Partial Proposal for 802.11N: ITRI Preamble Specification

August 2004 doc.: IEEE 802.11-04/0931r0

IEEE P802.11 Wireless LANs Partial Proposal for 802.11n: ITRI Preamble Specification

Date: August 13, 2004

Author: Yung-Yih Jian(1), Pangan Ting, Wei-Ping Chuang, Chun-Chun Kuo, Chang-Lung Hsiao

Wei-De Wu(2)

Chih-Kai Chen(3)

(1)Industiral Technology Research Institute (ITRI) Computer and Communications Research Laboratories (CCL) Bldg.14, 195 Sec. 4, Chung Hsing Rd. Chutung, Hsinchu, Taiwan 310, R.O.C Phone : +886-3-5914707 Fax : +886-3-5820371 e-Mail: {yyjian, pating, joeChuang, godeman, clhsiao}@itri.org.tw

(2)National Tsing Hua University Institute of Communications Engineering [email protected]

(3)Stanford University Department of Electrical Engineering chihkai@ stanford.edu

Abstract In this report, we propose a novel preamble structure for IEEE 802.11n standard. The proposed preamble structure is compliant with the FRCC documents and has good properties for frame detection and channel estimation. The structure consists of 10 periods of 32-sample short training symbols (STSs), and 4 periods of 64-sample long training symbols (LTSs).

Submission page 1 August 2004 doc.: IEEE 802.11-04/0931r0

1 Introduction The orthogonal frequency division multiplexing (OFDM) technique is regarded as an efficient method for high data rate systems 12 due to its robustness to multipath channels and high bandwidth efficiency. On the other hand, information theory indicates that the employment of multiple antennas can give enormous capacity improvement. Specifically, the capacity of a multiple-input and multiple-output (MIMO) system approximately grows linearly with the minimum number of the transmit antennas and receive antennas 34. However, the development of MIMO systems conventionally assumes frequency flat fading channels while the channels experienced by the high rate systems are usually frequency selective. Hence it is wise to incorporate the OFDM and MIMO techniques since the OFDM scheme can efficiently convert a frequency selective channel into multiple frequency flat subchannels. Some research works have shown that the MIMO-OFDM systems give very good performance and capacity improvement 5.

In a MIMO-OFDM system, the receiver should correctly estimate the frequency-domain channel responses of any antenna pair between the transmit side and the receive side to achieve coherent signal detection. In order to obtain accurate channel estimates, a MIMO-OFDM system requires a new preamble design due to the essential differences of the underlying channels, for example, the training symbols of distinct transmit antennas must be orthogonal to each other 67. With accurate channel estimates, most space-time coding schemes can be applied to the MIMO systems to obtain good performance. Possible choices can be space-time block code (STBC), space-time trellis code (STTC), vertical Bell Lab’s layered space-time code (V-BLAST), diagonal Bell Lab’s layered space-time code (D-BLAST) 8, singular value decomposition (SVD) based code 5 and so on. Hence, the channel estimate is crucial in MIMO-OFDM systems.

Several channel estimation algorithms are proposed in the literature 9-16. The least square (LS) method 9 can estimate the channel coefficients with a single MIMO-OFDM symbol. With the proposed preamble structure in 10, the LS estimator can achieve the lower bound of the estimation error. However, the performance of the LS estimator degrades severely if the guard band is considered in MIMO-OFDM 1112. Instead of using only one MIMO-OFDM symbol, a set of cyclic comb-type training symbols is suggested in 11, which gives better performance compared to the LS estimator.

In this report, we propose a novel preamble structure for IEEE 802.11n standard. The proposed preamble structure is compliant with the FRCC documents 1718 and has good properties for frame detection and channel estimation. The structure consists of 10 periods of 32-sample short training symbols (STSs), and 4 periods of 64-sample long training symbols (LTSs). The STSs are designed for frame detection, automatic gain control (AGC) and automatic frequency compensation (AFC) and the LTSs are used for accurate channel estimates. Regarding the coexistence with IEEE 802.11a systems, we design a novel STS structure with very low detection probability by IEEE 802.11a receiver. Besides, the proposed LTSs can solve the performance degradation of channel estimation in presence of guard band with very low complexity.

