**CHAPTER 4 A Low Complexity and High Throughput Frame**

**4.3 M ULTI -B AND OFDM D ESIGN**

**4.3.1 Frame Synchronizer (MB-OFDM)Flow：**

**Band**

**RF Receiver Band Select**
**Band Boundary**

**FFT**
**Window**
**Detection**

**FFT Boundary**

FIG. 4.11 Frame synchronizer flow of MB-OFDM UWB system

51

FIG 4.11 is the frame synchronizer flow of MB-OFDM UWB system. In the initial, control FSM fixes RF receiver at sub-band 1 to transfer data, and AGC tunes correct RF gain of noise signals. After AGC tunes the RF gain stably, packet detection uses auto-correlation scheme to the valid packet. At the same time band detection decides the correct switching time of time-interleaved OFDM symbols transferred at the three sub-bands. Once packet valid is asserted, control FSM changes sub-bands of RF receiver at corresponding tine duration by the band boundary information of band detection. Then FFT window detection finds FFT window boundary during band boundary ±16 sample cycles. Finally, preamble timing detection distinguishes three kinds of sync symbols (PS, FS, CES) in preamble and controls FSM cutting OFDM data symbols for FFT.

**4.3.2 Proposed ** **Algorithm **

*4.3.2. 1 Training AGC *

In our system platform, we assume that the variable gain amplifier (VGA) of RF receiver can tune gain from 0 to 70 dB and implement AGC block by signal power measurement algorithm. For low cost consideration, we used the estimated power information of band detection and build up one AGC lookup table with effective range from –10 to 10 dB to tune VGA gain. The drawback of the AGC lookup table is long searching time under high SNR condition. In LDPC-COFDM system, there are sufficient packet sync symbols for AGC tuning VGA gain. However, MB-OFDM

52

system enormously reduces the available sync symbols for AGC, and too long AGC time under high SNR region will fails frame synchronizer because of insufficient sync symbols. To solve this problem, we proposed the training AGC with binary search to tune VGA gain. Before transferring the valid data, transmitter sends a training packet for receiver and AGC tunes the correct gain at most 4 effective packet sync symbol (12 OFDM symbol duration). The tune valid gain of noise signal and data signal in training packet will be stored as training gain. When transferring the valid data, AGC will reference the training gain and tunes VGA gain finely by AGC lookup table. Thus only one effective packet sync symbol (3 OFDM symbol duration) will be cost by AGC. The algorithm of AGC is shown as follows：

### 2

In (Eq 4.11), GAIN*est *is the estimated gain from AGC lookup table with effective range
from –10 to 10 dB；GAIN*max* and GAIN*min* is the possible maximum and minimum VGA gain (In
our design, GAIN*max*=70dB and *GAIN**min*=0dB)； *GAIN**now* is the VGA gain at now time and
*GAIN**next *is the computed gain of next time. The detail data flow of training AGC is shown as FIG
4.12.

53

** of noise signal**
**Yes**

** of data signal**

**AGC training**

FIG. 4.12 Detail data flow of training AGC

54

*4.3.2. 2 Band Detection *

In MB-OFDM system, band detection must decide the correct switching time of sub-bands to receive time-interleaved OFDM symbols, like FIG 2.4. FIG 4.10 shows that before band detection, only 242.4ns (128 samples) has data for every 937.5ns period (3 OFDM symbols). If we accumulate the power of received signal for continuous 128 samples, the accumulated value will reach a local maximum value in time domain for every 937.5ns period. FIG 4.13 shows the accumulated power distribution in time domain and apparently the end of sub-band 1 locates at the index of local maximum value.

