Impulsive Interference

Impulsive interference is a variety of naturally occurring and man-made phenomena exhibit impulsive behavior. A sentence that summarizes the chaotic nature of impulsive interference is “no two impulsive events are the same”. There are many potential sources of impulsive interference [12]:

1500 1510 1520 1530 1540 1550 1560 1570 1580

0.06

Instantanous Impulse Response of Sample Clock Offset SCO 0 ppm SCO 400 ppm SCO 1000 ppm SCO 10000 ppm

1. House appliances (washing machine, dish washer, food mixer, iron, oven, kettle, electric razor, drill, microwave oven, etc.).

2. Central heating thermostats.

3. Light switches (fluorescent, incandescent, etc.).

4. Ignition systems (traffic, lawn mower, etc.).

Based on [12], [13], [14], a set of impulsive interference models are modeled as a train of pulses.

i i

n(t)= A ( )

wi i

P t−τ

∑

^(2.7)

where the amplitude A , duration _i W and arrival time _i τ_i of each pulse is a random variable whose distribution is a priori unknown.

Figure 2-11: Parametric model for impulsive interference

Figure 2-12: Interference impulsive model of Cooker ignition

0 1000 2000 3000 4000 5000

0 0.5 1 1.5 2 2.5 3 3.5 4

Time (ns)

Receiver Power (dB)

Instantaneous Impulse Response of Cooker ignition

Chapter 3

Proposed Algorithm

N this chapter, a synchronization algorithm is proposed. The 4*4 MIMO-OFDM system with complicated channel model is aimed. The proposed synchronization scheme is shown in Figure 3-1.

The packet synchronization, it contains two parts: packet detection and symbol boundary detection, which simultaneously perform the correlation and detection is shown in the section 3.1. While doing the packet detection, the symbol boundary detection must be done to determine the starting of the symbol. The packet synchronization only uses first two preambles.

In section 3.2, the timing synchronization which gets the boundary coefficients form symbol boundary detection uses only one preamble (the third L-STS) by the sharing resource scheme. One symbol locked sampling acquisition, which measures received power under different sampling phases, is proposed not only to achieve the half sampling rate with large tolerant range, but also to get a “good” sampling phase.

Packet

Packet Synchronization Timing Synchronization

Figure 3-1: The proposed Synchronization Flow

I

3.1 Packet Synchronization

3.1.1 Packet Detection 3.1.1.1 Decision Variable

Consider with the AWGN channel first, we denote the k transmitted signal _th from the j transmit antenna as _th S k , the _j( ) k received time domain signal at the _th

i receive antenna as th R k , and the additive white Gaussian noise between the _i( ) j _th transmit antenna and the i receive antenna as _th N . When a transmitted signal is _ij presented

( )R_i =S k_j +N_ij (3.1)

otherwise,

( )R k_i =N_ij (3.2)

As pointed out before, L-STS can be used for packet detection. Because of the preamble has a repetitive structure, auto-correlation method will produce a useful decision statistic.

Based on algorithm in [9], assume the preamble repeats itself every L samples, the auto-correlation between the first and second L samples is

1

The received power for the second L samples is

2

And the decision variable on the i receive antenna is _th

2

Based on L received samples, we compared three methods to combine u to a _i stable u:

15

B. Geometric mean method:

4

C. Root-mean-square method:

4 2

A. Mean method B. Geometric mean method C. Root-mean-square method

Figure 3-2: u distribution under different method _i

The result of different method under the same channel condition is shown in Figure 3-2. Before a packet is detected, those are called leading noises. Symbol location defines the different of signal and noise, in general positive means signal is presented and negative means noise is presented.

At symbol location is zero, the (2L-1) samples are all noises except the least one.

Both mean and RMS method have unexpected peak which may cause by correlation buffer full of both noises and signal. It will make packet detection complexity higher and less reliable. As a result, the geometric mean method is chose.

3.1.1.2 Detection Algorithm

The set of samples ( (f R k L_{i i} − +1), (R k L_i − +2), (R k L_i − +3),... ( ))R k_i formed the decision variable u is depend on the decision window of size L. The decision _i variable u is calculate by the four u . Finally the _i u is compared to a preset

threshold u in the following hypothesis test: _Th H , packet is present if 1 u u> _Th; H , packet is not present if 2 u u≤ _Th.

