H m H m H m H m+ + + += + − − , * * * *

2 1, 4, 2, 3, 3, 1 2, 1 4, 1 1, 1( ) (2 ) (2 ) (2 ) (2 ) (2 ) (2 ) (2 ) (2 )l l l l l l l la m H m H m H m H m H m H m H m H m+ + + += − − + . ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯−⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Let i,lH denote the frequency-domain complex channel gains from the transmitter Txi (i=1,2,3,4) to the receiver and

lW denote the i.i.d., zero-mean complex AWGN with the

variance of 2Wσ at the l-th time slot. Then the received signal

can be expressed as (6) shown on top of this page. Let H(m) denote the channel response matrix, i.e.

1, 2, 3, 4,* * * *

2, 1, 4, 3,* * * *

3, 1 4, 1 1, 1 2, 1

4, 1 3, 1 2, 1 1, 1

(2 ) (2 ) (2 ) (2 )(2 1) (2 1) (2 1) (2 1)

(2 ) (2 ) (2 ) (2 )(2 1) (2 1) (2 1) (2 1)

l l l l

l l l l

l l l l

l l l l

H m H m H m H mH m H m H m H mH m H m H m H m

H m H m H m H m+ + + +

+ + + +

⎡ ⎤⎢ ⎥− + + − + +⎢ ⎥=⎢ ⎥− −⎢ ⎥

+ − + − + +⎢ ⎥⎣ ⎦

H(m)

(0 / 2 1)m N≤ ≤ − (7) In the so-called “quasi-static channel”, we assume that the

channel responses between both two adjacent frames and two consecutive sub-carriers are approximately the same, i.e.

, , , 1 , 1( ) (2 ) (2 1) (2 ) (2 1)i i l i l i l i lH m H m H m H m H m+ += ≈ + ≈ ≈ + ( 1, 2,3, 4 0 / 2 1)i m N= ≤ ≤ − (8)

Then left multiply HH (m) to the both sides of (6) and we get

'

'** *

' *** 1

'1

(2 , ) (2 )(2 , )( ) 0 0 ( )(2 1)(2 1, ) 0 ( ) ( ) 0 (2 1, )

0 ( ) ( ) 0 (2 )(2 , 1)(2 , 1)( ) 0 0 ( ) (2 1, 1)

(2 1, 1)

l

l

l

l

X m l W mX m la m b mW mX m l a m b m X m l

b m a m W mX m lX m lb m a m X m l W

X m l

∧

∧

∧+

∧ +

⎡ ⎤⎢ ⎥ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ++ − +⎢ ⎥ ⎢ ⎥⎢ ⎥= +⎢ ⎥ ⎢ ⎥⎢ ⎥− +⎢ ⎥+ ⎢ ⎥⎢ ⎥⎢ ⎥ + +⎢ ⎥⎣ ⎦⎣ ⎦⎢ ⎥+ +⎣ ⎦

(2 1)m

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥+⎣ ⎦

(0 / 2 1)m N≤ ≤ − (9)

with ' ( )lW k still complex AWGN, 4

2

1( ) ( )i

ia m H m

=

= ∑ , and

* *1 4 2 3( ) 2Re( ( ) ( ) ( ) ( ))b m H m H m H m H m= − . It can be seen

that at the receiver, the symbol pairs of ( (2 , ), (2 1, 1))X m l X m l+ + and ( (2 1, ), (2 , 1))X m l X m l+ + can be decoded separately.

IV. THE SIMPLE ITAI CANCELLATION SCHEME FOR THE STFC-OFDM SYSTEM

With the conventional STC-OFDM or SFC-OFDM systems purely encoded in either time or frequency dimension [14][15], the channel responses within four consecutive OFDM frame duration or four consecutive sub-carriers are supposed to be approximately the same. This assumption usually doesn’t hold in the double selective fading channel and the system performance therefore, degrades significantly. From (8), in the STFC-OFDM system, the channel responses are assumed to be roughly the same only between two adjacent frames and two consecutive sub-carriers. This greatly relaxes the restrictions on the channel assumptions and that is why STFC-OFDM scheme can effectively improve the transmission performance in the double selective fading channels. However in some cases, the channel could change very fast (i.e., from frame to frame, hence not constant over two frames), and the STFC-OFDM scheme will also suffer performance loss (though not as severely as that of STC-OFDM system) from ITAI. Therefore, a simple ITAI cancellation method is proposed in this section.

