Time Synchronization Algorithm for 802.11a Wireless Standard System Using Channel Estimate Based on CSMA/CA Mechanism Cong Luong Nguyen and Anissa Mokraoui
Pierre Duhamel
Nguyen Linh-Trung
L2TI, Institut Galil´ee LSS/CNRS, SUPELEC Vietnam National University Universit´e Paris 13, Sorbonne Paris Cit´e 3 rue Joliot Curie University of Engineering and Technology 99 Avenue J.-B Cl´ement F91192 Gif sur Yvette, France 144 Xuan Thuy, Cau Giay F93430 Villetaneuse, France Email:
[email protected] Hanoi, Vietnam Email:
[email protected] Email:
[email protected] [email protected]
Abstract—The wireless system performance is seriously degraded in the presence of multipath fading. Hence the need to develop solutions to enable the receiver to synchronize over the transmitter before processing the received data. A novel time synchronization algorithm for DATA physical packet in IEEE 802.11a OFDM (Orthogonal Frequency Division Multiplexing) wireless standard network under multipath channel is proposed. Our algorithm takes advantage the channel estimate performed from the RTS (Request To Send) control frame reception when the CSMA/CA (Carrier Sense Multiple Access with Collision Avoidance) mechanism is triggered. The channel estimate is then used as an additional information for the time synchronization process of the DATA packet. Simulation results show that the proposed algorithm improves the time synchronization performance compared to existing algorithms. Index Terms—IEEE 802.11a; OFDM; Channel estimation; Time synchronization; RTS control frame; CSMA/CA.
I. I NTRODUCTION IEEE 802.11a standard supports a high-speed data transmission at rate up to 54Mbps and employs Orthogonal Frequency Division Multiplexing (OFDM) as transmission technique [1]. Before demodulating a physical packet at the receiver, time and frequency synchronization are required to eliminate eventual inter-symbol interference (ISI) and inter-carrier interference (ICI). In [2], the authors presented a blind synchronization algorithm exploiting the Cyclic Prefix (CP) to jointly estimate the symbol timing and frequency offset in OFDM systems. The receiver uses the Auto-Correlation Function (ACF) between the CP and its copy at the end of OFDM symbol to estimate the symbol timing and the frequency offset. The method achieves a good spectral efficiency. However, the performance is low because usually the CP has short length and furthermore it is overlapped by the previous OFDM symbols due to multipath dispersion. To improve the synchronization performance, in [3], the authors proposed a training sequence composed of
two symbols. The first symbol consists of two identical halves. Based on these two halves, the ACF is applied on the received signal. The maximum absolute value of this function allows the receiver to estimate the symbol timing while its argument helps to estimate the frequency offset. The method is well exploited in a single path environment but unsatisfied in a multipath fading channel because there is an overlap between the consecutive two halves. In order to solve this problem, in [4], authors proposed to insert a Guard Interval (GI) between two symbols of the training sequence. Based on the structure of IEEE 802.11a physical packet, the proposed time synchronization algorithm in [5] proceeds in two main steps: the Coarse Time Synchronization (CTS) step followed by the Fine Time Synchronization (FTS) step to estimate the remaining time offset. The CTS relies on the Cross-Correlation Function (CCF) using the Short Training Field (STF) as specified by the standard. In addition to the training sequence commonly used, the CTS proposed to exploit the SIGNAL field since its unknown parts are predictable when the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) mechanism is active. To improve the performance of the CTS step, a joint FTS and channel estimation based on the Minimum-Mean SquaredError (MMSE) criterion is developed. In [6], the authors considered the joint FTS and channel estimation performing the MAP criterion instead of the MMSE criterion. The performance in terms of channel estimation and Probability of Synchronization Failure (PSF) is improved compared to [5]. Inspired of the advantages of exploiting the CSMA/CA mechanism in [5] and the MAP criterion for time synchronization in [6], we propose to use the channel information obtained from the Request To Send (RTS) control frame reception when the CSMA/CA mechanism is triggered, for DATA packet synchronization. This paper is organized as follows. Section II briefly introduces the IEEE 802.11a wireless communication system.