**-2812.5** **-1875** **-937.5** **0312.5 937.5** **1875** **2812.5**
**2**

**4**
**6**
**8**
**10**

**Pac ke t Start** **Nois e **

**Time [ns]**

**ac** **cu** **mulate** **d POWER**

**Band Boundary**

FIG. 4.13 Accumulated power of continuous 128 samples

55

To detect the end of sub-band 1, we use a dynamic searching window to find the corresponding index of local maximum value. It compares the accumulated power at two different samples with ‘m’ sample distance to get a sub-detection flag. When all the sub-detection flags satisfy the pre-defined condition, the valid searching window will be announced. Eq 4.12 shows the algorithm of proposed dynamic searching window：

1 2

In Eq 4.12, D(k) means the accumulated power between ‘m’ samples and ‘m’=8 in our proposed design. The compared result flag f(k) represents the increasing trend (f(k)=1) and decreasing trend (f(k)=0) for accumulated power. Thus the local maximum value and can be detected. When any searching window has been cut, packet detection will calculate the

56

corresponding auto-correlation value and compare with pre-defined threshold to prevent false announcement at low SNR condition. Also the detected end index of sub-band1 may has some variations from the true band boundary because of white noise and multi-path interference. Thus the dynamic searching window detects the boundary coarsely. After matched-filter detects the FFT window boundary, band detection will adjust band boundary finely by the FFT window boundary information.

*4.3.2. 3 Other Function Block *

Besides band detection, the other three function blocks (packet detection, FFT window detection, and preamble timing detection) can be implemented by applying the same design algorithms of LDPC-COFDM system (from Eq 4.4 to Eq 4.6). However, they still have some differences from LDPC-COFDM system design:

(1) Packet Detection: In LDPC-COFDM system, reduction factor ‘ω’ of normalized auto-correlation algorithm (Eq 4.4) is set to ‘4’ and used two packet sync symbols pairs for threshold comparison. In MB-OFDM system, to save required packet sync symbols, we proposed reduction factor ‘ω’=2 to improve auto-correlator accuracy and only one packet sync symbol pair are sufficient (However, matched-filter still use ‘ω’=4 with 32-tap). Moreover, auto-correlator of LDPC-COFDM packet detection needs to turn on during noise signals until valid packet coming.

But by using dynamic searching window of MB-OFDM system, only some possible window candidates cut by band detection are needed to turn on auto-correlator to check valid packet. We

57

normalized the turn on time of SB-OFDM system to ‘1’ and measures the turn on ratio by adding noise signals with 30 OFDM symbols time duration. In our simulation, the turn on ratio of MB-OFDM system is only 4.76% compared with LDPC-COFDM system.

(2) FFT Window Detection: In LDPC-COFDM system, FFT window detection uses matched-filter to find FFT window boundary during one OFDM symbol time duration (312.5ns).

But for MB-OFDM system, band detection by using dynamic searching window decides band boundary coarsely. Thus matched-filter only need to find the FFT boundary during ±16 samples (60.6ns) from the coarse band boundary, meaning that the turn on time ratio of MB-OFDM system is only 20% of LDPC-COFDM system. Some simulation shows FFT boundary variation probability for coarse timing synchronization (only band boundary information, without matched-filter) and fine time synchronization (FFT-window boundary information, with matched-filter) chapter 5.

(3) Preamble Timing Detection: In MB-OFDM system, time interleaving at three sub-bands makes effective packet sync symbols reduce to 1/3 from LDPC-COFDM system. Therefore, the turn on ratio of MB-OFDM system is only 33% from LDPC-COFDM system also.

58

**CHAPTER 5 **

**CHAPTER 5**

**Simulation Result and Performance Analysis **

**Simulation Result and Performance Analysis**

In this chapter, the simulation result and performance analysis in 802.11a and OFDM-based UWB system is shown. Based on the system platform introduced in chapter 2, framer error rate (FER) of proposed design and packet error rate (PER) of our system between perfect case (FER=0) and proposed design will be compared.

