Pseudo-Multipath Iteration Algorithm (PMIA)

In 2005, C. C. Wu [12] in his thesis introduced a concept of pseudo multipath. The scheme is based on the AST algorithm. First, the algorithm defined a pseudo path with preamble which is two-OFDM symbol long (a section A preamble and a section B preamble). We can get a unique peak at the end of the preamble. Then, we exploit the peak index for the start position of the pseudo path that we want to insert in. We would use the original signal added with a preamble multiplied a factor α, and moves forward

same way, we must iterate several times to get the final outcome of the PMIA algorithm. After several times of iteration, the peak’s position of the last iteration will then become our estimated start position. The PMIA algorithm can further increase the precision of the estimation of start position.

In PMIA, three variables must be set: 1) the strength of pseudo path, 2) the timing of pseudo path inserted and 3) times of iteration. Because there are three variables that should be optimized, it is difficult to get the trade off among these variables. The PMIA needs a lot of computation complexity for the iterative operation, and need more hardware for the computation.

Although PMIA has some disadvantages but it still has advantages. The PMIA is not only more precise than AST algorithm but also able to fine-tune the system performance when we select a smaller value of α. The timing of inserting the pseudo path in PMIA is shown in Figure 4.2.3- 1.

From the computer simulation results within the thesis [12], we can see that the optimized value of these parameters in fixed SUI-3 environment is: α=0.1, λ=6 and 4 times of iteration. We will show our computer simulation results using the same optimized value [12] as listed above and compare the system performance with PMIA and PMA in fixed SUI-3 environment as shown in the section 5.1.1.

Figure 4.2.3- 1 The timing of pseudo path inserted for AST algorithm

Chapter 5 Modified Pseudo-Multipath

Algorithm

n this chapter, we will present a new method by putting a section B preamble in the receiver when we use the pseudo-path for the frame timing synchronization. This modified pseudo multipath algorithm (PMA) can increase the accuracy of frame timing estimation without adding more hardware. We apply this method in TDD, downlink OFDM system which fits IEEE 802.16-2004/e Std. environment [2], [3].

5.1 Modified Pseudo-Multipath Algorithm (PMA)

To increase the precision of estimation of the start position, we apply the concept of pseudo-multipath [12]. The pseudo multipath algorithm uses a section B preamble in the receiver as a pseudo-multipath (4^th tap) shown in Figure 3.2.2- 1. First, we exploit a

I

section A preamble of the original signal to find the position of the first peak of M(k) curve, see Equation (4.2.2-3). Then, we put a section B preamble prior to the first peak whose length is λ, and used it as a pseudo-path. This section B preamble multiplied by a factor α, then adds the original signal to become a new received signal for following calculation. Then we can find the only peak on the curve of MM(k), and the position of the peak is defined as the symbol start position. The block diagram is shown in Figure 5.1- 1. In Figure 5.1- 1, the green part shows the differences between pseudo multipath algorithm and AST algorithm. We just add only a set of adder and one multiplexer.

In Figure 5.1- 1, the multiplier is replaced by a bit shifter to save a set of multiplier. Therefore, we limit our value of the factor α to 2 where n can be any ⁿ positive or negative integer, including 0. We select the value of the factor α as 1, 0.5,

0.25 and 0.125 in our hardware design. We also show PMA algorithm flow chart in

Figure 5.1- 2. In the proposed scheme (PMA), we will increase the precision of estimation of the start position and eliminate a variable of times of iteration of the PMIA. The PMA only uses a section B preamble in the receiver (note that: PMIA needs a section A preamble and a section B preamble in the receiver) and reduce the hardware and computation complexity successfully.

