PN Code Tracking for STBC Transmit Diversity RAKE Receivers in Closely Spaced Multipath Environments 1

Bagawan S. Nugroho, 2 Raja D. Balakrishnan, 3 Hyuck M. Kwon, and 4 Dong H. Kang 1,2,3

Wichita State University, Department of Electrical and Computer Engineering Wichita, KS 67260-0044 Tel: (316) 978-6308, Fax: (316) 978-5408, Email: [email protected]

4

Samsung Electronics, IMT-2000 System R&D Team, IT Center, Suwon, Kyunggi-Do, Korea Tel: 011-82-31-279-4830, Fax: 011-82-31-279-4606, Email: [email protected]

Abstract – Conventional early-late -gate (ELG) pseudo-noise (PN) code tracking shows poor performance in closely spaced multi -path environments where multiple path separation is less than 1.5 times PN chip interval for example. Recently, Fock et al in [1] proposed an efficient PN code tracking scheme for a RAKE receiver with a single transmit antenna and a single receive antenna by canceling the self-interference coming from the closely spaced adjacent multipaths. However, a general trend for 3G or future wireless communication system development is to employ multiple transmit and multiple receive antennas instead of a single transmit antenna. The space time block code (STBC) in [4] is one of popular transmit antenna diversity schemes. In this paper we propose a PN code tracking algorithm for the STBC transmit diversity system under 3GPP specifications, extending the work by Fock et al [1]. Channel estimation for the transmit diversity system is provided with the aid of primary common pilot channel (PCPICH) pattern. S imulations show that the proposed algorithm can eliminate the effects of the adjacent paths and can make an improvement in the root mean square (RMS) of the timing error compared to system without transmit diversity, e.g., 2 dB in chip-energy-to-noise-density ratio Ec /N 0 at RMS=0.1.

tracking and synchronization plays a very crucial and challenging, especially in severe multipath environment where the paths are closely spaced. In this paper, considering STBC as an example, we present a scheme for channel tracking and multipath delay estimation for STBC with two transmit antennas and one receive antenna. For simplicity we will consider the case of two most strong paths per antenna, where each antenna has the same path delay for a given path. The paper is organized as follows. In section II we will briefly introduce the PN code tracking scheme in [1] and describe the proposed scheme for the STBC transmit diversity. In section III we will describe the simulation procedure and discuss the results. Finally in section IV we draw some conclusions. II. SYSTEM MODEL The spread sequence with spreading factor Nc, transmitted using pulse shaping filter g(t), is given by 2

I. INTRODUCTION The tracking performance of a RAKE receiver, one of the prominent low-complexity receivers, depends heavily on the detection of the multipath delays and the channel estimation. However, in closely spaced multipath environments, a RAKE receiver in conjunction with conventional early-latetiming error detector (TED) without adjacent multipath interference cancellation suffers severe performance degradation as addressed in [2] and [3]. Fock et al [1] proposed a scheme for channel tracking in closely spaced multipath environment for a single system with a single transmit antenna, and demonstrated improvements in performance by means of interference cancellation. The popularity of STBC [4] has grown leaps and bounds in a short span of time prompting its inclusion in 3GPP specifications [5, pp. 16-17]. The STBC provides a spacetime diversity gain with a simple processing. The system operation with the STBC may require synchronization at a significantly reduced Ec/N0 because of the expected diversity gain. For proper performance of the STBC scheme, PN code

∞

N c −1

s( t) = ∑ ∑ aqn ∑ dnN c +ν g( t − nT − νTc ) q =1 n = 0

ν =0

(1)

where q is the transmit antenna index, d nNc +ν is a complex PN sequence with spreading sequence period longer than symbol period, T denotes the symbol duration, Tc is the chip duration, and anq is a combination of complex valued data a n,data (spread with orthogonal variable spreading factor (OVSF) sequence wn , also known as Walsh code) and pilot pattern P-CPICH anq, pilot :

a qn = a n, data wn + a nq, pilot

(2)

for the q-th transmit antenna. Note that data symbol duration and pilot symbol duration may not be the same. For simplicity of analysis we consider anq has the duration of pilot symbol. The data OVSF sequence wn is orthogonal to the pilot symbols . Hence, ignoring the data term we denote a qn, pilot as anq . The 3GPP specification for transmit diversity scheme [5] recommends 37 repetitions of basic pattern {A A A A} for the first antenna and {A -A -A A} for the second

