ROBUST MOBILE WIMAX PREAMBLE DETECTION Ernest Seagraves, Christopher Berry, and Feng Qian Digital Receiver Technology, Inc. Germantown, MD
[email protected],
[email protected],
[email protected]
ABSTRACT Mobile WiMAX is a wireless protocol for broadband wireless access that utilizes TDD OFDMA. The WiMAX frame begins with a preamble symbol that establishes frame timing and initial symbol timing for the mobile. In a mobile, the preamble symbol detection is often accomplished by a delay correlation detector. Delay correlation detectors take advantage of the preamble symbols redundancy. Previous detection methods tend to focus on high SNR environments and when applied to Mobile WiMAX a small model mismatch exists. Mobile WiMAX is being deployed with frequency reuse factors of 1 or 3. The resulting RF environment often contains heavy noise and interference. In this paper a new detection metric is proposed that takes advantage of the redundancy in both the preamble and its cyclic prefix as well as compensates for the model mismatch. The proposed metric is shown to offer improved performance of timing estimates over existing techniques, specifically in multipath and low SNR environments. Simulation results are presented demonstrating an improvement of about 3 dB at low SNR.
lel orthogonal narrowband subcarriers. The subcarrier spacing Δf , is chosen such that the channel frequency response is approximately flat over Δf . This along with the orthogonality enables each subcarrier to be independently equalized with a single complex coefficient [3]. OFDM modulation is efficiently accomplished by use of the DFT(FFT). At the transmitter data is mapped into complex constellations, each complex constellation point X(k) is modulated onto a subcarrier by the IDFT N −1 1 x(n) = X(k)ej2πnk/N (1) N k=0
for n = 0, 1, ..., N − 1, with some subcarriers set to zero to establish a guard band. An OFDM symbol is the set of N points coming out of the IDFT, resulting in a low symbol rate. The reverse is implemented in the receiver. X(k) =
N −1
x(n)e−j2πnk/N
(2)
n=0
I. INTRODUCTION Mobile WiMAX, defined by the IEEE 802.16e-2005 standard [1] and the WiMAX Forum Mobile System Profile [2], is one of several new 3.5/4G wireless technologies based on OFDMA in the downlink. OFDMA is a variant of OFDM allowing multiple users to simultaneously access the link. OFDM is a more spectrally efficient modulation scheme than single carrier modulations. It has been applied to applications including wireline modems (ADSL), powerline modems, broadcast video (DVB), digital radio (DAB, DRM) wireless LAN (802.11a/n), military communications (WNW), and cellular/BWA (WiMAX, UMB, LTE). The main concept in OFDM is the use of paralc 2008 IEEE 978-1-4244-2677-5/08/$25.00
for k = 0, 1, ..., N − 1. The WiMAX frame is split into two subframes separated by guard periods T T G and RT G. The first subframe contains the downlink symbols Dn , the later subframe contains the uplink symbols Un , Figure 1. The downlink subframe begins with a Preamble symbol that has a special structure. The last section of the symbol is copied and inserted at the beginning of the symbol. This is called the cyclic prefix (CP). At the mobile station (MS) the CP allows the signal to be treated as circular after its removal. The received signal has been modified by the channel and additive noise. It also contains a carrier frequency offset due to reference oscillator error. The resulting
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5 msec Frame n-1
P r e a m b l e
D1
D2
Frame n
D3
...
Dp
T T G
length of the cyclic prefix. If this condition is not met, then ISI will be present and the performance limited. The Preamble’s time domain structure, shown in Figure 2. The Preamble symbol is composed of a
Frame n+1
U1
U2
...