The rest of this report is organized as follows: Section 2 introduces the MIMO-OFDM system model for IEEE 802.11n systems. Section 3 proposes both the design and the properties of the proposed preamble for IEEE 802.11n systems with 3 transmit antennas and 3 receive antennas, i.e., 33 mode, and with 4 transmit antennas and 4 receive antennas, i.e., 4 4 mode. Finally,

Section 4 summarizes the whole report.

x1 IFFT CP CP FFT y1

x2 IFFT CP CP FFT y2

y x3 IFFT CP CP FFT 3

Figure 1: The system model of MIMO-OFDM systems

2 System Model Under the consideration of power consumption and the system complexity, in general, the MIMO-OFDM systems should not have greater than 4 antennas in the subscriber units, such as laptops and PDA’s. Thus, the proposed preamble is designed for the MIMO-OFDM systems with less than 4 transmit antennas. Without loss of generality, we take 3 transmit antennas and 3 receive antennas (33 MIMO-OFDM) system as an example.

We adopt the same OFDM modulation, frequency band, and channelization as in IEEE 802.11a standard 2. Specifically, the number of the subcarriers is 64, and the data is transmitted on 52 subcarriers, i.e., subcarrier –26 to –1 and subcarrier 1 to 26. Thus, the power spectrum of the transmitted signal can satisfy the requirement of the spectrum mask described in 2. Therefore, the system is fully compatible with IEEE 802.11a systems.

The system model is shown in Figure 1, where xi and y j are the preamble symbols transmitted at ith transmit antenna and the received signals at jth receive antenna, respectively. The frequency domain signals xi and y j are both vectors of length 64. The hj,i (z) represents the time domain channel response from ith transmit antenna to jth receive antenna. The channel between each pair of transmit antenna and receive antenna is assumed to be independent and static over a packet. The receive signal y j can be expressed as 3 y j  H j,ixi  n j , i1 where H j,i is a 6464 diagonal matrix with the diagonal elements L1 [H ]  h(n)exp( j2nk / 64) n j,i kk n0 , and j is frequency domain noise vector at jth receive antenna. The components of n j are assumed i.i.d complex Gaussian random variables with zero

2 mean and variance  n .

3 Proposed preambles for IEEE 802.11n systems The wireless LAN system is a packet-switched system with random access protocol. This essentially means that the receiver has no a priori knowledge about the arrival time of the packet. To perform synchronization of the system, a packet is preceded with a known sequence, i.e., a preamble. The preamble is carefully designed to provide sufficient information for the receiver to perform packet detection, frequency offset estimation, symbol timing acquisition, and channel estimation. However, the conventional SISO preamble structure is no longer proper for synchronization in MIMO-OFDM systems. It is necessary to design a new preamble structure for MIMO-OFDM systems.

In Section 3.1, an efficient preamble structure for IEEE 802.11n systems is presented. In Section 3.2, a set of STSs for IEEE 802.11n systems is proposed. Section 3.3 will present a set of LTSs for IEEE 802.11n systems.

3.1 Proposed IEEE802.11n Training Structure Several preambles for MIMO-OFDM systems are proposed 19-24. In general, the preamble structures can be classified into two categories, non-overlapped and overlapped in time. Due to the non-overlapped property, the length of the preambles grows linearly with the number of transmit antennas. Since the overhead of the preamble will limit the throughput of the system, the overlapped preamble structure turns out to be a better choice. The proposed overlapped preamble structure is shown in Figure 2

802.11n 802.11n 802.11n 802.11n 802.11n 802.11n 802.11n 802.11n 802.11n 802.11n 802.11n LTS11 802.11n LTS12 802.11n LTS13 802.11n LTS14 Tx1 STS1 STS1 STS1 STS1 STS1 STS1 STS1 STS1 STS1 STS1