**5.1 Simulation of IEEE 802.11a System **

**5.1 Simulation of IEEE 802.11a System**

Performance of the proposed low-complexity correlation scheme versus number of correlation taps for IEEE 802.11a system is shown in this section. To illustrate the influence of tap reducing, we simulate FER of FFT window detection by assuming perfect packet detection. In wireless communication, frame synchronization may dominate system performance in the lowest data rate. Thus, we claim our FER performance requirement by FIG 5.1. It simulates PER in 6M data rate under perfect frame synchronization (FER=0) in AWGN and IEEE-fading channel, with CFO=200KHz, SCO=40ppm, and delay spread RMS=100ns. FIG 5.1 shows PER reaches 10%

requirement at SNR=2.7dB in multi-path channel, and SNR=0.95 dB in AWGN channel.

Therefore, we claim FER=1% ≦ SNR=1dB in AWGN channel and FER=1% less than SNR=3dB in multi-path channel.

59

**0** **0.5** **1** **1.5** **2** **2.5** **3** **3.5** **4**

**10**

^{-1}**10**

^{0}**6Mb/s: IEEE fading channel** **6Mb/s: AWGN channel**

**SNR[dB]**

**PER **

FIG. 5.1 PER of perfect frame synchronization at 6Mb/s data rate (IEEE-fading channel channel: RMS =100ns, CFO=200KHz, SCO=40ppm)

**-5** **-4** **-3** **-2** **-1** **0** **1** **2** **3** **4** **5**

**10**

^{-4}**10**

^{-3}**10**

^{-2}**10**

^{-1}**N=64 taps**
**N=56 taps**
**N=48 taps**
**N=40 taps**
**N=32 taps**
**N=24 taps**
**N=16 taps**
**N=8 taps**

**SNR[dB] **

**FER**

FIG. 5.2 FER of pure AWGN channel, CFO=0KHz, RMS=0ns

60

**-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10** **10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**N=64** **N=56** **N=48** **N=40** **N=32** **N=24** **N=20** **N=16** **N=8**

**SNR[dB] **

**FER**

FIG. 5.3 FER of IEEE-fading channel: RMS=100ns, CFO=0KHz

**-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10** **10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**N=64**
**N=56**
**N=48**
**N=40**
**N=32**
**N=24**
**N=20**
**N=16**

**FER **

**N=8**

**SNR[dB] **

_{ }

FIG. 5.4 FER of IEEE-fading channel: RMS=150ns, CFO=0KHz

61

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

**10**

^{-4}**10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}

_{N=64}**N=56**
**N=48**
**N=40**
**N=32**
**N=24**
**N=16**
**N=8**

**SNR[dB] **

**FER **

FIG. 5.5 FER of AWGN channel with CFO=20KHz

**-5 -4 -3 -2 -1** **0** **1** **2** **3** **4** **5** **6** **7** **8** **10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**N=64** **N=56** **N=48** **N=40** **N=32** **N=24** **N=16** **N=8**

**SNR[dB] **

**FER **

FIG. 5.6 FER of AWGN channel with CFO=100KHz

62

**-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10** **10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**N=64** **N=56** **N=48** **N=40** **N=32** **N=24** **N=16** **N=8**

**SNR[dB] **

**FER **

FIG. 5.7 FER of AWGN channel with CFO=200KHz

**-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10** **10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**N=64** **N=56** **N=48** **N=40** **N=32** **N=24** **N=20** **N=16** **N=8**

**SNR[dB] **

**FER **

FIG. 5.8 FER of IEEE-fading channel: CFO=20KHz, RMS=100ns

63

**-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10** **10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**N=64** **N=56** **N=48** **N=40** **N=32** **N=24** **N=20** **N=16** **N=8**

**SNR[dB] **

**FER **

FIG. 5.9 FER of IEEE fading channel: CFO=20KHz, RMS=150ns

**-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10** **10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**N=64**