Section III reviews the time synchronization algorithms on which modifications are made to improve their performance. Section IV presents the proposed time synchronization approach where the channel estimation is firstly performed using the information contained in the RTS control frame when the CSMA/CA mechanism is triggered. Simulation results are shown and discussed in section V. Finally, section VI concludes the paper. II. W IRELESS COMMUNICATION SYSTEM The IEEE 802.11a physical packet is composed of three fields: a PREAMBLE training field, a SIGNAL field and a DATA field (see Fig. 1). The PREAMBLE training field is used to enable the receiving station to synchronize with respect to the transmitting station. This field is composed of (i) ten Short Training Field (STF) repetitions usually used for Automation Gain Control (AGC), diversity selection, signal detect and Coarse Frequency Synchronization (CFS); and (ii) two Long Training Field (LTF) repetitions dedicated to the channel estimation and fine frequency synchronization of the receiving station. The physical packet is modulated according to the IEEE 802.11a wireless communication system summarized by the block diagram in Fig. 2. An Inverse Fast Fourier Transform (IFFT) is applied to the symbols X(k) (with 0 ≤ k ≤ N − 1 and N the number of IFFT points). The samples x(n) are then shaped using a specific window. Each OFDM symbol is preceded by a Cyclic Prefix (CP). The sequence x(n) is then transmitted via a multipath fading channel described by a Finite Impulse Response (FIR) filter of length L. In this paper, we only consider the time synchronization problem, assuming a perfect knowledge of the frequency
offset. The received discrete baseband signal r∆ (n) free from frequency offset is then given as follows: r∆ (n) =
L−1 X
h(i)x(n − i − θ) + g(n),
(1)
i=0
where h(i) denotes the slowly time-varying discrete PL−1 time complex Channel Impulse Response (CIR) with i=0 E{ |h(i)|2 } = 1 (E is the expectation operator), L is the number of channel taps and g(n) is the complex additive white Gaussian noise. In order to correctly demodulate the received signal r∆ (n), the symbol timing θ must be first estimated by the receiver. This is the objective of the next section. III. T IME SYNCHRONIZATION ALGORITHM PREVIOUSLY PROPOSED
This section reviews the time synchronization algorithms developed in [5] and [6]. These algorithms are based on two main stages (see Fig. 3): the Coarse Time Synchronization (CTS) stage followed by the Fine Time Synchronization (FTS) stage which is related on Joint Time Synchronization and Channel Estimation (JTS-CE). A. First stage: Coarse time synchronization The symbol timing of equation (1) is first estimated by θˆ = arg max |Z(θ)|,
(2)
θ
where Z(θ) is the Cross-Correlation Function (CCF) expressed by LX STF −1 Z(θ) = c∗ (n)r∆ (n + θ), (3) n=0
with c(n) the known bit stream constructed from ten STF repetitions (see Fig.1) and LSTF the number of c(n) samples. The signal with a remaining time offset is then given by
PREAMBLE of 802.11a physical frame Short training field (STF) STF 1
Long training field (LTF)
STF STF STF STF 8 9 10 7
θ ∆ θ S θ
LTF2
LTF1
GI2
GI
SIGNAL
DATA
rs (n) =
∆θS Fig. 1. Interleaving
FEC Encoder
Scrambler
DATA bits
X(k)
IFFT 64-Points
Insert GI and Window
x(n)
DAC and Up-RF x(t)
PREAMBLE symbols
Synchronization block Estimated Channel
X(k) FFT 64-Points
Fine time synchroni -zaion
g(t)
c(n)
cs (n )
Estimated Channel
Frequency synchronization
Deinterleaving
FEC Decoder
Descramber
DATA bits
r(n) AGC, Signal detect
r(t) ADC And Down-RF
r∆ ( n )
rs ( n ) STF
rf (n ) SIGNAL
θ Coarse time sync.
SIGNAL bits
Fig. 2.