antenna, plus a spare pattern {A A} and {A -A} at the end of a frame, for the first and second antenna respectively, in one frame of P-CPICH. Here A=1+j and the spreading factor of the pilot symbol A is fixed to 256, which may be larger than that for the data symbol. 1  A = A, A, A, AL for q = 1 anq = anq, pilot =  n2 . (3) An = A,− A,− A, AL for q = 2 The key idea of this paper is to exploit this pilot pattern for the channel estimation and timing tracking. From the pattern we observe that the identification of the basic pattern should be performed for the duration of at least two symbols. The channel from the 1st transmit antenna element to the receive antenna can be estimated by summing the two received symbols in a block of two (even and odd) symbol intervals since the signal carried by the 2nd transmit antenna will be cancelled when the fading coefficients are almost unchanged during the two consecutive symbol intervals . Similarly, the channel from the 2nd transmit antenna element to the receive antenna can be estimated by subtracting the second symbol from the 1st symbol in a block of the two symbols. The channel is modeled with Np independent paths for each transmit antenna. Each of these paths is characterized by its delay τi and fading coefficient ciq N p −1

h q (τ ) = ∑ ciq (t )δ (τ − τ i )

(4)

i =0

for two transmit antennas where δ(t) is the Dirac delta function. In practice, delay τ iq is almost independent of q since the spacing between transmit antennas is negligible , compared to the wave traveling distance. White Gaussian noise m(t) is added to the signal at the receiver and hence the received signal can be written as 2

N p −1

q =1

i =0

r (t ) = ∑

q ∑ ci (t )

(5) ∞ q Nc − 1 ∑ an ∑ d nN + ν g (t − nT − νTc − τ i ) + m( t ) ⋅ c n=0 ν =0 The signal is then filtered with a filter matched to the pulse shaping filter g(t) used in the transmitter. The signal at the output of the pulse matched filter is given by 2

z (t ) = r ( t) * g(Tc − t ) = ∑

q =1

N c −1

N p −1

∞

∑ ci ( t) ∑ anq i =0 n =0 q

(6)

~ ( t) ∑ dnN c +ν Rg (t − nT − νTc − τ i ) + m

ν =0

~ ( t) is the new noise where * denotes the convolution and m term representing the filtered version of the noise and the interference due to the other users. Multiple access interference is modeled as an additive white Gaussian noise (AWGN). The combined transmit and receive filter pulse form is denoted by Rg(t), the effective pulse form at the output of the pulse matched filter, can be written as

+∞

Rg (t ) = ∫ g ∗ (τ ) g( t + τ ) dτ .

(7)

−∞

The matched filter output signal is used as input for the RAKE receiver (see Fig. 1 which shows one finger). The RAKE receiver operates on samples from the matched filter output taken at rate 2/Tc. The two samples taken in a chip interval are alternatively demultiplexed to two processors . One is for the on-time demodulation and the other sample is for the early-late timing tracking processor. In each of the M finger of the RAKE, the sample sequence zl,n ,k is processed by means of timing compensator at rate 1/Tc to compensate for the delay t l where l denotes the desired path index, n is the symbol index, and k is the sampling index. The signal after the sample timing compensation can be expressed as 2

N c −1

z l , n, k = ∑ anqclq, n ∑ d nN c +ν R g (kTc − nT − νTc + τˆl − τ l ) q =1

ν =0

2

N p −1

N c −1

q =1

i = 0, i≠ l

ν =0

+ ∑ anq ∑ ciq, n ∑ dnN c +ν Rg ( kTc − nT − νTc + τˆl − τ i ) ~ +m l, n, k . (8) After pulse matched filtering and compensation of the path delay using the estimate τˆl , only one transmitted symbol a nq contributes to the resulting output from path l if perfect timing (τˆl = τ l ) is assumed. The fading coefficients

clq (t ) are assumed to be constant over a symbol interval and are thus replaced by clq, n . Furthermore, for transmit diversity scheme, we consider the even numbered symbol interval to have the same fading coefficient as the subsequent odd numbered symbol interval, i.e., clq, n = clq, n +1 , n=even. The signal zl,n,k is then multiplied with the complex conjugate of the PN sequence d k* , summed over one symbol interval, and normalized by Nc. Hence 2 1 ( n+1) N c −1 ∗ 1 2 q q q yl , n = ∑ d k zl , n, k = ∑ an cl , n + ∑ an N c k = nNc N c q=1 q =1 (9) ( q ∗ ˆ ∑ ci, n dk d nNc +ν Rg ( kTc − nT − νTc − τ l + τ i ) + ml, n, k ⋅ i , k ,ν