Uq
R T G
Ng
N
CP
Preamble
vk,2(end)
vk,0
vk,1
vk,2
Fig. 2. Preamble Time Domain Symbol Structure DL Symbols
UL Symbols
Fig. 1. WiMAX Frame Structure
signal model is given by y =H·x+w
(3)
where x, and y are N × 1 vectors representing the transmitted and received; w is an N × 1 vector of samples of additive Gaussian noise; H is an N × N circulant matrix representing the channel response. In the frequency domain this becomes Y = HX + W , where H is a N × 1 channel response vector. When the MS first powers on or enters a new area it must first scan for a valid WiMAX basestation (BS). The first step of the synchronization process is to detect the preamble and estimate the coarse symbol timing in the presence of carrier frequency offset (CFO). The symbol timing and CFO can be estimated jointly or individually. The most practical approach is to decouple the estimates. The timing estimation has been studied by many authors [4]–[12]. This paper will build upon some of these ideas. The CFO estimation has been studied by several authors [6], [11], [13], [14]. The CFO is then compensated and the symbol is extracted prior to FFT processing. It will not be discussed further here because the detection techniques proposed here are immune to CFO. OFDM has been shown to be sensitive to symbol timing errors [15]. Symbol timing estimation is typically performed in two steps; a coarse estimate in the time domain, and a fine estimate in the frequency domain [4]. The coarse timing estimate allows removal of the CP prior to the DFT processing in the receiver. The course timing error should be much less than the
CP and 3 sections that are repetitions of the same waveform. The structure of the WiMAX Preamble has been exploited [10], [12], [16], but not optimally. These approaches do not take into account that dividing a symbol into a number of pieces that is relatively prime to the overall number of samples causes the three repetitions the be fractionally delayed. This fractional delay reduces the correlation peaks maximum value. Also existing OFDM synchronization techniques take advantage of either the CP redundancy or some portion of the preamble’s redundancy but not all. The focus of this paper is on the initial preamble detection and alignment to the preamble defined symbol and frame timing. In this paper we provide a more accurate model of the preamble that improves existing detectors performance. We also propose a new detection metric that fully utilizes the redundancy of the preamble combined with the redundancy of the cyclic prefix to provide improved detection sensitivity and lower timing estimation error while maintaining the same false alarm rate. In section II an overview of the existing approaches related to initial detection and coarse synchronization of OFDM is provided. The preamble structure is analyzed and the proposed detectors are described in section III. The performance of the proposed detector is compared to previous results via simulation in section IV. II. COARSE TIMING ESTIMATION There have been several approaches to coarse timing estimation. There are two basic distinctions between the various approaches. First is the property exploited. This includes the redundancy in the CP and the redundancy in the Preamble. A shortcoming of using the CP alone is that it is short by design, in Mobile WiMAX the CP length is N/8, so only small fraction
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of the signal information is utilized. This results in decreased detection sensitivity. Another drawback of using the CP alone is that it occurs every symbol. So frame timing cannot be determined. By utilizing the Preamble’s redundancy more of the signal’s energy can be utilized. The second distinction is the optimization criterion. Several types of optimization detection metrics have been developed: maximum correlation (MC) [7], maximum normalized correlation (MNC) [8], Schmidl and Cox maximum normalized correlation (SC) [5], maximum normalized correlation using a geometric mean (GM) [9], minimum mean squared error (MMSE) [17] [4], maximum likelihood (ML) [6] [11], and maximum normalized time reversed correlation (MTRC) [10] [12]. The first six are functions of the same statistics, the correlation at lags equal to the Preamble’s repetition period of the signal. The delayed correlation is the autocorrelation of the received waveform evaluated at a specific lag d Ryy (n, d) =
1 M
M −1
MM,L (n) =
M −1 1 |y(n + m)|2 M m=0
Here d represents the correlation lag, and is fixed. The value of the lag is determined by the repetition period of the signal. The delay correlate computational burden is minimized by using an iterative moving average implementation Ryy (n + 1, d) = Ryy (n, d) + y ∗ (n + d)y(n + d + M ) − y ∗ (n)y(n + M )
(4)
where N is the FFT size, Ng is the cyclic Prefix length, and M is the correlation integration length. The simplest detection metric is the un-normalized maximum correlation metric [7]. This approach is problematic for determining a threshold that will work well under a varied channel conditions. A normalized version of this idea was developed by Schmidl and Cox [5] |Ryy (n, L)|2 MSC (n) = (5) 2 (n, 0) Ryy
(6)
1 MM,L (n − k) Ng + 1 Ng
MM inn (n) =
(7)
k=0
At high SNR this has a clearly defined peak, Figure 4. Minn describes another metric that takes advantage of additional redundancy present in preambles that have 4, 8, and 16 repeated sections. In the next section it will be clear that this concept, with 3 sections, applies to WiMAX preambles. Applying Minn’s second metric for a preamble with 3 repeated sections the resulting metric is given by
y(n + m)y ∗ (n + m + d)
The power estimate is given by
2|Ryy (n, L)|2 (Ryy (n, 0) + Ryy (n + L, 0))2
Minn also added a length Ng + 1 smoothing filter to remove the plateau, reducing the variance of the timing estimates.