(4)
ˆ To estimate ∆θs , the authors of [5] and where ∆θs = θ − θ. [6] proposed to exploit the 802.11a SIGNAL field as an additional training sequence at the receiver when the CSMA/CA mechanism is triggered. After predicting its unknown parts, the SIGNAL field is then known both at the transmitter
Channel multipath
SIGNAL bits
BPSK Demapping
h(i)x(n − i − ∆θs ) + g(n),
i=0
IEEE 802.11a physical packet
BPSK Mapping
L−1 X
Wireless communication system using OFDM
Fig. 3.
MMSE/MAP
∆ θ s
r (n)
∆ θ Fine time sync.
Previous time synchronization algorithms ([5], [6])
and receiver. The remaining time offset is then estimated as follows: ∆θbs = arg max |Z(∆θs(k) )|, (5) (k)
∆θs ∈Θ
m
(k)
where Θ = {∆θs |k = −K, . . . , K} with K a predefined (k) integer value and Z(∆θs ) the CCF given by Z(∆θs(k) )
=
LX SIG −1
c∗s (n)rs (n
+
∆θs(k) ),
(6)
with cs (n) the known bit stream corresponding to the SIGNAL field and LSIG the CP length added to the SIGNAL length. B. Second stage: Joint time synchronization and channel estimation After the CTS stage (in section III-A), the received signal is written as follows: L−1 X
k
∆θk ∈Λ
where β is a given threshold. Therefore, the set Λ becomes Γ 0
Γ = {ω0 , . . . , ωM 0 ; M ≤ 2M }.
n=0
rf (n) =
b ∆θ obtained from (11) or Among 2M + 1 estimates of h m (9) (after FFT operation), the optimal time offset is one that satisfies the following condition: ˆ ∆θ (0)| > β max |h ˆ ∆θ (0)|, |h (12)
h(i)x(n − i − ∆θ) + g(n),
(7)
i=0
with ∆θ = ∆θs − ∆θbs the remaining time offset. For convenience reasons, equation (7) is rewritten in a matrix form. The received vector rf of size N × 1 is then given as follows: rf = Gh∆θ + g,
(8)
where G = FH XF with F being the N × N FFT matrix and X the N × N diagonal matrix whose diagonal elements are H the known LTF symbols. Notation (·) denotes the conjugate transpose operator. g is the noise vector of size N × 1, h∆θ is the CIR vector of size N ×1 following a Gaussian distribution with a mean vector µh . Define a set Λ = {−∆θM , .., ∆θM } that contains 2M + 1 possible time offset values. In [5], for a given value ∆θm ∈ Λ, the CIR in the frequency-domain (i.e. H∆θm ) is estimated according to the MMSE criterion as follows: ˆ ∆θ = RH (RH + H m
σg2 −1 e ∆θ , I) H m σx2
(9)
e ∆θ is the Least-Square (LS) where the N × 1 vector H m channel estimate, σx2 and σg2 are, respectively, the variance of the transmitted signal and the noise. I is the identity matrix. RH = FRh FH is the frequency-domain correlation matrix of the true channel with Rh = E{hhH } which is estimated according to the LS approximation as follows: ˜ ∆θ h ˜H Rh = E{hhH } ≈ E{h m ∆θm }.
b ∆θ = (GH G + σ 2 R−1 )−1 (GH rf + σ 2 R−1 µh ). h g h g h m
Finally, the remaining time offset is estimated by ∆θb = arg max{Z(ωm0 )},
(11)
(14)
ωm0
where Z(ωm0 ) is the energy associated to the estimated CIR ˆ ω 0 and is given by h m Z(ω
m0
)=
L−1 X
ˆ ω 0 (n)|2 . |h m
(15)
n=0
IV. P ROPOSED TIME SYNCHRONIZATION ALGORITHM To improve the performance of the previous time synchronization algorithms, we propose to modify mainly the coarse time synchronization stage. The proposed algorithm is summarized in Fig. 4 and is described below. A. First stage: New coarse time synchronization We start from the following observation. To deduce an accurate symbol timing, the comparison between the training sequence c(n) should be done with its nearest equivalent i.e. the transmitted signal x(n). Therefore instead of calculating the cross-correlation between the training sequence c(n) and the received signal r∆ (n), as explained in section III-A (see (3)), we propose to replace the received signal by the transmitted signal x(n) which is however considered as an unknown information at the receiver. Faced with this problem we developed an estimation strategy related on the RTS control frame when the CSMA/CA medium reservation procedure is triggered. 1) CSMA/CA medium reservation procedure: If any transmitting station in the same wireless network wishes to send data, it initiates the process by sending a RTS control frame to ask the receiving station if it is free [7]. The receiver, if it is free, replies with a Clear To Send (CTS) frame to the transmitter and also informs other stations in the same network of its unavailability to receive information coming from other stations during a specified period of time. The transmitting station then sends the DATA frame to the receiver.