**N=56** **N=48** **N=40** **N=32** **N=24** **N=16** **N=8**

**SNR[dB] **

**FER **

FIG. 5.10 FER of IEEE fading channel: CFO=100KHz, RMS=150ns

64

**0** **0.5** **1** **1.5** **2** **2.5** **3** **3.5** **4**

**10**

^{-2}**10**

^{-1}**10**

^{0}**Perfect sync(FER=0)** **N=64 taps**

**N=32 taps** **N=24 taps** **N=16 taps** **PER=10%**

**SNR[dB]**

**PER **

FIG. 5.11 PER of IEEE fading channel with RMS delay spread=100ns CFO=200KHz, SCO=40ppm

**0** **0.5** **1** **1.5** **2** **2.5** **3** **3.5** **4** **4.5** **5** **10**

^{-2}**10**

^{-1}**10**

^{0}**Perfect sync(FER=0)** **N=64 taps**

**N=32 taps** **N=24 taps** **N=16 taps** **PER=10%**

**SNR[dB] **

**PER **

FIG. 5.12 PER of IEEE fading channel with RMS delay spread=150ns CFO=200KHz, SCO=40ppm

65

FIG 5.2 is the FER performance versus tap number from N=64 to N=8 in AWGN channel. It shows that 32 most significant taps reaches FER=1% at SNR=-5dB and 16 most significant taps reaches 1% at SNR= -2.4dB. Since our system needn’t work at –5dB, ‘N’=16 is sufficient to FFT window detection in AWGN channel. For ‘N’=8, FER=1% at SNR=2dB may degrade system performance in AWGN channel. Furthermore, the SNR loss between ‘N’=16 and ‘N’=8 is more than 4dB. Thus ‘N’=16 is an efficient and reasonable tap number in AWGN channel.

Next, we take multi-path fading channel effect into account. FIG 5.3 and FIG 5.4 are simulation results in IEEE-fading channel with RMS delay spread=100ns and 150ns. As mention earlier, multi-path influences cross-correlation scheme a lot by different arrival paths. The most performance degradation happens to ‘N’=8. Only using most-significant 8 taps for matched-filter to detect FFT window is insufficient to resist multi-path effect, leading FER saturation in 10%.

FIG 5.3 shows ‘N’=16 is sufficient to reach 1% FER in 2.4 dB. But for 150 RMS delay spread, 16 most-significant taps is not robust enough, thus we proposed ‘N’=20 to resist 150ns RMS delay with FER=1% in 2.8dB.

Besides, enormous CFO effect may eliminate correlation characteristics between received signal and matched-filter coefficient because of large linear phase error in time domain. In our receiver data flow, coarse AFC will roughly compensate CFO effect before FFT window detection.

Thus, we simulate FER versus tap number under three different CFO conditions from FIG.5.5 to FIG 5.7. In FIG 5.5, it shows FER versus tap number for a typical coarse AFC compensating CFO

66

effect from 200KHz to ≦ 20KHz as our system platform required. The performance curve of and 20KHz CFO (FIG 5.5) is very similar to 0KHz CFO (FIG 5.2), and SNR loss of ‘N’=16 from CFO=0KHz to 20KHz is only 0.1 dB in FER=1%. It means that with a typical coarse AFC, CFO degrades only a little for the proposed low-complexity correlation scheme. FIG 5.6 is using a coarse AFC with worse performance that compensates CFO effect to≦100KHz. In 802.11a system, performance of cross-correlation algorithm start degrading when CFO effect ≧50KHz [31]. Thus SNR loss of ‘N’=16 from CFO=20KHz to 100KHz will be enlarged to 1 dB. But it still can resist CFO=100KHz to reach FER=1% at –1.2dB, fitting ≦1dB requirement in AWGN channel. FIG 5.7 simulates CFO=200KHz without coarse AGC. In this figure, all the simulated curves can not reach our performance requirement (FER=1% with SNR≦1dB). Without coarse AFC, serious linear phase error distorts received signals and fails FFT-window detection.