MM inn2 (n) =
m=0
Ryy (n, 0) =
Minn [8] modified the Schmidl metrics denominator to average all the signal samples used in the calculation of Ryy (n, d)
|Ryy (n, L) + Ryy (n + L, L)|2 (8) ( 12 Ryy (n, 0) + 12 Ryy (n + L, 0))2
where M = L = N3 . Another approach to normalize the metric uses the geometric mean of two delayed power estimates to normalize the metric [9], |Ryy (n, L)| MGM (n) = (9) Ryy (n, 0)Ryy (n + L, 0) The square root can be avoided by squaring the metric. This metric performs well at higher SNR. At low SNR the performance falls off. The minimum mean squared error (MMSE) criterion [4], [17], has been shown to be equivalent to the Minn metric. Maximum likelihood (ML) techniques based on the CP have been developed [6], [11]. The ML detector is essentially the MMSE metric with a threshold that is a function of the SNR. The drawback is that the SNR is computationally expensive to estimate prior to synchronization. So this approach is not well suited for initial synchronization. The time reverse correlation metric takes advantage of the fact that in the time domain the preamble consists of three parts, each symmetric in time. The resulting metric utilizes a time reverse correlation [10], [12]. The decision metric is given by
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MT RC (n) =
|QM (n)|2 2 (n, 0) Ryy
(10)
where QM (n) =
M −1
y(n + m)y(n − m)
m=0
Kim applied time reverse correlate to a WiMAX preamble [12]. The author claims this works 1dB better than the Schmidl detector in terms of probability of false alarm at high SNR. But at low SNR it does not perform as well. A drawback to this approach is that it is highly sensitive to CFO, sample time alignment, and multipath. Another drawback are the large side peaks, see Figure 6. This results in a higher false alarm rate. In [12] the time reverse correlate approach is compared to the Schmidl technique. Both exhibit a peak metric value of 0.68, a loss of about 1.6 dB in detection range. Other approaches exist [18], but they have increased computational requirements. In the next section the preamble will first be analyzed and shown that the correlations previously discussed are not optimal due to the structure of the WiMAX preamble. A modification to the delay correlate structure and a new detection metric that utilizes the preamble structure along with the CP were proposed. In the next section we develop present analysis of the WiMAX Preamble and show how to improve existing detectors as well as propose a new composite detector that takes advantage of all the redundant energy within the preamble symbol. III. PREAMBLE DETECTION A modified preamble signal model is presented in this section, followed by a description of the proposed composite detection metric. A. MODIFIED PREAMBLE SIGNAL MODEL The Mobile WiMAX Preamble waveforms are defined in the frequency domain [1] and can be represented by N + NGL ) = Wk (m) (11) 2 for m = 0, ..., NP SC − 1, where sk = 0, 1, 2 represents the segment index, Wk is the unique sequence of ±1 s representing the preamble index k = 0, ..., 113. NGL represents the number of the guard subcarriers on the left (low frequency) side. NP SC is the number of subcarriers assigned for preambles in each segment. For the 10 MHz case N = 1024, NGL = 86, and NP SC = 284. Xk (3m + sk −
Modulating each subcarrier the time domain preamble waveform can be written as N SC −1 1 P N + NGL ) xk (n) = Xk (3m + s − N 2 m=0
·e =
1 N
NP SC −1
e
j2πn(3m+s− N +NGL ) 2 N
j2πn(s− N +NGL ) 2 N
Wk (m)e
(12) j2π(3n)m N
m=0
In the frequency domain define the zero padded signal j2πn(sk − N +NGL ) 2 N Wk (m) if m < NP SC e Vk (m) = 0 otherwise, for m = 0, 1, ..., N − 1. Then equation (12) can be rewritten as N −1 j2π(3n)m 1 xk (n) = Vk (m)e N (13) N m=0 The right side of the expression is easily seen to be vk (3n), therefore xk (n) = vk (3n), n = 0, 1, ..., N − 1
(14)