As will be seen from (10), a RAKE receiver needs estimate values for the path delays τ l and the fading coefficients clq to be functional. Since yl,n contains information from both the first and second antenna, it needs to be decoupled. Recall that anq contains orthogonal pilot pattern either [{A A}, {A -A}] or [{A A}, {-A A}] in the odd and even numbered symbol intervals , respectively. The other information of anq is data, but due to the properties of OVSF, data portion of anq become zero. To exploit the orthogonal properties, we define two linear combiners as

y1l , n = 12 ( yl , n + yl , n +1) = B1nc1l , n +

other paths on the desired path timing error signal xlq, n . The

B1n ) (10) ∑ c1i, n Rg ( kTc − nT − νTc − τˆl + τ i ) + m1l, n N c i, k , v i≠ l

yl2,n +

= ( yl , n − yl , n+1 ) = Bn2cl2,n 1 2

Bn2 ) (11) ∑ ci2,n Rg ( kTc − nT − νTc − τˆl + τ i ) + ml2, n N c i , k ,ν

compensated timing error signal can be written as N p −1    q  q q∗ ~ ˆ xl ,n = Re  xl ,n − cl , n cˆ iq, n S (τˆ i − τˆ l ) . (16)   i =0 , i ≠ l Finally, the total timing error detector output for the l-th finger is given by

∑

2 q ~ xl ,n = ∑ ~xl ,n .

i ≠l

q =1

where n is an even integer, superscripts denote the transmit antenna index, and

B1n = ( A1n + A1n+1 ) / 2

B. Channel estimation with interference cancellation .

(12)

Bn2 = ( An2 − An2+1 ) / 2 The second terms of (10) and (11) represent the adjacent multipath interferences. A. Timing tracking with interference cancellation Following (10) and (11), the output of the conventional early-late-TED is given by

x lq, n = x lq ( nT ) q∗

= Bnq* cˆ l, n

1 Nc

( n +1) N c −1

∑ {z(kT

c

+ T c / 2 + τˆl )

(13)

k = nN c

− z (kTc − T c / 2 + τˆl )} d k∗ where cˆlq, n denotes the estimate of the l-th channel from the q-th antenna at the n-th symbol interval, q=1,2, and superscript * is complex conjugate. The output of the early-late TED, conditioned on the set of fading coefficients c q , becomes strongly influenced by the additional multipaths, and its conditional average can be written as 2  N P −1   E xlq, n | c q = E  Bnq  Re clq, ∗n ∑ ciq, nS (τ i − τˆl )    i =0  

[

(17)

]

2 2    = E  Bnq  Re  clq, n S (τ l − τˆl )  (14)     N P −1 2    + E  Bnq  Re  clq, ∗n ∑ ciq, n S (τ i − τˆl )    i = 0 , i ≠ l   where S (τ − τˆ) is the open-loop S-curve depending on the residual timing error τ − τˆ which can be written as T   T  S (τ i − τˆl ) = R g  c + τˆl − τ i  − R g  − c + τˆl − τ i  . (15)  2   2      As seen above, the TED output is influenced by interference from the adjacent paths. From (14), it can be seen that by eliminating the second term, we can construct a signal without interference. Since we can have estimates cˆ and τˆ from the other fingers for the second term in (14), we can compute compensation terms that cancel the effect of the

Since the performance of the tracking algorithm is dependent on the quality of channel estimation, we provide channel estimation scheme for transmit diversity. From (10) and (11) we can extract channel coefficient information since pilot symbols An and An+1 are known. Under assumption that interference (the second terms in (14)) contribution is negligible, channel can be estimated cˆlq, n = Bnq∗ ylq, n , n = even (18) cˆlq, n +1 = cˆlq, n . Expression (18) may be sufficient if τ =1.5Tc , but the interference terms in (10) and (11) are getting bigger as t decreases, e.g., τ < Tc . Note that the finger with a weaker path will suffer more, compared to the stronger one. Thus, to increase the quality of the channel estimates, (18) is modified as *