Furthermore, tap number ‘N’ from 24 to 16 have better performance than N=64 to 32 in CFO=200KHz. Since received data corresponding to less-significant taps are distorted by CFO, thus correlation result will be interfered. Only using 16 most-significant taps may obtain more accurate correlation value than using all the taps of matched filter at this circumstance.

TAP Number **64 56 48 40 32 24 20 16 8 **

CFO=0KHz (dB) **-3.4 -3.4 -3 -2.4 -1.7 -0.2 1 2.3 Fail **

CFO=20KHz( dB) **-3.4 -3.2 -2.9 -2.2 -1.5 -0.1 1.1 2.6 Fail **

SNR loss (FER=1%) **0 0.2 0.1 0.2 0.2 0.1 0.1 0.3 X **

TABLE 5.1 SNR loss from CFO=0 to 20KHz at IEEE fading channel delay spread=100ns.

67

TAP Number **64 56 48 40 32 24 20 16 8 **

CFO=0KHz (dB) **-2.4 -2.3 -2.1 -1.3 -0.5 1 2.8 5 Fail **

**CFO=20KHz (dB) -2.4 -2.2 -1.9 -1.2 -0.3 1.1 3.1 5 Fail **

SNR loss (FER=1%) **0 0.1 0.2 0.1 0.2 0.1 0.3 0 X **

TABLE 5.2 SNR loss from CFO=0 to 20KHz at IEEE fading channel delay spread=150ns

TAP Number **64 56 48 40 32 24 16 8 **

CFO=0KHz (dB) **-2.4 -2.3 -2.1 -1.3 -0.5 1 5 Fail **

CFO=100KHz (dB) **0 0.1 0.6 2 3.1 5 10 Fail **

SNR loss (FER=1%) **2.4 2.4 2.7 3.3 3.6 4 5 X **

TABLE 5.3 SNR loss from CFO=0 to 100KHz at IEEE fading channel delay spread=150ns

We simulate FER versus tap number by considering both CFO and multi-path effect from FIG 5.8 to FIG 5.10. FIG 5.8 is the typical case for IEEE fading channel delay spread=100ns and residue CFO=20KHz compensated by coarse AFC. It shows that ‘N’=16 can achieve 1% FER requirement at 2.6dB. FIG 5.9 simulates condition of worse multi-path effect with RMS delay spread=150ns. This case is similar to FIG 5.4 that resisting RMS delay=150 ns with N=’20’.

Maximum SNR loss between CFO=0KHz and CFO=20KHz listed in TABLE 5.1 (RMS delay=100ns) and TABLE 5.2 (RMS delay=150ns) is ≤ 0.3 dB. FIG 5.10 is the simulation in worst case of our system for IEEE fading channel delay spread=150ns and residue CFO=100KHz with a low performance coarse AFC. In such serious interference, performance degradation is highly

68

dependent on tap number ‘N’, as TABLE 5.3. We suggest ‘N’=32 for our proposed scheme to reach FER=1% in SNR=3.1dB in such harmful channel condition.

FIG 5.11 and FIG 5.12 is the PER simulation of our system with CFO=200KHz, SCO=40ppm, and IEEE fading channel for different RMS delay spread. It shows that for 100ns RMS delay spread (FIG 5.11), SNR loss between perfect synchronization (FER=0) and using the most 16 significant taps is 0.35dB in 10% PER. Comparing simulation curve of total 64 taps and the most 16 significant taps, 75% correlation complexity can be reduced with 0.3dB SNR loss for 10% PER as trade off. However with 150ns RMS delay spread (FIG 5.12), SNR loss between perfect synchronization and the most 16 significant taps increases to 1dB and begin to dominate system performance. Another curve for using 20 most significant taps only results 0.5dB loss for 10% PER compared with the ideal case. Thus ‘N’=20 is more suitable than ‘N’=16 to resist RMS delay spread=150ns, similar to our FER simulation result.