We stack the received signal for 2L samples, use equation (3.7) to calculate u. At the beginning of packet detection, we start with the state No Peak. If H is true, ₁ the state change to Finding Maximum Peak.

There are two cases in the state Finding Maximum Peak. One is that if H is ₁ true, every time u exceeds the threshold u the peak count will increase by 1, and _Th once if peak count exceeds the threshold Peak , which means packet is already _Th detected, the state change to End Detection. The other is that once H is true, the ₂ state change to Temporary accordingly.

In the state Temporary, if H is true, every time ₂ u under the threshold u _Th the no peak count will increase by 1, and once if no peak count exceeds the threshold NoPeak , which means packet is not presented (it might be noise or interference Th

impulsive), the state change back to No Peak. On the other hand, if H is true, the ₁ state change to Finding Maximum Peak and reset some parameters which includes peak count and no peak count to zero.

Figure 3-3: The flow chart of the packet detection algorithm.

17

3.1.2 Symbol Boundary Detection 3.1.2.1 Definition

In an OFDM system, PL complex signal symbols are modulated onto PL

sub-carriers by using the inverse fast Fourier transform (IFFT) on the transmitter side.

The last Pc IFFT samples are used to form a guard interval (GI) that is inserted at the beginning of each OFDM symbol.

Symbol Figure 3-4: FFT symbol window

The misplaced FFT window can cause two different kinds of behaviors. First, the misplaced FFT window including the parts of the GI of the symbol is the case 1 as shown in Figure 3-4. In this case, the P^th FFT window has reordering alignment that means cyclic shift in time domain. It will produce frequency error in frequency domain and this effect can be compensated by equalization [8]. Second, the misplaced FFT window is the case 2 as shown in Figure 3-4, the P^th FFT window not only has the current symbol P but also includes a part of GI^P+1. In this case, the P^th FFT window has information lose, and the GI^P+1 will cause inter-symbol interference (ISI) which cannot be recovered.

After the packet detection has provided an estimate of the start point of the packet, the symbol timing algorithm revise the estimate precision to achieve sample level which align the correct position of FFT symbol.

3.1.2.2 Detection Algorithm

First, we get the 2L samples of received signal for packet detection. In the other word, when a packet is presented change to the state End detection, while using those 2L samples of received signal in correlation buffer. Generally, those samples are mixed with noise and a part of L_STS. Therefore, an appropriately u is chose to _Th

ensure using the specific number of L_STS in correlation buffer.

This refinement is performed by calculating the parallel cross-correlation of the received signal R k and the known short training sequence _i( ) Q k to be reference. ( ) Figure 3-5 shown the proposed symbol boundary detection architecture, the algorithm includes 6 steps:

Step 1. By using the repetitive property of L_STS, we define a L x B matrix of ( )

Step 2. An appropriate correlation window size B is chose and it must be smaller than the packet detection correlation window L.

Step 3. The parallel cross-correlation with each Q k indicate the correlation _L( ) power P k . _{i L,} ( )

Step 5. Combining the Symbol^ˆ _index and the timing of packet detected; we can easily know the symbol timing and the right FFT symbol window.

Step 6. Using the correct symbol index, left and right neighbors that those provide for timing synchronization are defined as follow:

19

Data Stack Buffer of Size L

short training Figure 3-5: The proposed symbol boundary detection architecture

3.2 Timing Synchronization

3.2.1 Coarse Timing Synchronization 3.2.1.1 Basic Assumption

In this section, we introduce timing synchronization scheme. First, we consider with the boundary correlation buffer (BCB) fill with ideal short training sequence. We define Q k , ₁( ) Q k , and ₂( ) Q k by equation (3.9), and set the BCB initial as ₃( )

2( )

Q k . From equation (3.10), P k , _i,1( ) P k , and _i,2( ) P k are calculated. Proposed _i,3( ) correlation architecture is shown as in Figure 3-6.