MIMO frame detect, Coarse freq. Channel estimation, MIMO AGC offset estimation, fine frequency offset estimation MIMO timing synchronization

Figure 2: The proposed training structure for MIMO-OFDM systems

3.2 Short Training Symbols As shown in Figure 2, the proposed preamble for IEEE 802.11n systems can be divided into two parts, STS part and LTS part. The STS part consists of 10 consecutive STSs with 32 samples, and STSs for different transmit antenna are distinct. Denote the STS on the nth transmit antenna by STSn. Three main purposes of the STS for IEEE 802.11n systems are frame detection, automatic gain control (AGC), and automatic frequency compensation (AFC)20.

3.2.1 Construction of STSs The task of frame detection is to identify the preamble in order to detect packet arrival. It can also be used as a coarse timing algorithm. Different data-aided frame detection algorithms are proposed for OFDM and MIMO-OFDM systems 2526. All these algorithms are based on the correlation between the repeated symbols in the preamble. Thus, the preamble of IEEE 802.11n system should be periodic.

To perform AFC, we have to estimate the carrier frequency offset (CFO) caused by the oscillator mismatch between the transmitter and the receiver. In order to estimate CFO, periodicity in the preamble is desired. The phase rotation between time-delayed versions of the same symbol can be regarded as a measure of CFO 27. Therefore, the preamble consists of a concatenation of 10 identical training STSs per transmit antenna.

For AGC, the gain control amplifier of each receive antenna has to be adjusted to the optimal power level. Thus, the receiver has to calculate the received signal power at each receive antenna. In order to calculate the received power correctly, the cross correlation of STSs from different transmit antennas should be zero in 20. Thus, the STSs for different transmit antennas should be sophistically designed.

In addition to the three purposes of the STS, backward compatibility should be considered in the design of STSs. As the backward compatibility between IEEE 802.11g and IEEE 802.11b, a protection mechanism is established for IEEE 802.11g systems to maintain the backward compatibility. Thus, similar to the backward compatibility between IEEE 802.11g and IEEE 802.11b, the proposed STSs for IEEE 802.11n should not be detected by IEEE 802.11a systems.

If the preamble of IEEE 802.11n system can be detected by a legacy IEEE 802.11a device, the IEEE 802.11a device wakes up to decode the received data. Since the signal is transmitted by multiple antennas, the legacy IEEE 802.11a devices can not recover the received data correctly but consume the power. Therefore, we suggest that IEEE 802.11n short preamble should not be detected by the IEEE 802.11a devices. This will save the power consumption. Regarding the common frame detection methods, the new STSs for IEEE 802.11n systems should have different period from the STS of IEEE 802.11a.

Considering the above three purposes and backward compatibility, we propose that the new STSs for IEEE 802.11n should have following three properties:  Periodicity with period 32.  Zero cross-correlation among different STSs.  Low detection probability for IEEE 802.11a receivers.

The conventional frame detection algorithm of IEEE 802.11a systems usually computes the

Submission page 5 August 2004 doc.: IEEE 802.11-04/0931r0 complex correlation  between two consecutively received STSs, s(n), at the receiver, where  is defined as 15 * (n)   s((n  k))32 s ((n  k 16))32 . k0 If  is larger than the threshold, the receiver accepts a packet arrival. In order to design a set of

STSs with the third property, we design si(n) so that (n)  0 .

A set of IEEE 802.11n STSs in 3  3 mode is given by

S1,{-26,26} = (13/12)  {0, 0, 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, 1+j, 0, 0, 0, 0, 0, 1+j, 0, 0, 0, 0, 0, -1-j, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, 1-j, 0, 0, 0, 0, 0, 1-j, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, 0}

S2,{-26,26} = (13/12)  { 0, 0, 1+j, 0, 0,0, 0, 0, 1+j, 0, 0, 0, 0, 0, -1–j, 0, 0, 0, 0, 0, 1+j, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, 1–j, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0 }

S3,{-26,26} = (13/12)  { 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, 1+j, 0, 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-j, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, 1-j, 0, 0, 0, 0, 0, 1-j, 0, 0 }

The multiplication by a factor (13/12) is to normalize the average power of the resulting OFDM symbol.