Although the proposed scheme can efficiently save complexity of matched-filter used for FFT window detection with less performance degradation, it still decreases the ability to resist multi-path interference. According to our simulation result, the most 16 significant taps is sufficient to resist IEEE fading channel with RMS delay=100ns. Considering design margin in general, we proposed using the most 20 significant taps scheme since it is sufficient for IEEE fading channel with RMS delay=150ns for only 0.5dB SNR loss for 10% PER.

69

**5.2 Simulation Result of LDPC-COFDM System **

**5.2 Simulation Result of LDPC-COFDM System**

**5.2.1 Frame Error Rate of Tap-Reduction Scheme **

In the proposed design, tap-reduction scheme reduces correlation taps for low-complexity improvement. The trade-off is performance degradation for synchronizer FER. Therefore, a reasonable reduction factor ‘ω’ is needed to save computation cost with acceptable performance loss. In this section, we first discuss FFT window detection versus different number of taps used for matched-filter, then adding auto-correlation scheme (packet detection and preamble timing detection) for our analysis.

**-3** **-2** **-1** **0** **1** **2** **3** **4** **5**

**10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**Tap=128 (conventional)**

**Tap=64**

**Tap=32 (proposed)**
**Tap=16**

**Tap=8 (fail detection)**

**SNR[dB] **

**FER **

FIG. 5.13 Tap number versus FFT window detection

Condition: Multi-path channel RMS delay spread=5ns [21], CFO=400KHz

70

FIG 5.13 is the frame error rate of FFT window detection under perfect packet detection and preamble timing detection. Similar to 802.11a, we require FER=1% for SNR≦3 dB in multi-path channel. The simulation circumstance is Intel channel model proposed in [21] with RMS delay spread=5 ns, CFO=400KHz with AFC compensating to ≦100KHz. It shows that ‘ω’=4 reaching 1% FER in 0 dB SNR can meet our requirement. For ‘ω’=8, FER converges a little slowly and reaches 2% FER in 5dB; ‘ω’=16 fails the detection with too much performance loss.

**-2 -1** **0** **1** **2** **3** **4** **5** **6** **7** **8** **9 10**

**10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**'w'=1, (conventional)** **'w'=2, **

**'w'=4, (proposed)** **'w'=8, (fail design)**

**SNR[dB] **

**FER **

FIG. 5.14 Tap-number versus Framer Synchronizer

Condition: Multi-path channel RMS delay spread=5ns [21], CFO=400KHz

FIG 5.14 is the performance of frame synchronizer versus tap-reduction scheme for different parameter ‘ω’ (with AFC compensating to ≦100KHz). The main function of packet

detection and preamble timing detection is auto-correlation scheme, which is sensitive to high AWGN noise, and it degrades FER about 2 to 3 dB compared with FIG 5.13. However, the

71

proposed design with ‘ω’=4 still can reach our performance requirement in FER=1% at SNR=2.1dB. For ‘ω’=8, it will be a failed design since frame error rate converges slowly and seriously degrades system performance. The FER degradation from the conventional (‘w’=1) to the proposed (‘ω’=4) design is about 2.5dB in FER=1%. But for our system, the proposed frame synchronizer results only a little loss for 8% PER as FIG 5.15. From FIG 5.15, simulation curve of

‘ω’=8 results in synchronization loss more than 3dB SNR for 8% PER from simulation curve of

‘ω’=4, seriously degrades system platform. On the other hand, synchronization loss of ‘ω’=4 for 8% PER is < 0.4dB SNR compared with perfect synchronization. Therefore, we propose ‘ω’=4 to reduce matched-filter complexity. By setting ‘ω’=4,the proposed design can save 75% correlation complexity which greatly reduce area cost of matched-filter and auto-correlator from conventional design.