where vk (n) is the IDFT of Vk (m). Since NP SC + 2 < N3 the N point IDFT is zero padded with > 2N 3 zeros. It is bandlimited by a factor of 3, therefore the time domain sequence is smooth and can be decimated by up to three [19]. Since 3 and N are relatively prime (for all values of N defined in [2]), as n goes from 0 to N − 1 the argument 3n cycles through the range 3 times, taking each value only once. Then equation (14) can be rewritten as ⎧ ⎪ if 0 ≤ n < N3 ⎨vk (3n) xk (n) = vk (3n + 1) if N3 ≤ n < 2N (15) 3 ⎪ ⎩ 2N vk (3n − 1) if 3 ≤ n < N . These three cycles can be separated into three sets as shown in Figure 2. We can define three new sequences vk,0(n) = vk (3n), vk,1 (n) = vk (3n + 1), vk,2 (n) = vk (3n + 2). These can be viewed as a polyphase filter factorization or a fractional delay of the decimated vk . The time domain preamble waveform xk (n) can be written as the concatenation of these three sequences {vk,0 , vk,1 , vk,2 }, i.e. ⎧ ⎪ if 0 ≤ n < N3 ⎨vk,0 (n) xk (n) = vk,1 (n − N3 ) if N3 ≤ n < 2N 3 ⎪ ⎩ 2N 2N vk,2 (n − 3 ) if 3 ≤ n < N . (16)
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B. PROPOSED COMPOSITE DETECTION METRIC Now reconsider the metrics described in the previous section. For L = N3 and M = N3 the crosscorrelation parameter can be written at the peak (n=0) as −1 1 M ∗ |Rxx (0, L)| = vk,0(m)vk,2 (m) M m=0 −1 1 M ∗ vk (3m)vk (3m − 1) = M m=0
< Rxx (0, 0)
1
a/3 Sample Delay
(n+M)
M,M
M
(n)
M,2M
M
(n)
CP
0.5
MPROP(n)
0 1 0.5 0 1
Cross Correlation b/3 Sample Delay
M
0 1
y a(n)
y(n)
MM,M(n)
0.5
M(n)
From here it is clear that the detection metric peak is reduced. This effect is displayed by Kim [12]. The metrics shown achieve a peak of approximately M = 0.65. A loss in detection range of about 1 dB. It can easily be verified that none of the metrics discussed in the previous section will achieve their full peak value unmodified. Therefore they operate at reduced detection performance. Since the fractional delays are multiples of 13 , this can be handled by processing the signal at a 3x sample rate. Given the rest of the OFDM system is setup to operate at 1x therefore we propose a different approach. To compensate for this degradation, fractional delay filters can be used to align the correlator inputs. This can be implemented using a fractional delay FIR on each correlator input. In order to minimize the computational burden the
Existing detectors take advantage of either some of the preamble redundancy or the CP redundancy. The proposed detector metric utilizes all the the information in the preamble as well as the CP to enhance performance. It also takes advantage of the fractional delay enhancement discussed previously using a simple two point interpolation that requires no multipliers. The motivation behind the proposed detection metric is to combine the redundancy of the various parts of the preamble and its CP. By itself the preamble offers better false alarm protection than the CP but the CP provides a much lower variance on its timing errors. By combining all the energy of the Preamble and its CP better performance can be achieved. From Figure 3 the various Preamble crosscorrelation lags can be seen. They all overlap the desired time instant. The CP lag is the only metric that does not have a plateau. The CP metric offers the best timing th error variance. However the CP is only 18 the symbol rd length but the Preamble metrics are 13 the symbol length. Therefore the CP detector does not perform as well as a Preamble detector in terms of sensitivity or false alarm rate. The proposed metric is given by
0.5
Ry a y b (n,d )
0 1
y b(n)
0.5 0 −1000
−500
0
500
1000 n
1500
2000
2500
3000
Fig. 3. Fractional Delay Correlation Structure Fig. 4. Proposed Preamble Detection Metric fractional delays can be approximated using a two point linear interpolation. This can be implemented using 3y(n + a3 ) ≈ (3 − a)y(n) + ay(n + 1) for a = 0, 1, 2. This provides 97% of the peak value, a loss of only about 0.1 dB. Now the appropriate metric calculation for the WiMAX Preamble has been discussed we turn our attention to the use of composite metrics for further detection improvement.