N P −1

cˆlq, n = Bnq ylq, n − ∑ cˆiq, n Rg (τˆi − τˆl ) . i = 0, i≠ l

(19)

III. SIMULATION RESULTS A high speed data transmission with a chip rate of 3.84 Mchips/s for indoor environment is considered. Multiple access data consist of pilot pattern (P-CPICH) and data from 4 other active users, scrambled by OVSF. Each antenna element in the transmit diversity scheme transmits 50% of total power to make fair comparison with system without transmit diversity. Jakes’ fading channel model is used with 4 independent paths. We use the two strongest paths with the average power of the second path 3 dB lesser than that of the first path. It is assumed that all antennas have the same path delay for a given path. We assume the speed of the mobile to be 20 km/h. Tracking loop uses a 2nd order loop filter with normalized loop bandwidth Bl Tc = 0.457. Based on the above simulation set-up, we observe the following results: Fig. 2(a) and 2(b) exhibit the output of timing error detector (TED) for the first path by using the channel coefficient values from the channel estimator. The two strongest paths have a path delay t = Tc. The former has no interference cancellation whereas the latter employs interference cancellation. It can be seen that the system

using interference cancellation performs nearly as the one with perfect channel estimates as shown in Fig. 2(c) wherein the TED output is centered on zero. It is observed that the low frequency component of the TED output is not suppressed as shown in Fig. 2(a) when interference cancellation is not employed. Channel estimation scheme for transmit diversity system is also simulated as shown in Figs. 3(a) and 3(b). The “true channel 1” and “true channel 2” in the figure legends denote the perfect channels from transmit antenna element 1 and 2 respectively. To demonstrate the effects of adjacent path interference, we chose t = 0.5Tc. It is observed that the system without interference cancellation in Fig. 3(a) cannot estimate the true channel values well enough while the one with interference cancellation almost follows the true values . From simulation we find that for τ ≥ Tc , the effect of the adjacent paths is negligible. Hence we refrain from discussion of such results. Performance comparison of the transmit diversity system with the system without transmit diversity (a single antenna case), is presented in terms of RMS of TED output in Figs. 4 for a weaker path. The RMS is given by σ = E[( ~ x − E[ ~ x ]) 2 ] . (20) It is observed that the system with interference cancellation reduces the RMS of TED significantly, compared to the system without interference cancellation. Also, for system with transmit diversity, there is further improvement over the system without transmit diversity at low Ec/N0 values, e.g., about 2 dB improvement at RMS = 0.1. For high Ec/N0 system without transmit diversity performs as good as the transmit diversity one when interference cancellation is used. However, the system without transmit diversity is worse than the one with transmit diversity even at a high Ec/N0 when interference cancellation is not used. For fair comparison, the system with single transmit antenna, i.e., no transmit diversity, als o uses P-CPICH for channel estimation, and the same parameters for the loop filter. IV. CONCLUSIONS It is observed from the simulation that the performance of the system with transmit antenna diversity is enhanced by employing the interference cancellation of [1]. The ability of the system with transmit antenna diversity to estimate the channel perfectly, plays a very crucial role in decoding. It is clear that the system with interference cancellation is capable of estimating the channel almost perfectly thereby increasing the reliability of the system. The RMS of timing error detection output also shows that systems with

interference cancellation perform better than one without interference cancellation. For system with interference cancellation, transmit diversity improves RMS further for low Ec/N0 , e.g., about 2 dB at RMS = 0.11, whereas for high Ec/N0 the one without transmit diversity performs as good as transmit diversity.