**1** **2** **3** **4** **5** **6** **7** **8** **9** **10**

**10**^{-1}**10**^{0}

**PER**

**120Mb/s perfect Sync**

**120Mb/s w=1 (conventional)**
**120Mb/s w=4 (proposed)**
**120Mb/s w=8 (poor design)**
** PER=8%**

**SNR[dB]**

FIG. 5.15 Tap-number versus PER

Multi-path channel RMS delay spread=5ns [21], CFO=400KHz, SCO=40ppm

72

**-3** **-2** **-1** **0** **1** **2** **3** **4** **5**

**0**
**0.05**
**0.1**
**0.15**

**0.2** **Simulated value to achieve lowest error rate**
**Mean threshold value of proposed design**

**SNR[dB] **

FIG. 5.16 Simulated threshold value of preamble timing detection Multi-path channel: RMS delay spread=5ns [21], CFO=400KHz

**-3** **-2** **-1** **-1** **0** **1** **2** **3** **4** **5**

**10**

^{-3}**10**

^{-2}**10**

^{-1}**10**

^{0}**Fixed threshold value=0.02**
**Fixed threshold value=0.04**
**Fixed threshold value=0.06**
**Fixed threshold value=0.08**
**Fixed threshold value=0.1**
**Proposed Dynamic threshold**

**SNR[dB] **

FIG. 5.17 Performance of dynamic and fixed threshold design Multi-path channel: RMS delay spread=5ns [21], CFO=400KHz

**Thr** **es** **h** **old val** **ue ** **E** **rro** **r D** **ec** **isi** **on** ** R** **at** **e **

73

**5.2.2 Performance of Dynamic Threshold **

In preamble timing detection, since auto-correlation result has different probability distribution in different channels, the pre-defined threshold to reach lowest error probability will vary with environment conditions. In FIG 5.16, we simulate the threshold value to reach lowest error probability (curve with squarer mark) in multi-path channel with RMS delay =5ns and CFO400KHz from –3 to 5 dB. Because auto-correlation scheme is highly sensitive to AWGN, the simulated threshold value changes a lot with different SNR regions. Another simulation curve is the mean value of proposed dynamic threshold (10000 packets for each SNR). It shows that by tuning the constant factor ‘ε’ properly in Eq 4.10, the dynamic threshold design can approach the simulated threshold value of lowest error probability with different SNR regions. Therefore, the dynamic threshold will have better performance than the conventional fixed threshold design by automatic varying its threshold according to channel conditions.

FIG 5.17 is the error decision probability of preamble timing detection for fixed threshold in some values and proposed dynamic threshold. In fixed-threshold design, each threshold value curve has low error decision rate only in a few SNR regions. For example, “threshold value=0.04”

has low error decision rate from -3 to -1 dB (low SNR region). On the other hand, “threshold value=0.1” has low error decision rate from 4 to 5 dB (high SNR region). However, the proposed dynamic threshold can have lower error decision rate from -3 to 5 dB (suitable for both high or low SNR region). Thus it can have lower error decision probability for much larger SNR regions compared with the conventional fixed threshold design setting at certain value.

74

**5.2.3 System Performance **

Simulation of our system for perfect synchronization and proposed design (‘ω’=4) is shown as FIG 5.18 and FIG 5.19. We focus on 8% PER [8] for performance loss comparison at the three supported data rates (120M, 240M, 480M b/s). FIG 5.18 simulates in pure AWGN channel and performance loss between perfect synchronization and proposed design is less than 0.1dB SNR for the three supported data rates. FIG 5.19 simulates in multi-path channel with 5ns RMS delay

Simulation of our system for perfect synchronization and proposed design (‘ω’=4) is shown as FIG 5.18 and FIG 5.19. We focus on 8% PER [8] for performance loss comparison at the three supported data rates (120M, 240M, 480M b/s). FIG 5.18 simulates in pure AWGN channel and performance loss between perfect synchronization and proposed design is less than 0.1dB SNR for the three supported data rates. FIG 5.19 simulates in multi-path channel with 5ns RMS delay