It apparent that P k is much higher than _i,2( ) P k and _i,1( ) P k since the BCB _i,3( )

is exactly the same as Q k . ₂( ) P k and _i,1( ) P k should be the same because of _i,3( ) each of them has B− samples in common with 1 Q k . ₂( )

Figure 3-6: Proposed correlation architecture

On further consideration, we define φ_ini as phase error which might cause by channel effect like AWGN, mutipath, CFO, SCO …etc. When φ_ini =2π means signal is misplaced for one sample (delay one sample). In other word, the signals inside BCB are exactly the same as Q k , and result in ₃( ) P k become the highest _i,3( ) one. When φ_ini = −2π also means that signal is misplaced for one sample (early one sample). Similarly, the signal inside BCB is exactly the same as Q k , and result in ₁( )

,1( )

P k become the highest one. The correlation between i P and phase error is _{i L,} shown as in Figure 3-7.

Take consideration with 4*4 MIMO-OFDM system with 64 QAM modulation and TGn channel E (RMS=100ns, Tap=15). The relation of boundary coefficients is shown in Figure 3-8. A multiphase generator is used to generate 22 phases.

21

Correlation

Figure 3-7: Correlation between P and Phase error _{i L,}

-21 -19 -17 -15 -13 -11 -9 -7 -5 -3 -1 0 1 3 5 7 9 11 13 15 17 19 21 0

50 100 150

Phase (sample)

Correlation coeffocoent(Boundary)

Boundary_i1 Boundary_i2 Boundary_i3

Figure 3-8: The boundary coefficient distribution (Packet no. = 1000)

3.2.1.2 Decision Region

As shown in Figure 3-7, different relationships between P can be divided into _{i L,} four regions. The different condition of each region is described as follow:

Rough Forward (RF) Region: P k is the highest one means the sampler _i,1( ) sampled too early, φ_ini > − . In other word, we need to enlarge phase different π of sample, equivalent to decrease sampling rate quickly. So that in this region we rotate the phase by π , φ π₁= .

Smooth Forward (SF) Region: P k is the highest, and _i,2( ) P k > _i,1( ) P k _i,3( ) , 0>φ_ini > − . In other word, we still need to enlarge phase different of sample, π but to decrease sampling rate slowly. In this region we rotate the phase by

2 π ,

1 2

φ = . π

Smooth Backward (SB) Region: P k is the highest, and _i,2( ) P k_i,1( )≤P k _i,3( ) , 0<φ_ini < . In other word, we need to narrow phase different of sample, π equivalent to increase sampling rate slowly. In this region we rotate the phase by

2

− , π ₁ 2 φ = − . π

Rough Backward (RB) Region: P k is the highest one means the sampler _i,3( ) sampled too slow, φ_ini > . In other word, we still need to narrow phase different π of sample, but to increase sampling rate quickly. So that in this region we rotate the phase by −π, φ₁= − . π

As mentioned before, after symbol boundary detection there are three boundary coefficients are passed to timing synchronization. Base on the relation of three boundary coefficients, a region is decided. The first rotation angle is decided by the region. After the rotation, the phase error will be:

23

1

1

, if in Rough Region;

, if in Smooth Region.

2

rot ini ini

rot ini ini

φ φ φ φ π

φ φ φ φ π

= + = ±

= + = ± (3.15)

3.2.1.3 Decision Algorithm

After the first rotation, it came out three new P , named as _{i L,} P rot . These _ _{i L,}

_ _{i L},

P rot index a new region. By the regions of the two sets of boundary coefficients

we estimation the phase error after rotated φ_fin.

From RF Region to RF Region:

In this case, it appears at φ_ini = −2π and after rotated π result in φ_rot = − π (see Figure 3-9). There still need one rotation to make phase error zero. φ₂ = , π

2

fin rot

φ =φ + . φ

φ

ini

Ideal phase

φ

2

φ

fin

Figure 3-9: From RF Region to RF Region diagram

From RF Region to SF Region:

In this case, as shown in Figure 3-10, initial phase had phase error φ_ini and P _{i L,} located on red line, and after first rotation the phase became φ_rot and P rot _ _{i L,} located on blue line. Assumeφ_rot = − , and φ₂ φ_rot =φ_ini+ , from the π P and the _{i L,}

_ _{i L},

P rot we can calculate the second rotation angle by followed equations:

,2 ,1

Figure 3-10: From RF Region to SF Region diagram

25

From SF Region to SF Region:

In this case, as shown in Figure 3-11, initial phase had phase error φ_ini and P _{i L,}

P rot , we can calculate the second rotation angle by followed equations:

2 ,2 .1

Figure 3-11: From RF Region to SF Region diagram

From SF Region to SB Region:

In this case, as shown in Figure 3-12, initial phase had phase error φ_ini and Boundary located on red line, and after first rotation the phase became ix φ_rot and

_ _ix

Boundary rot located on blue line. Assumeφ_rot = , and φ₂

rot ini 2

φ =φ + , from the π

Boundary and the ix Boundary rot we can calculate the second rotation angle by _ _ix followed equations:

( )

Figure 3-12: From RF Region to SF Region diagram

27

From SB Region to SF Region:

The φ₂ is the same as φ₂ in equation(3.25), but φ_rot = − . φ₂ From SB Region to SB Region:

The φ₂ is the same as φ₂ in equation(3.22), but φ_rot = . φ₂ From RB Region to SB Region:

The φ₂ is the same as φ₂ in equation(3.18), but φ_rot = − . φ₂ From RB Region to RB Region:

It appear at φ_ini =2π and after rotated −π result in φ_fin = . π

The flow chart is shown in Figure 3-13. The first rotation depends on the initial region, and the second rotation depends on the calculation.

Second Rotation Start

Compare {Pi,D-1, Pi,D, Pi,D+1}

RF SF SB RB

RF SF SF SB SF SB SB RB

Calculate Phase error Φ2

Compare {Pi,D-1, Pi,D, Pi,D+1} & {P_roti,D-1, P_roti,D, P_roti,D+1} Rotate

π

Rotate π/2

Rotate -π/2

Rotate -π

End

Figure 3-13: The flow chart of the proposed coarse timing synchronization

3.2.2 Fine Timing Synchronization

In real systems, channel effect is much complicated. The correlation between

,

P and phase error might not as smooth as the model, neither does the correlation i L

between P and _{i L,} P rot . To make a better phase error estimation, we need to do _ _{i L,} fine timing synchronization to confirm:

As mention before, we have Rotated ini_ _D with phase error φini,Rotated rot with phase error _ _D φ_rot, andRotated_ fin with phase error _D φ_fin.

Rotated is calculated to get D E_phase by equation(3.26). E_phase finds the better phase which suppose to be Rotated_ fin by three rotated value. If it is not, means _D we need to modify the estimated phase error φ_fin.

Start Figure 3-14: Modification of phase error φ^fin

Chapter 4 Simulation

E use simulation to evaluate the receiver’s performance both in the AWGN channel and in a Rayleigh fading channel with additional channel effect. In the AWGN channel, as equation(3.1) mention before,

i j( ) ij

R =S k +N ; On the other hand, in the Rayleigh fading channel with additional channel effect, we can express the received signal sample as:

(

^{( ) ( , ) *}

)

^{i(2 ft ) sin (( n) ) ( ) ( )}

i j ij ij ij

k T n

R S k H k e c N k I k

k

π θ

τ ^{Δ + − Δ}

= ⊗ ∗ + + (4.1)

Where the H k is the multipath with time-variant model, the exponential term is _ij( )

CFO effect, the sinc part is SCO effect, N k is AWGN, and ( )_ij( ) I k is impulsive _ij interference.

4.1 Simulation Platform

MATLAB is chosen as simulation language, due to its ability to mathematics, such as matrix operation, numerous math functions, and easily drawing figures. A MIMO-OFDM system based on IEEE 802.11n Wireless LANs, TGn Sync Proposal Technical Specification [7], is used as the reference simulation platform. The major parameters are shown in Table 4-1.

W

Table 4-1 Simulation parameters

PSDU Length 1024 Bytes Carrier Frequency 2.4 GHz

Bandwidth 20 MHz

IFFT / FFT Period 3.2 sμ

4.2 Simulation Result

4.2.1 Packet Synchronization Simulation Condition

In this section, the simulation environment is as follow:

Table 4-2 Packet synchronization simulation condition Condition Value

T-variant Jakes model

Velocity 60 km/hr

Interference Cooker ignition Burst Duration

( pulses per burst) 20 Pulse Spacing 1.5 0.5 s± μ

SIR -10 dB

31

4.2.1.1 Packet Detection

Figure 4-1 present the symbol location when packet detected under different SNR condition. The symbol location indicates the start of packet. A negative symbol location means packet is not present; there is only so-called leading noise.