The following equation tells us how the pseudo multipath can be used to fight against channel delay spread [12]. Equation (5.1-1) is the outcome of the auto-correlation of the received signal. When

h is much larger than

₁ ²

h

₂ ². The result of auto-correlation will be dominated by

h term. Also, when

₁ ²

h

₂ ² is much larger than

h , the result of auto-correlation will be dominated by

₁ ²

h

₂ ² term. This also means that the estimated start position is mainly influenced by one of the taps of

Figure 5.1- 1 Block Diagram of PMA algorithm

∑

= + + − + + + + + − + + + + + −

From Equation (5.1-1), we can easily find that the outcome signal

f

(d) is the auto-correlation sum of the original signal passing through the channel with some fading and delay. Similarly, α is a factor multiplying the pseudo-path to define its influence on the original signal. Then, we use λ to set the position of the influence of pseudo-path, adding with the original signal, and produce a new signal. Figure 5.1- 3 shows the timing of pseudo-path, and Equation (5.1-2) shows the outcome of adding pseudo-path, and ε is the offset between the first estimated peak from the timing metric M(k) and the ideal peak position of the timing metric M(k). Noise term is still not considered here.

Therefore, when the value of

α

² is large, this equation may be dominated by the

α

2 term (pseudo-path term), which means that the signal will be dominated by pseudo multipath. If the value of each term is similar, the outcome would be the sum of each term, not dominated by any single term.

We use Equation (5.1-3) and Equation (5.1-4) to evaluate the system performance (the deviation of the frame start point) in either fixed or mobile environments.

Estimate index RMS =

Figure 5.1- 2 Flow chart of PMA

Figure 5.1- 3 Timing of pseudo-path insert

Next, we simulate 20000 frames, at SNR=5dB to SNR=30dB in SUI-3 channel environment. In Figure 5.1- 4 and Figure 5.1- 5, we show the system performance of PMA compared with normal mode (ASTA mode) when the system is in the AWGN channel. Then, we try to set different values of α and λ in the SUI-3 channel to examine the variations of system performance by different values of α and λ. We limit the value of α to be 1, 0.5, 0.25 or 0.125, to avoid the use of multiplier. We only show the optimized λ value in each α that we found from Figure 5.1- 7 to Figure 5.1- 15.

Then, we can get the optimized value of α and λ in SUI-3 channel environment.

From the result of the previous description and simulation, we find that α=0.5 and λ=33 is the optimized value in SUI-3 environment for IEEE Std. 802.16-2004. Because its RMS value and mean value are closer to the center than other combinations of α and λ, it indicates that the average estimated start position of every frame is very close to the ideal start position of frames.

Figure 5.1- 16 shows the system performance when α=0.5 and λ=33, and it also shows the comparison with timing error probability distribution between normal mode and PMA mode at 10dB SNR and 30dB SNR. These results are shown in Figure 5.1- 17 and Figure 5.1- 18. From the result of computer simulations, we can find that the PMA’s system performance is much better than AST algorithm without pseudo path. It also shows that pseudo multipath algorithm apparently makes the estimated start position much closer to the center (which is the ideal start position; that is, index 0 as shown in Figure 5.1- 17 and Figure 5.1- 18).

Figure 5.1- 4 RMS of PMA mode in AWGN channel (α=0.5, λ=0)

RMS (SUI-3):

Figure 5.1- 6 RMS PMA mode in SUI-3 channel (α=1)

Figure 5.1- 8 RMS PMA mode in SUI-3 channel (α=0.25)

Mean (SUI-3):

Figure 5.1- 10 Mean PMA mode in SUI-3 channel (α=1)

Figure 5.1- 12 Mean PMA mode in SUI-3 channel (α=0.25)

Comparison (SUI-3):

Figure 5.1- 14 PMA mode in SUI-3 channel (RMS)

Figure 5.1- 16 RMS and Mean of PMA mode in SUI-3 channel (α=0.5, λ=33)

Figure 5.1- 17 Time Error at SNR=10dB of PMA mode in SUI-3 channel (α=0.5, λ=33)

The green line sets α=0 and λ=0, that is, the system works using AST algorithm.

In this mode, the system without pseudo path is called “Normal Mode” in our simulations. The blue line shows the system performance after adding pseudo path.

From the results of simulations, we see that PMA algorithm can improve system performance a lot. In the same way, when we find the optimized value of α and λ in SUI-3, we put the same parameters α and λ in the other SUI channels (SUI-1/SUI2 and SUI-4 to SUI-6 environments), to check if it can improve the system’s performance.