REFERENCES [1] G. Fock, J. Baltersee, P. Schulz-Rittich, and H. Meyr, “Channel Tracking for Rake Receivers in Closely Spaced Multipath Environments”, IEEE JSAC, Vol. 19, No. 12, pp. 2420-2431, Dec 2001. [2] Wern-Ho Sheen and Gordon L. Stuber, "Effects of Multipath Fading on Delay-Locked Loops for Spread Spectrum System," IEEE Transaction on Comm., Vol. 42, No 2/3/4, Feb./Mar./Apr. pp. 1947-1956, 1994. [3] Essam Sourour, G. Bottomley, and R. Ramesh, "Delay Tracking for Direct Sequence Spread Spectrum Systems in Multipath Fading Channels," IEEE 49th Vehicular Technology Conference, pp. 422-426, 1999. [4] S. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communication,” IEEE JSAC, vol. 16, pp. 1451-1458, Oct. 1998. [5] Third Generation Partnership Project, TS25.211, vol. 3.6.0, “Physical Channel and Mapping of Transport Channel onto Physical Channel (FDD),” March 2001. [6] H. Meyr, M. Moeneclacey, and S. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation and Signal Processing. New York: Wiley, 1998. [7] A. J. Viterbi, CDMA Principles of Spread Spectrum Communication, Addison Wesley, New York, 1995.

d*

B1n* To data decoding 1 Nc

y

yl ,n + y l ,n +1

∑

yl ,n − y l ,n +1

Nc

Channel estimator

1 l,n

+

y l2,n

+

B

N p −1

∑ cˆ

i = 0 , i≠ l

2 l ,n

cˆ

-

Linear combiner Timing Compensator

zl ,n ,k

cˆ1l ,n

-

N p −1

∑ cˆ

2 i, n

2* n

1 Nc

∑ Nc

R g (τˆi − τˆl )

}

R g (τˆi −τˆl )

}

i = 0 , i≠ l

N p −1

B1n* cˆ1l *,n

τˆl

1 i, n

yl ,n + yl ,n +1

-

yl ,n − yl ,n +1

+

cˆl1*,n -

∑ cˆ

1 i, n

i= 0 , i ≠ l

~ xl1,n

x1l ,n +

~ xl ,n Re{.}

1 Nc

Z-1

∑ Nc

yl ,n + y l ,n +1

-

yl ,n − y l ,n +1

+

x 2l,n +

~ xl2,n

-

N p −1

cˆl2,*n

B 2n* cˆ 2l,*n

Linear combiner

∑ cˆ

2 i, n

}

S (τˆi − τˆl )

Loop Filter & NCO

Channel & timing error estimates from itself and other RAKE finger

τˆl

}

S (τˆi − τˆl )

i =0 , i ≠l

. . .

. . .

Fig. 1. A proposed RAKE receiver and PN code tracking loop with transmit diversity, channel estimation, and interference cancellation. TED output, x-tilda

0.80 0.40

1.0

0.00

0.9

-0.40

0.8

true channel 1 true channel 2 estimated channel 1 w/ i.c. estimated channel 2 w/ i.c. -0.80

0.7 50

100

150

200

250

300

350

normalized power

0

update index (2N )

(a) TED output, x-tilda

0.80 0.40

0.6 0.5 q

0.4 0.3

0.00

0.2 -0.40

0.1 -0.80 0

50

100

150

200

250

300

350

0.0

update index (2N )

0

64

128

192 256 update index (2N)

(b)

384

(b)

0.80 TED output, x-tilda

320

Fig. 3. Channel estimation of the 3-dB weaker path, i.e., the 2nd path: (a) without interference cancellation, and (b) with interference cancellation.

0.40 0.00 -0.40 -0.80 0

50

100

150

200

250

300

350

update index (2N )

1

(c)

Fig. 2. TED output: (a) conventional, (b) with interference cancellation, and (c) with interference cancellation and with true channel values. 1.0

true channel 2 estimated channel 1 w/o i.c.

0.8

TED RMS

true channel 1

0.9

0.1

estimated channel 2 w/o i.c.

normalized power

0.7 0.6

transmit diversity,w/ i.c. transmit diversity, w/o i.c.

0.5

w/o transmit diversity,w/ i.c. w/o transmit diversity, w/o i.c.

q

0.4

0.01 -20

0.3

-16

-12

-8

-4

0

4

8

Ec/No (dB)

0.2

Fig. 4. RMS of TED output for the 3-dB weaker path, i.e., the 2nd path.

0.1 0.0 0

64

128

192 256 update index (2N)

(a)

320

384