A. ITAI Cancellation Scheme Because of the time-variation in the channel, (8) is not valid

any longer. But we can still use the assumption that the channel responses between two adjacent sub-carriers are approximately the same, i.e. , ,(2 ) (2 1)i l i lH m H m≈ + . In practice, even in the time-varying channels, this is a very sound assumption in most OFDM applications. So under this scenario, by left multiplying HH (m) to both sides of (6) and we can get (10), shown on top of this page, with ( )l kη as the

complex noise. Obviously, the result of HH (m)H(m) doesn’t have the quasi-orthogonal structure as shown in (9) and 1( )a m represents the interference


Fig. 2. The diagram of the proposed ITAI cancellation scheme.

caused by the channel time-variation.

From (10), the pair-wise ML detection strategy introduced in section III can’t be applied directly here, even the perfect channel state information (CSI, i.e., i,lH ) has been obtained. The main reason is that the likelihood function used for detection can no longer be divided into the sum of two independent, pair-wise functions. So if the pair-wise ML detection described in section III is still utilized, an irreducible error floor in BER curves in the high SNR region will appear. To mitigate the ITAI by taking the advantage of the perfect CSI estimation, a three-step ZF scheme has been developed in this paper with the diagram shown in Fig. 2.

Step 1: From the above analysis, let HH (m) left multiply the received signal to get (10). For simplicity purpose, we denote

1

1

( ) 00 ( )

g mg m

⎡ ⎤= ⎢ ⎥

⎣ ⎦1G (m)

2

2

( ) 00 ( )

g mg m

⎡ ⎤= ⎢ ⎥

⎣ ⎦2G (m)

1 2* *

2 1

( ) ( )( ) ( )

a m a ma m a m

⎡ ⎤= ⎢ ⎥−⎣ ⎦

A(m)

Then we get ⎡ ⎤

= = ⎢ ⎥⎣ ⎦

1HH

2

G (m) A(m)Φ(m) H (m)H(m)

A (m) G (m) (11)

Step 2: Construct the following matrix Z(m) as ⎡ ⎤

= ⎢ ⎥⎣ ⎦

2H

1

G (m) -A(m)Z(m)

-A (m) G (m) (12)

It is easy to prove that ( )g m= ⋅ = ⋅ = ⋅H

4D(m) Z(m) Φ(m) Z(m) H (m)H(m) I (13)

where 2 21 2 1 2( ) ( ) ( ) ( ( ) ( ) )g m g m g m a m a m= − + , and 4I is

the 4 4× identify matrix. So the decision equation is given by

** *

*** 1

1

'(2 , ) '(2 )(2 , )' (2 1)' (2 1, ) (2 1, )

' (2 )(2 , 1)' (2 , 1)(2 1, 1) '(2 1)

'(2 1, 1)

l

l

l

l

X m l mX m lmX m l X m l

mX m lX m lX m l m

X m l

ηη

ηη

∧

∧

∧+

∧ +

⎡ ⎤⎢ ⎥ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ++ +⎢ ⎥ ⎢ ⎥⎢ ⎥= +⎢ ⎥ ⎢ ⎥⎢ ⎥+⎢ ⎥ ⎢ ⎥+ ⎢ ⎥⎢ ⎥ + + +⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦⎢ ⎥+ +⎣ ⎦

D(m)

(0 / 2 1)m N≤ ≤ − (14) With the coefficient matrix being diagonalized as shown in (14), the ITAI has been totally canceled.

Step 3: Let Y(m) denote the estimation vector, i.e.