Figure 5.1- 19 to Figure 5.1- 23 show the system performance when we set α=0.5 and λ=33 (the optimized value at SUI-3 channel) in different SUI channels.

Figure 5.1- 19 SUI-1 (α=0.5, λ=33 )

Figure 5.1- 20 SUI-2 (α=0.5, λ=33 )

Figure 5.1- 22 SUI-5 (α=0.5, λ=33 )

From the result of the simulations, we find the fact that the same set of parameters can not be suit to every SUI environment. To further analyze the result, we can find that the Doppler shift and tap’s power of each multipath of SUI-1 and SUI-2, respectively, are weaker than other SUI channels. This means that in the SUI-1 and SUI-2 environments, signals are transmitted in a good channel environment. Therefore, if we add a pseudo-path, its strength and the length moved forward by λ would be the same as that in SUI-3 channel. It does not improve or degrade the performance of the estimated start position. But if the system is in a serious multipath delay spread environment, we can improve the estimation accuracy a lot by adding the pseudo path.

How do we solve the problems that the system performance may be degraded in SUI-1 and SUI-2 channels by using PMA? First, we use a few frames at the start of bursts and set α=0 and λ=0 to detect the current system channel environment. By the result of detection, the system will figure out the current channel environment. Then we switch to PMA mode and dynamically set the new α and λ values that are suitable for the channel. This procedure can work periodically when we need. We can get better system performance than ASTA mode after training. The same procedure can be applied to either fixed or mobile environment.

We care about the individual optimized value of α and λ in the different SUI channels. Next, we will show the computer simulation results to see the optimized values of α and λ in SUI-1, SUI-2, SUI-4, SUI-5 and SUI-6 as shown in Figure 5.1- 24 to Figure 5.1- 33.

Figure 5.1- 24 SUI-1 (RMS)

Figure 5.1- 26 SUI-2 (RMS)

Figure 5.1- 28 SUI-4 (RMS)

Figure 5.1- 30 SUI-5 (RMS)

Figure 5.1- 32 SUI-6 (RMS)

Table 5.1- 1 Optimization parameter of IEEE Std. 802.16d

SUI-1 SUI-2 SUI-3 SUI-4 SUI-5 SUI-6

α 0.25 0.5 0.5 1 1 0.5

λ 26 26 33 0 32 14

From the result of all the above mentioned, we list the recommended individual optimized values of α and λ in each SUI channel, as shown in Table 5.1- 1.

5.1.1 Comparison of PMA with Schmidl & Cox Algorithm and PMIA

In the previous section, we have introduced Schmidl & Cox algorithm [10]. Now, if we put the system in the same SUI environment (SUI-3) and set the system parameter as α=0.5 and λ=33 in PMA mode, and then compare the performance of PMA mode and that of Schmidl & Cox algorithm. The performances are shown in Figure 5.1.1- 1 and Figure 5.1.1- 2. We also compare the performance of PMIA and PMA. The results are shown in Figure 5.1.1- 3 and Figure 5.1.1- 4.

From the result of the simulations, we can see that PMA algorithm is much better than Schmodl & Cox algorithm and PMIA on frame-timing estimate.

Figure 5.1.1- 1 Schmidl & Cox vs. PMA in fixed SUI-3 (RMS)

Figure 5.1.1- 3 ASTA and PMIA vs. PMA in fixed SUI-3 (RMS)

We compare all the algorithms we introduced above including precision of the estimated start position of signals, the complexity of computations and the complexity of hardware [23]. The results are summarized as:

1) Precision of estimation: PMA > PMIA > ASTA >> Schmidl & Cox.

2) Complexity of computation: PMIA >> PMA = ASTA

≅ Schmidl & Cox.

3) Hardware complexity: PMIA >> PMA

≅ ASTA ≅ Schmidl & Cox.

By comparing the computation complexity and hardware complexity, PMIA has the highest effort and the effort of Schmidl & Cox, ASTA and PMA algorithms are very similar. But PMA has the highest precision of estimated start position among all the algorithms.