(10)
ˆ ∆θ , is then transformed into the time The channel estimate H m ˆ ∆θ . domain using a FFT to obtain the time-domain estimate h m In [6], for a given value ∆θm ∈ Λ, the authors proposed to estimate the channel according to the MAP criterion rather than the MMSE criterion which is expressed by
(13)
h ( n ) c ( n )
r∆ ( n )
STF
rs ( n )
θ Coarse time sync.
Fig. 4.
h ( n )
cs (n )
SIGNAL
rf (n )
r (n) MMSE/MAP
∆ θ
∆ θ s Fine time sync.
Proposed time synchronization algorithm
2) Channel estimation based on RTS control frame: Note that the PREAMBLE field of RTS, CTS and DATA frames is exactly the same (see Fig.1). So we propose to exploit the LTF field of the RTS PREAMBLE to estimate the channel thus allowing an approximation of the unknown transmitted signal (i.e. x(n)) as introduced at the beginning of this section. To do so, the RTS frame is assumed to be correctly demodulated (i.e. no synchronization problem) and the channel environment is considered slowly time-varying and not variable for at least the transmission duration between the RTS and DATA frames. The channel is estimated according to the MAP criterion using equation (11) in which the received signal rf is replaced by the synchronized RTS signal r: r = Gh + g.
(16)
ˆ 3) Transmitted signal estimate: Let H(k) (with 0 ≤ k ≤ N − 1) be the frequency-domain channel estimate exploiting, as explained above, the RTS control frame; and r∆ (n) (see equation (1)) be the received signal corresponding to the DATA frame in the time domain. The estimate of the transmitted DATA signal in the time domain is given by x ˆ(n) =
N −1 n 1 X ˆ X(k)ej2πk N , N i=0
(17)
with ˆ ˆ X(k) = R∆ (k)/H(k),
(18)
where R∆ (k) is the received DATA signal in the frequency domain. 4) Symbol timing estimate: The symbol timing estimate is expressed by θˆ = arg max{|Z(θ)|}, θ
(19)
where the cross-correlation Z(θ) is performed between the known bitstream c(n) (constructed from ten STF repetitions) and the transmitted signal x ˆ(n) obtained in section IV-A3: Z(θ) =
LX STF −1
c∗ (n)ˆ x(n + θ),
(20)
n=0
where LSTF is the number of c(n) samples. As in section III-A, the signal with a remaining time offset ∆θs is given by equation (4). To estimate ∆θs we also exploit the 802.11a SIGNAL field as an additional training sequence at the receiver since the CSMA/CA mechanism is assumed to be triggered. Indeed after predicting its unknown parts, the SIGNAL field is known both at the transmitter and receiver. The remaining time offset is then estimated according to equations (5) and (6).