* *'(2 , ) ' (2 1, ) ' (2 , 1) '(2 1, 1)T

X m l X m l X m l X m l∧ ∧∧ ∧⎡ ⎤

= + + + +⎢ ⎥⎣ ⎦

Y(m) .

From (14), it is observed that a simple least square (LS) symbol-wise detection method can be adopted:

[ ]{ }2arg min ( )

jjic C

g m c∈

−Y(m) (15)

where 1, 2,3, 4i = , C is the transmitted symbol set, and [ ]iY(m) is the i-th element in the vector Y(m) for detection.

B. Algorithm Discussion 1) Optimality: We consider the statistics of the complex

noise '( )l kη in (14). Let W(m) , η(m) and η'(m) denote the nose vectors in (6), (10) and (14). We have

2E Wσ⎡ ⎤ =⎣ ⎦H

4W(m)W (m) I (16)

2E E Wσ⎡ ⎤ ⎡ ⎤= =⎣ ⎦ ⎣ ⎦

H H H Hη(m)η (m) H (m)W(m)W (m)H(m) H (m)H(m) (17)

2

2

2

E E

( )

( )

W

W

W

g m

g m

σ

σ

σ

⎡ ⎤ ⎡ ⎤=⎣ ⎦ ⎣ ⎦=

=

=

H H H

H H

H

η'(m)η' (m) Z(m)η(m)η (m)Z (m)

Z(m)H (m)H(m)Z (m)

Z (m)

Z(m)

(18)

In general, Z(m) is neither diagonal as it should be in the orthogonal designs nor quasi-diagonal as it should be in the quasi-orthogonal schemes. Therefore, (15), by nature, is a suboptimum approach instead of an ML detector.

If the channel is time-invariant over two consecutive OFDM frame periods, i.e. in the “quasi-static channel”, 1( )a m

is zero and E ⎡ ⎤⎣ ⎦Hη'(m)η' (m) will have the quasi-orthogonal

structure from (12) and (18). So in this special case, the optimum pair-wise ML detector can be performed as introduced in section III. If we still use the suboptimal decoder shown in (15), certain performance loss will be introduced. From the following simulation results, it can be seen, however, that the performance loss introduced by this scheme is still affordable.

2) Complexity: From (10)-(14), under the perfect CSI estimation, only two 4 4× complex matrix multiplications are required and there is no matrix inversion in the proposed three-step ZF scheme. Comparing with the existing methods applied for the quasi-orthogonal design [12], this scheme greatly reduces the computational complexity.

Moreover, (15) is a linear processing detector. So the complexity of the detection for the M-ary constellation is

( )O M per symbol, while it is 2( )O M per symbol in the pair- wise detector in the conventional quasi-orthogonal designs [16]. As the proposed scheme also inherits the virtue of the simple implementation of the STFC-OFDM at the transmitter end, the computational load of this scheme should therefore not be a problem.


3) Flexibility: As mentioned earlier, if the channel is almost time-invariant over two consecutive OFDM frame periods in practice, we only need to perform Step 1 and adopt the pair-wise detector as described in section III, avoiding the performance loss. To save the power consumption, two synchronous switches, K1 and K2, could be used as shown in Fig. 3. Whether using the conventional pair-wise detector or the proposed linear detector (i.e. single-symbol detector) is simply determined by the comparison result between the channel responses of the two adjacent OFDM frames (the detailed strategy in determining when to switch from our proposed ITAI cancellation scheme to ML decoder is a part of future work). The structure presented in Fig.3 provides a very flexible solution for the various wireless fading environments.

Finally, by setting zero for the channel gains from transmitter Tx4 to the receiver in (6) and all the other related equations, the introduced scheme can essentially be used in the three- transmit-antenna system without any other modifications.

Fig. 3. The diagram of the combined scheme switching between the conventional pair-wise symbol detector and single-symbol detector.