MP rop (n) = MCP (n) · MM,2M (n) · MM,M (n) · MM,M (n + M )
where MCP (n) = MNCP ,N (n). Modification to take advantage of fractional delay compensation yields
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MP rop (n) = MCP (n) · MM,2M,0,2 (n) · MM,M,0,1(n) · MM,M,1,2 (n + M )
where 2|Rya yb (n, L)|2 MM,L,a,b (n) = (Rya ya (n, 0) + Ryb yb (n + L, 0))2
MMINN(n)
0.06
MMINN2(n) M
(n)
GM
0.05
M
(n)
PROP
and 1 M
0.04
ya (n + m)yb∗ (n + m + d)
M(n)
Rya yb (n, d) =
M −1
0.03
m=0 0.02
with a ya (n) = (3 − a)y(n) + ay(n + 1) ≈ 3y(n + ) 3 and similarly for yb (n). This metric utilizes the stronger false alarm protection of the preamble detector to effectively gate, or mask, the estimates from the CP detector. Enabling it to minimize the false alarm rate while maintaining a low timing error variance. The resulting detector appears to maintain the best qualities of both detectors. The product of the preamble metrics acts as a gating or masking function for the more accurate timing of the cyclic prefix. This gating effect minimizes the false alarms that would occur if using the CP alone.
M
(n)
MINN
1
M
(n)
MINN2
MGM(n) MPROP(n)
M(n)
0.8
0.01
0 400
500
600
700
800
900
n
Fig. 6. Metric Sidelobes
were tested under multipath fading conditions, using the ITU Vehicular A model at 60 km/hour. The simulation included the effects of poor oscillators in mobile stations. The oscillator was assumed to have a 10 ppm error, with the band at 2.5 GHz, resulting in a 25 kHz CFO. All detectors used with thresholds that generated false detect probability of PF = 10−5 with a white Gaussian noise input. At each SNR 10,000 WiMAX frames were processed. SNR is defined using the total power in the sampled bandwidth. Figure 7 shows the results.
0.6 3
10 0.4
Mgm Mtrc Mminn Mminn2 Mprop
0.2 2
0 n
500
1000
t
−500
σ (Samples)
10 0 −1000
1
Fig. 5. Preamble Detection Metric Comparison
10
Figures 5 and 6 demonstrate the proposed metric compared to existing metrics in high SNR conditions. The new metric exhibits improved timing error variance and lower sidelobes.
0
10 −9
−6
−3
0 SNR (dB)
3
6
9
Fig. 7. Timing Estimation Error
IV. SIMULATION In this section the proposed detection metric along with several previously discussed are simulated. All metrics were tested using the same data. The detectors
Clearly the time reverse correlation MT RC metric does not hold up under the simulated conditions. In a
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static channel with no CFO, MT RC typically outperforms other methods in terms of timing error. However in realistic channel conditions the other metrics performed much better. From all tested scenarios the proposed detector outperforms the existing detectors in terms of timing error and probability of detection. In Figure 7, at SN R = 0dB the proposed detection scheme offers about 3dB of performance improvement over existing detection schemes.