B. Second stage: Joint time synchronization and channel estimation The received signal with a remaining time offset is given by r(n) =
L−1 X
h(i)x(n − i − ∆θ) + g(n),
(21)
i=0
ˆ with ∆θ = θ − θ. To estimate ∆θ, the joint time synchronization and channel estimation, described in section III-B, is performed with a slight modification. Indeed, to calculate the time-domain correlation matrix of the true channel Rh (i.e. equation (10)), the MAP channel estimate (provided in section IV-A2) is performed instead of the LS approximation as follows: ˆh ˆH } Rh = E{hhH } ≈ E{h
(22)
V. S IMULATION R ESULTS The performance of the proposed time synchronization algorithm is discussed in this section. Table I lists the simulation parameters as specified by the IEEE 802.11a standard [1]. As shown in the table, COST207-RA is used for multipath channel following the Rice model with a Line-Of-Sight (LOS). To simulate a realistic situation, frequency offset has been introduced between the transmitter and the receiver. Two frequency offsets are considered: 0.32∆Fc and 0.5∆Fc where the sub-carrier spacing ∆Fc is equal to 0.3125 MHz. Since we only consider the time synchronization problem, the frequency offset is perfectly compensated by multiplying the received signal (after coarse time synchronization stage) with e−j2π² where ² is the true normalized frequency offset given by ² = ∆Fc Ts with Ts the sampling rate (see Table I). To evaluate the performance of the proposed time synchronization algorithm, Fig. 5 (with a frequency offset equal to 0.32∆F ) and Fig. 6 (with a frequency offset equal to 0.5∆F ) provide the probability of synchronization failure of the following time synchronization algorithms: i) Algorithm 1 (MMSE-SIGNAL) [5]: This algorithm has been described in section III where the coarse time synchronization exploits an additional training sequence (i.e. SIGNAL field) and the fine time synchronization (second stage of the algorithm) is based on the MMSE criterion. ii) Algorithm 2 (MAP-SIGNAL) [6]: In this algorithm, the MMSE criterion implemented in algorithm 1 is replaced by the MAP criterion as described in section III. iii) Algorithm 3 (CE-MMSE-SIGNAL): This is the proposed algorithm presented in section IV where the fine time synchronization is based on the MMSE criterion. iv) Algorithm 4 (CE-MAP-SIGNAL): This is also the proposed algorithm developed in section IV where the fine time synchronization exploits the MAP criterion. The curves of Fig. 5 and Fig. 6 show that the probabilities of synchronization failure of the proposed time synchronization
TABLE I S IMULATION PARAMETERS Values 20 MHz 50 ns 52 64 0.3125 MHz Rice with COST207-RA (0, 200, 400, 600) ns (0, -2, -10, -20) dB 6 Mbps 0.7 160 80 30 80
algorithms (in solid lines) are much lower than those of the previous time synchronization algorithms (in dash lines). Indeed for a given SNR=15 dB and a frequency offset equal to 0.5∆F (see Fig. 6), the PSF of algorithms 1, 2, 3 and 4 are respectively: PSF(MMSE-SIGNAL)=4.4 × 10−2 , PSF(MAPSIGNAL)=3.4 × 10−2 , PSF(CE-MMSE-SIGNAL)=5.4 × 10−5 and PSF(CE-MAP-SIGNAL)=4.4 × 10−5 . It is clear that our method has significantly improved the time synchronization performance.
Probability of Synchronization Failure (PSF)
Parameters Bandwidth (B) Sampling time (Ts ) Number of subcarriers (Nc ) Number of points FFT/IFFT Subcarrier spacing (∆F ) Channel model Channel time delay Power of channel paths (Pc ) Data rate Threshold (β) LSTF LSIG M K
0
10
−1
10
−2
10
−3
10
−4
10
−5
10
0
MMSE−SIGNAL CE−MMSE−SIGNAL MAP−SIGNAL CE−MAP−SIGNAL 5
10 SNR (dB)
15
20
Fig. 6. Probability of synchronization failure performance (with a frequency offset = 0.5∆Fc )
synchronization process of the DATA packet. Simulation results show that the proposed algorithm improves the time synchronization performance compared to existing algorithms.
0
Probability of Synchronization Failure (PSF)
10
MMSE−SIGNAL CE−MMSE−SIGNAL MAP−SIGNAL CE−MAP−SIGNAL
−1
10
−2
10
−3
10
−4
10
0
5
10 SNR (dB)
15
20
Fig. 5. Probability of synchronization failure performance (with a frequency offset = 0.32∆Fc )
VI. C ONCLUSION This paper proposed a novel time synchronization algorithm for 802.11a standard wireless communication. The channel estimation is firstly performed using the information contained in the RTS control frame at the receiver when the CSMA/CA mechanism is triggered. The channel estimate is then exploited as an additional information for the time
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