A set of IEEE 802.11n STSs in 4  4 mode is given by

S1,{-26,26} = (13/ 9)  { 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, 0, 0, 1+j, 0, 0, 0, 0, 0, 0, 0, 1+j, 0, 0, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, 0, 0, 1-j, 0, 0, 0, 0, 0, 0, 0, 0 }

S2,{-26,26} = (13/ 9)  { 0, 0, 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0, 0, 0 }

S3,{-26,26} = (13/ 9)  { 0, 0, 0, 0, 0, 0, 0, 0, 1+j, 0, 0, 0, 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, 0, 0, -1-j, 0, 0, 0, 0, 0, 0, 0, 1-j, 0, 0, 0, 0, 0, 0, 0, 1-j, 0, 0, 0, 0, 0, 0, 0, -1+j, 0, 0, 0, 0 }

S4,{-26,26} = (13/ 9)  { 0, 0, 1+j, 0, 0, 0, 0, 0, 0, 0, 1+j, 0, 0, 0, 0, 0, 0, 0, 1+j, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1-j, 0, 0, 0, 0, 0, 0, 0, 1-j, 0, 0, 0, 0, 0, 0, 0,1-j, 0, 0 }

The multiplication by a factor (13/ 9) is to normalize the average power of the resulting OFDM symbol.

3.2.2 Numerical Results In this section, some numerical results of the proposed STSs are presented. We evaluate the properties of the proposed STSs for both 33 and 4 4 modes. The time domain of a period of STS is obtained by 2 1 63 j nk s(n)   S(k)e 64 . 64 k0

The PAPR of the proposed STSs for33 system is shown in Table 1

Table 1: PAPR of the proposed STSs for 3 x 3 system PAPR(dB) STS1 6.57 STS2 5.33 STS3 5.33

The PAPR of the proposed STSs for 4 4 system is shown in Table 2

Table 2: PAPR of the proposed STSs for 4 x 4 system PAPR(dB) STS1 4.2597 STS2 5.2069 STS3 4.2597 STS4 4.7712

Since the pilot tones of STSs in each mode are designed to be non-overlapped, the cross- correlation between the proposed STSs are 0. With this important property, the receiver can perform AGC correctly.

For backward compatibility, assume an IEEE 802.11a system received an IEEE 802.11n packet over an AWGN channel with high SNR, the received signal s(n) can be expressed as

Nt s(n)   si (n) , i1 where s(n) still has a period of 32. The complex correlation  of s(n) for 33 and 4 4 systems is shown in Figure 3 and Figure 4, respectively. As shown in Figure 3 and Figure 4, the proposed STSs have the property,   0 , and from Figure 5 and Figure 6, the probability of detecting the proposed STSs by an IEEE 802.11a system is very low.

The detection probability of an IEEE 802.11n receiver in 33 and 4 4 mode is shown in Figure 7 and Figure 8, respectively. Because of the periodic STSs, we can detect the packet arrival simply.

- 0 . 1

- 0 . 2

- 0 . 3

- 0 . 4

- 0 . 5 0 5 1 0 1 5 2 0 2 5 3 0

Figure 3: The correlation of the proposed STSs (3x3 mode) in a legacy 11a receiver.

- 0 . 1

- 0 . 2

- 0 . 3

- 0 . 4

- 0 . 5 0 5 1 0 1 5 2 0 2 5 3 0

Figure 4: The correlation of the proposed STSs (4x4 mode) in a legacy 11a receiver.