Table 5.1.1- 1 Comparison of PMA with Schmidl & Cox Algorithm and PMIA

Schmidl &

Cox

ASTA PMIA PMA

Precise of estimation

Low High High The Highest

Complexity of computation

Low Low The Highest Low

Hardware complexity

Low Low The Highest Low

5.2 IEEE 802.16e System

All the above simulations fit IEEE Std. 802.16-2004 OFDM PHY specification [2]. If we put PMA in mobile environment to fit IEEE Std. 802.16e [3], what influence it might have on the system performance?

By reference [13], we rebuild the channel model for mobile environment, and set the system to work in 2.5GHz band, mobile velocity at 120km/hr. We use Equation (5.2-1) to calculate the corresponding Doppler frequency, and obtain 277.8 hz.

θ

After rebuilding the channel in mobile environment, the system performances from software simulations are shown in Figure 5.2- 1 to Figure 5.2- 12.

Figure 5.2- 1 Mobile SUI-1 RMS

Figure 5.2- 3 Mobile SUI-2 RMS

Figure 5.2- 5 Mobile SUI-3 RMS

Figure 5.2- 7 Mobile SUI-4 RMS

Figure 5.2- 9 Mobile SUI-5 RMS

Figure 5.2- 11 Mobile SUI-6 RMS

From the result, we list the recommended optimized values of α and λ in each SUI channel in Table 5.2- 1.

We will investigate if the system works in 3.5 Ghz licensed band, with 7 Mhz bandwidth, or in the other frequency bands and bandwidth. Figure 5.2- 13 to Figure 5.2- 20 show the performances when the system is in IEEE Std. 802.16-2004, IEEE Std. 802.16e / 120 km/hr / 2.5 Ghz licensed band, IEEE Std. 802.16e / 120 km/hr / 3.5 Ghz licensed band, with bandwidth is 7 Mhz, and IEEE Std. 802.16e / 120 km/hr / 6 Ghz license-exempt band with bandwidth 10 Mhz in the SUI-3 channel [2] [3].

Table 5.2- 1 Optimization parameter of IEEE Std. 802.16e

SUI-1 SUI-2 SUI-3 SUI-4 SUI-5 SUI-6

α 0.25 0.5 1 1 1 1

λ 3 5 3 13 15 10

Figure 5.2- 13 802.16d SUI-3 (RMS)

Figure 5.2- 15802.16e SUI-3 at 2.5 Ghz band (RMS)

Figure 5.2- 17 802.16e SUI-3 at 3.5 Ghz band (RMS)

Figure 5.2- 19 802.16e SUI-3 at 6 Ghz license-exempt band (RMS)

From the simulation results listed above, PMA in IEEE Std. 802.16e environment, no matter the system is in 2.5 Ghz licensed band or in 3.5 Ghz licensed band or in 6 Ghz licensed-exempt band, PMA still has better performance than AST algorithm for estimation of start position.

Furthermore, when the system is in a severer multipath delay spread environment, we can get the simulation result in the environment that fits IEEE Std. 802.16-2004 or IEEE Std. 802.16e environment. PMA algorithm still can improve the system performance by adjusting the factors α and λ. When signals in the good channel environment, the strength of pseudo-path (the value of α) does not need to be strong to avoid interference of the original signal which already has good quality.

We can also use the procedure discussed in section 5.1. The system can select the best parameters. In this technique, we may design a system which is suitable for different SUI channels under fixed or mobile environments.

5.3 Fix-Point Simulation

Because of the limit of chip area and routing complexity, and other problems, we often avoid implementing VLSI circuit by floating paint data format in the real world.

Generally, if we use finite numbers of bits in implementation of the chip, and if its result is very close to that of using floating-point data format, we can choose finite-bit format to implement on VLSI. In this way, we can save not only chip area but also routing complexity, and thus decrease the cost. Next, engineers must find how many bits we implement in real chips and make system performance close to the result of floating-point.