[8]
[9]
[10]
V. CONCLUSION In this paper the topic of initial detection and coarse timing estimation for the Mobile WiMAX has been discussed. A review of prior contributions was presented followed with an analysis of the preamble properties. This lead to a proposed modification to the metric calculations that increases the dynamic range by about 1 dB. This coupled with the new proposed detection metric that utilizes the redundancy in the preamble and it’s cyclic prefix using a masking scheme, are shown to offer an improvement of about 3dB over existing techniques, through simulation. The results have been verified in hardware.
[11]
[12]
[13]
VI. REFERENCES [1] Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, IEEE Std. 802.16e-2005, 2005. [2] WiMAX Forum Mobile System Profile, WiMAX Forum Std. Revision 1.6.1, 2008. [3] L. J. Cimini, “Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing,” IEEE Trans. Commun., vol. 33, no. 7, pp. 665–675, Jul. 1985. [4] H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequency syncronization for OFDM systems,” IEEE Trans. Wireless Commun., vol. 2, no. 4, pp. 822–838, Jul. 2003. [5] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun., vol. 45, no. 12, pp. 1613–1621, Dec. 1997. [6] J.-J. van de Beek, M. Sandell, and P. O. Borjesson, “Ml estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Process., vol. 45, no. 7, pp. 1800–1805, Jul. 1997. [7] T. Keller and L. Hanzo, “Adaptive multicarrier modulation: A convenient framework for timefrequency processing in wireless communica-
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tions,” in Proc. IEEE, vol. 88, May 2000, pp. 611–640. H. Minn and V. K. Bhargava, “On timing offset estimation for OFDM systems,” IEEE Commun. Lett., vol. 4, no. 7, pp. 242–244, Jul. 2000. A. J. Coulson, “Maximum liklihood synchronization for OFDM using a pilot symbol: Algorithms,” IEEE J. Sel. Areas Commun., vol. 18, no. 12, pp. 2486–2494, Dec. 2001. B. Park, H. Cheon, C. Kang, and D. Hong, “A simple preamble for OFDM timing offset estimation,” in Proc. IEEE VTC’02, vol. 2, Sept 2002, pp. 729–732. J.-C. Lin, “Maximum-likelihood frame timing instant and frequency offset estimation for OFDM communications over a fast rayleigh-fading channel,” IEEE Trans. Veh. Technol., vol. 52, no. 4, pp. 1049–1062, Jul. 2003. H. Kim and S. Choe, “A timing synchronization of OFDMA-TDD systems over multipath fading channels,” in Proc. IEEE ICACT’06, Feb 2006, pp. 398–400. P. H. Moose, “A technique for orthogonal frequency division multiplexing freuency offset correction,” IEEE Trans. Commun., vol. 42, no. 10, pp. 2908–2924, 1994. K.-C. Hung and D. W. Lin, “Joint detection of integral carrier frequency offset and preamble index in OFDMA WiMAX downlink synchronization,” in Proc. IEEE WCNC’07, 2007. T. Pollet, M. V. Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise,” IEEE Trans. Commun., vol. 43, no. 2, pp. 191–193, Feb. 1995. H. Lim and D. S. Kwon, “Initial synchronization for WiBro,” in Proc. IEEE APCC’05, Oct 2005, pp. 284–288. P. R. Chevillat, D. Maiwald, and G. Ungerboeck, “Rapid training of a voiceband data-modem receiver employing an equalizer with fractionalT spaced coefficients,” IEEE Trans. Commun., vol. 35, no. 9, pp. 869–876, Sep. 1987. R. Negi, “Blind OFDM symbol synchronization in ISI channels,” IEEE Trans. Commun., vol. 50, no. 9, pp. 1525–1534, Sep. 2002. J. Proakis and D. Manolakis, Digital Signal Processing. Macmillan, 1992.