D e t e c t e d p r o b . o v e r 1 0 0 0 p r e a m b l e s a n d 3 1 I E E E 8 0 2 . 1 1 n c h a n n e l s

1 1 n C h a n n e l B 1 1 n C h a n n e l D 1 1 n C h a n n e l E 0 . 4

- 0 . 1 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 S N R

Figure 5: The detection probability of the proposed STSs (3x3 mode) in a legacy 11a receiver.

D e t e c t e d p r o b . o v e r 1 0 0 0 p r e a m b l e s a n d 4 1 I E E E 8 0 2 . 1 1 n c h a n n e l s

1 1 n C h a n n e l B 1 1 n C h a n n e l D 1 1 n C h a n n e l E 0 . 4

- 0 . 1 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 S N R

Figure 6: The detection probability of the proposed STSs (4x4 mode) in a legacy 11a receiver.

D e t e c t e d p r o b . o v e r 1 0 0 0 p r e a m b l e s a n d 3 3 I E E E 8 0 2 . 1 1 n c h a n n e l s 1 1 1 n C h a n n e l B 1 1 n C h a n n e l D 0 . 9 8 1 1 n C h a n n e l E

0 . 9 6

0 . 9 4

0 . 9 2

0 . 8 8

0 . 8 6

0 . 8 4

0 . 8 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 S N R

Figure 7: The detection probability of the proposed STSs (3x3 mode) in a 11n receiver.

D e t e c t e d p r o b . o v e r 1 0 0 0 p r e a m b l e s a n d 4 4 I E E E 8 0 2 . 1 1 n c h a n n e l s 1 1 1 n C h a n n e l B 1 1 n C h a n n e l D 0 . 9 8 1 1 n C h a n n e l E

0 . 9 6

0 . 9 4

0 . 9 2

0 . 8 8

0 . 8 6 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 S N R Figure 8: The detection probability of the proposed STSs (4x4 mode) in a 11n receiver.

3.3 Long Training Symbols As shown in Figure 2, after time synchronization, the receiver starts to estimate channel information and perform fine frequency offset compensation. With accurate estimate of channel coefficients, the MIMO-OFDM receiver can separate the signal stream from the different transmit antennas and perform coherent detection.

3.3.1 Construction of LTSs When timing is synchronized correctly, the receiver can estimate the channel information with the known LTSs. Different channel estimation algorithms are presented 9-1623. In 109, LS methods for MIMO-OFDM channel estimation are proposed, and the estimators can estimate the channels of all the antenna pairs with a single received MIMO-OFDM symbol. Without taking the guard band into account, a design of preamble sequences achieving the lower bound of the mean square error for the LS channel estimator are proposed 10.

However, in order to avoid the interference from the adjacent channels, only a subset of subcarriers is used for transmission in practical applications 2. A lower bound of the mean square error of the LS estimator with the consideration of guard band is provided in 12. But, there is not any sequence to exactly achieve the bound, and the performance of the LS estimator degrades seriously compared to the case without guard band.

Instead of estimating the channel coefficients with a single MIMO-OFDM symbol, the channel estimators with multiple received MIMO-OFDM symbols are proposed in 112123. A cyclic comb-type training symbols are proposed in 11, where the training symbols are transmitted cyclically at each antenna. At the receiver, the channel frequency responses that are estimated using each training symbol are averaged with optimal weights. As shown in 11, the estimator with multiple received MIMO-OFDM symbols can have better performance than the conventional LS algorithms. Some training blocks are proposed in 1423, and the channel coefficients can be estimated by linear operations. These estimators also outperform the conventional LS estimators.

With the best of our knowledge, the channel estimation using multiple training symbols can achieve better performance and obtain lower complexity than using a single training symbol. Thus, we construct a block of multiple training symbols as a part of the proposed preamble for IEEE 802.11n systems. The proposed training block is shown in Figure 9, where k W4  exp( jk2 / 4) , cyclic prefix (CP) is of 16 samples, and L is the basis of the proposed LTS for IEEE 802.11n, which is the same with the LTS of IEEE 802.11a 2. Thus the L is

L{-26,26} = { 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 0, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1 }.