Figure 5.3- 1 Fix-Point structure

The fix-point data format is shown in Figure 5.3- 1. In the transmitter, the power of transceiver signal must be quantized and normalized. No matter what kind of modulation types, its real part and imaginary part are smaller than one after normalization. The maximum value of the transmitted signal will be in the preamble before IFFT. On the effect of signal passing through the channel, the amplitude value of signals may become larger in the receiver. Its value may be larger than three [12], [16]. Therefore, we use three bits to express the integer part. The MSB is the sign bit.

The reminding part is used to express the decimal part. The precision of the quantization depends on how many quantization bits that we use.

In fix-point simulation, in the circled dash line, the indexed position shows the part that MATLAB program must do the floating-point to fix-point translation, see Figure 5.3- 2. Before the signals are transmitted from the transmitter, we translate floating-point data format to fix-point data format in our programs. In a similar way, signals from the channel will also be translated from floating-point data format to fix-point data format in our program.

When we simulate in fix-point data format, we simulate both truncation mode and rounding mode to see the results when we use different translation data formats. The simulation result of rounding mode are shown in Figure 5.3.1- 1 and Figure 5.3.1- 2, and the results of truncation mode are shown in Figure 5.3.2- 1 and Figure 5.3.2- 2.

Figure 5.3- 2 The floating-point to fix-point position in system

5.3.1 Rounding Mode

Figure 5.3.1- 1 Rounding Mode in SUI-3 channel (RMS)

5.3.2 Truncation Mode

Figure 5.3.2- 1 Truncation Mode in SUI-3 channel (RMS)

We can get the same results of computer simulation of truncation and rounding mode, the result of fix-point simulation is consistent with floating-point simulation when we use 14-bit word length.

In fix-point simulation, even in the different floating-point to fix-point translation mode (rounding mode or truncate mode), we can see that no matter what kind of translation format, we can get the same outcome: we can use 14-bit to implement our system in VLSI circuit, and the system performance is very close to floating-point system performance as we simulate in the computer. Therefore, 14-bit word length is recommended to implement the system on VLSI circuit.

Chapter 6 Conclusion

n this thesis, we have presented a modified pseudo multipath frame timing synchronization scheme for TDD downlink OFDM system which fits IEEE Std. 802.16e. This scheme has higher precision of the estimated start position, low computation complexity and low hardware effort.

The modified pseudo multipath algorithm, denote as PMA, uses α and λ as the weighting factor and delay of the pseudo path, respectively. We list the recommended optimized values of every SUI channel environment, and compare this scheme with the conventional schemes. From the results of our computer simulations, PMA is a better solution when the system is in severer environments.

The PMA performance may degrade when using the same parameters in different SUI environments, especially when the channel is in the environment with small multipath delay spread or Doppler shift. We present a technique in which a few frames at the start of bursts and set α=0 and λ=0 are used to detect the current channel

I

environment, and by the result of detection, the system will figure out the current channel environment. Then we switch to PMA mode and set the new α and λ values that are suitable for the channel. With this technique, we can design a system which can work well in every SUI environment in both fixed and mobile environments.

In summary, PMA has better system performance in both fixed and mobile environments than other previously proposed schemes. It has the advantages of higher precision of estimated start position, and low computational complexity and easier to implement in VLSI.

References

[1] A. R. S. Bahai, B. R. Saltzberg, M. Ergen, Multi-Carrier Digital Communications Theory and Applications of OFDM, Springer, 2005.

[2] IEEE Standard for Local and metropolitan area networks PART16: Air Interface for Fixed Broadband Wireless Access Systems. IEEE Std. 802.16-2004 (Revision of IEEE Std. 802.16-2001.

[3] IEEE Standard for Local and metropolitan area networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems Amendment 2:

Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands and Corrigendum 1.

IEEE Std 802.16e-2005 and IEEE Std 802.16-2004/Cor 1-2005 (Amendment and Corrigendum to IEEE Std. 802.16-2004).

IEEE Std 802.16e-2005 and IEEE Std 802.16-2004/Cor 1-2005 (Amendment and Corrigendum to IEEE Std. 802.16-2004).

在文檔中 符合IEEE802.16e 時域雙工之正交分頻多工下鏈之碼框同步效能研究 (頁 61-0)