V. SIMULATIONS The BER performance of the proposed signal detection

scheme based on the four-transmit-antenna STFC-OFDM system was evaluated by computer simulations. We used the Time Domain Synchronous - OFDM (TDS-OFDM) system as an example to demonstrate its effectiveness. TDS-OFDM system is proposed by Tsinghua University as the key technique for the Chinese digital television terrestrial broadcasting (DTTB) standard [18]. It utilizes the pseudorandom noise (PN) sequences as the guard interval (GI) as well as the training symbols for the channel estimation and timing recovery. More detailed work on TDS-OFDM system can be referred to [19]-[21] and the literatures therein.

The channel model for simulations is from the Brazil digital television test report [22] with the parameters listed in Table I. This is a typical frequency selective fading channel model in DTTB. The parameters of the TDS-OFDM system used for the simulations are listed in Table II.

In our simulations, it was assumed that the transmit power of all the transmitters were equal, the fading paths from each transmitter to the receiver were independent, and the CSI of each transmit branch was perfectly estimated.

TABLE I

TYPICAL DTTB CHANNEL MODEL

Multi-path propagation

Relative Amplitude (dB)

Delay Time (μs )

1 0 0.00 2 -12 0.30 3 -4 3.50 4 -7 4.40 5 -15 9.50 6 -22 12.70

TABLE II

THE PARAMETERS OF TDS-OFDM SYSTEM Symbol Rate 7.56 MSPS

Number of Sub-carriers 3780 Frame Body Period (Ts) 500 sμ

Sub-carrier Interval 2 kHz Guard Interval 1/9

Sub-carrier modulation QPSK or 16QAM FEC none

Fig. 4. The relation between ε and d sf T .

It is usually true that the interference 1( )a m in (10) caused

by the channel time-variation is much smaller than the absolute value of the terms in the two diagonals of Φ(m) , i.e.

2 ( )a m , 1( )g m and 2 ( )g m . Let IΦ (m) denote the matrix including the nondiagonal terms of Φ(m) . Then we define “interference beyond QO-STBC structure” as

F

F

=Eε⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦

IΦ (m)Φ(m)

where F

Φ represents the Frobenius norm of Φ . Clearly, ε

is dependent on the Doppler frequency df of the channel. Fig. 4 shows the relation between ε and the normalized Doppler frequency d sf T . It is observed that for the normal range of df ,

1ε . Simulation results for the system with QPSK and 16QAM

modulation on each sub-carrier are shown in Fig.5 and Fig.6, respectively. We compare the BER performance between the


STFC-OFDM system in [16] and our proposed ITAI cancellation scheme (STFC-OFDM-ZF) under the different Doppler frequencies of df =0Hz, 50Hz, 100Hz, 150Hz and 200Hz. Correspondingly, the normalized Doppler frequencies are d sf T =0, 0.025, 0.05, 0.075 and 0.1. The maximal Doppler frequency df of 200 Hz corresponds to the receiver velocity of about 260 to 500 km/h in the TV UHF band (@470~862MHz). So the simulations here are sufficient to show the effectiveness of the proposed scheme under the different time-variant scenarios.

Fig. 5. The BER performance comparison with QPSK modulation on each sub-carrier of the TDS-OFDM system.

Fig. 6. The BER performance comparison with 16QAM modulation on each sub-carrier of the TDS-OFDM system.

Form the simulation results, it can be seen that the proposed STFC-OFDM-ZF scheme is quite effective in suppressing the negative impact of the channel time selectivity. When the channel is “quasi-static”, i.e. df =0Hz, from the slopes of the BER curves in the figures, we found that the two schemes have the same diversity order. As the detection scheme shown in (15) is not optimal in this case, the performance of the new scheme is around 1-dB worse than that of the conventional pair-wise detection. When the channel becomes much more

time selective, the performance of the conventional scheme degrades severely, suffering from an irreducible error floor in the high SNR cases. In contrast, there is no error floor with the adaptation of our proposed scheme and the BER performance degradation is less than 2-dB, even in the highest Doppler frequency case.