With the structure of the proposed LTS for IEEE 802.11n, the receiver can estimate channel responses with low complexity. Specifically, an efficient 4 x 4 FFT matrix can be used.

3 x 3 Mode:

0.8 µs 3.2 µs

Tx 1 CP IFFT(L) CP IFFT(L) CP IFFT(L) CP IFFT(L) CP CP 1 CP 2 CP 3 Tx 2 IFFT(L) W4 IFFT(L) W4 IFFT(L) W4 IFFT(L) CP CP 2 CP 4 CP 6 Tx 3 IFFT(L) W4 IFFT(L) W4 IFFT(L) W4 IFFT(L) t

4 x 4 Mode:

0.8 µs 3.2 µs

Tx 1 CP IFFT(L) CP IFFT(L) CP IFFT(L) CP IFFT(L) CP CP 1 CP 2 CP 3 Tx 2 IFFT(L) W4 IFFT(L) W4 IFFT(L) W4 IFFT(L) CP CP 2 CP 4 CP 6 Tx 3 IFFT(L) W4 IFFT(L) W4 IFFT(L) W4 IFFT(L) 3 6 9 Tx 4 CP IFFT(L) CP W4 IFFT(L) CP W4 IFFT(L) CP W4 IFFT(L) t

Figure 9: The structure of the proposed LTSs

3.3.2 Numerical Results In this section, some numerical results of the proposed LTSs are presented. The properties of proposed LTSs for both 33 and 4 4 systems are also evaluated.

As shown in Figure 9, the proposed LTSs are constructed by multiplying proper factors k W4  exp( jk2 / 4) to the basis L. Thus, the properties of the proposed LTSs can be determined by the basis L, where L is chosen to be the LTS of IEEE 802.11a. The PAPR of the basis L is 3.1658 dB, and the magnitude of the periodic autocorrelation function of basis L is shown in Figure 10.

Figure 11 and Figure 12 show the performance of the frequency domain channel estimation for IEEE 802.11n in33 and 4 4 modes, respectively, where we evaluate the mean square error (MSE) per data subcarrier. From these figures, we observe that the frequency domain channel information can be estimated effectively with the proposed LTSs. The performance is also comparable with the conventional IEEE 802.11a systems.

- 2 0 )

B - 2 5 d ( - 3 0

- 5 0 0 1 0 2 0 3 0 4 0 5 0 6 0

Figure 10: The magnitude of the periodic auocorrelation function of the basis L.

0 1 0 1 1 n C h a n n e l B f o r 3 x 3 s y s t e m 1 1 n C h a n n e l D f o r 3 x 3 s y s t e m r 1 1 n C h a n n e l E f o r 3 x 3 s y s t e m e i r

1a 0 c b u s

1z 0 n o n

r e p - 3

1E 0 S M

- 4 1 0 5 1 0 1 5 2 0 2 5 3 0 3 5 a v e r a g e d r e c e i v e d S N R

Figure 11: The MSE of the channel estimates with proposed LTSs for 3x3 mode over channel B, D and E.

0 1 0 1 1 n C h a n n e l B f o r 4 x 4 s y s t e m 1 1 n C h a n n e l D f o r 4 x 4 s y s t e m r

e 1 1 n C h a n n e l E f o r 4 x 4 s y s t e m i r

1a 0 c b u s

1z 0 n o n

r e p - 3

1E 0 S M

- 4 1 0 5 1 0 1 5 2 0 2 5 3 0 3 5 a v e r a g e d r e c e i v e d S N R

Figure 12: The MSE of the channel estimates with proposed LTSs for 4x4 mode over channel B, D and E.

References

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Appendix A The real part and imaginary part of time domain sequences of the proposed STSs are shown in Figure 1 to Figure 7.

R e a l p a r t 0 . 2

- 0 . 1