VI. CONCLUSIONS To deal with the irreducible error floor problem caused by

ITAI, from which the conventional pair-wise detectors normally suffer in the high SNR region under the time-varying channel condition, a novel signal detection method for the STFC-OFDM system over the time selective fading channels has been proposed in this paper. A simple yet very flexible switch-based structure associated with our proposed scheme is also presented which could potentially save the power consumption as well as avoiding the performance loss under the negligible Doppler frequency shift case. Both theoretical analysis and computer simulation confirm that the proposed scheme can handle both slow and fast fading channels extremely well, removing error floor in the normal Doppler frequency range. Moreover, under the perfect CSI estimation, the computational complexity of our scheme is very small. Considering that the four-transmit-antenna STBC system is much more vulnerable to the time selective fading than the two-transmit-antenna case, the proposed signal detection method will provide a useful option for the future applications when higher transmit diversity is indispensable.

It is also interesting to point out that, for the four-antenna quasi-orthogonal STBCs with the symbols from the same signal constellation set, the diversity order is two while the code rate is one [4]-[6]. Recently, the full diversity quasi-orthogonal designs have been proposed through the constellation rotation [7][8]. STFC-OFDM system can be easily extended to the constellation rotated quasi-orthogonal designs by simply introducing a phase-shift module before the space-time encoder shown in Fig. 1, achieving the full diversity and full rate simultaneously. In this regard, the novel ITAI cancellation method can also be effectively adopted in the constellation rotated design.

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Jin-Tao Wang (S’03-M’06) received his B.Eng and Ph.D degrees in Electrical Engineering both from Tsinghua University, Beijing, China in 2001 and 2006, respectively. He became a Student Member (S) of IEEE in 2003, and a Member (M) in 2006. Since 2006, he has been an assistant professor of Tsinghua's DTV Technology R&D center. He is the standard committee

member for the Chinese national digital terrestrial television broadcasting standard. His current research interest is in the area of the broadband wireless transmission, especially the channel estimation and space-time coding techniques.

Yu Zhang received the B.E. and M.S. degrees, both in Electronic Engineering, from Tsinghua University, Beijing, China, in 1999 and 2002, respectively, and the Ph.D degree in electrical and computer engineering from Oregon State University, Corvallis, OR, in 2006. From March 2007 to November 2007, he was an Assistant Professor with the Research Institute of Information

Technology, Tsinghua University. He is currently an Assistant Professor with the Department of Electronic Engineering, Tsinghua University. His current research interests include the performance analysis and detection schemes for MIMO-OFDM systems over doubly-selective fading channels, transmitter and receiver diversity techniques, and channel estimation and equalization algorithms.

Jun Wang received the B. Eng. and Ph.D degree from the Department of Electronic Engineering in Tsinghua University, Beijing, China, in 1999 and 2003 respectively. He is an assistant professor and member of Digital TV R&D center of Tsinghua University since 2000. His main research interests focus on broadband wireless transmission techniques, especially

synchronization and channel estimation. He is actively involved in the Chinese national standard on the Digital Terrestrial Television Broadcasting technical activities, and is selected by the Standardization Administration of China as the Standard committee member for drafting.

Jian Song received his B.Eng and Ph.D degrees in Electrical Engineering both from Tsinghua University, Beijing, China in 1990 and 1995, respectively and worked for the same university upon his graduation. He has worked at The Chinese University of Hong Kong and University of Waterloo, Canada in 1996 and 1997, respectively. He has been with Hughes Network Systems

in USA for 7 years before joining the faculty team in Tsinghua in 2005 as a professor. He is now the director of Tsinghua’s DTV Technology R&D center. His primary research interest is in physical layer and has been working in quite different areas of fiber-optic, satellite and wireless communications, as well as the powerline communications. His current research interest is in the area of digital TV broadcasting.

Zhi-Xing Yang is a full professor at the Department of Electronics Engineering of Tsinghua University, China. He is the executed director of the State Key Laboratory on Microwave & Digital Communications, China, and the executed director of the development group of the digital television terrestrial broadcasting state standard for China. He received several awards and held several

patents. His research interests are in high-speed data transmission over broadband digital television terrestrial broadcasting, wireless links, wireless communication theory and communication systems design.


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