When SNR<0, the packet detection shows false alarm, including detected at wrong time or detected when there is no packet, and the range of detection is too wide to be reliable. When SNR>0, the range of detection become narrow down to be acceptable one and the packet detection become more reliable.

-5 0 5 10 15 20 25 30

Figure 4-1: Packet detection distribution versus different SNR

48 49 50 51 52 53 54 55 56 57

Figure 4-2: The probability of packet detection under SNR 0

4.2.1.2 Symbol Boundary Detection

Figure 4-3 present the sample location when packet detected under different SNR condition. The packet and the symbol boundary are detected simultaneously.

Symbol location shows the packet start timing and similarly sample location help us to locate the symbol boundary. A multiphase generator is used to generate 22 different phases between one clock cycle, in other word, it means sample location is symbol location to multiply 22.

When SNR<5, because of the connection between packet detection and symbol boundary detection, symbol boundary detection suffer serious index errors due to packet detected errors, including packet loss (SNR<0) and packet detection false alarm (SNR<5) and weak signal power (as shown in Figure 4-4).

When SNR>5, the decrease of the packet detected errors result in the symbol boundary detection errors reduce apparently. We can also know from Figure 4-3 and Figure 4-4, the range of symbol boundary detection become narrow down to be acceptable one when SNR>5.

Figure 4-3: Symbol boundary detection distribution versus different SNR -5 0 5 10 15 20 25 30 500400

700600 900800

10000 20 40 60 80 100

SNR (dB) Sample Location

Probability (%)

33

Figure 4-4: Symbol index error analysis

4.2.1.3 Packet Synchronization

Figure 4-5 present the system performance of packet synchronization with two different channel types. One is AWGN channel; it means the channel suffer from only AWGN. The other is complex channel; the condition of complex channel is described in section 4.2.1.

The legend “Packet sync. on” means the performance of the proposed packet synchronization algorithm. Relatively, “Packet sync. off” means the performance of the ideal packet synchronization, including ideal packet detection and ideal symbol boundary detection, that is, to know exactly the timing of packet start and send the exactly correct symbol into FFT.

In AWGN channel, the proposed algorithm and the ideal packet synchronization have the similar curves; they have almost the same performance. In Complex channel, although the curves are not smooth, basically they are still similar. Eventually the result in about 2.7dB lost when PER <0.1, but it may be cause by using too few packet numbers in the simulation.

-5 0 5 10 15

14 16 18 20 22 24 26 28

Figure 4-5: System performance of packet synchronization under AWGN and Complex channels

4.2.2 Timing Synchronization

As mention before, the multiphase generator is used to generate 22 phases between one clock cycle. In other word, the phase error 22 means that signal is delay one cycle, and the phase error 0 means that sign is at ideal phase.

With different initial phase errors, after timing synchronization, including coarse and fine timing synchronization, the final phase errors are convergence into 2 phases.

As shown in Figure 4-6.

Figure 4-6: The final phase errors with AWGN and Multipath (TGn E)

35

First, consider with the 4*4 MIMO-OFDM system with 16 QAM modulation and TGn channel D (RMS=50ns, Tap=8). The performances are shown in Figure 4-7.The legend ideal sampling means to get each sample at right phase (phase error 0).

One symbol locked sampling means use the proposed algorithm in section 3.2 with an unknown initial phase errors to get sample.

Figure 4-7-(a) shows the required SNR for 10% PER is 16 dB, lost about 0.2 dB when compare with the ideal sampling. Take the SCO effect into consideration, the required SNR for 10% PER with SCO 200 ppm is about 16.7dB, lost about 0.7 dB when compare with no SCO effect. Figure 4-7-(b) shows the proposed algorithm can tolerance SCO effect about 200 ppm.

Figure 4-8 present the performance of 4*4 MIMO-OFDM system with 16 QAM modulation and TGn channel E (RMS=100ns, Tap=15). Figure 4-8-(a) shows the required SNR for 10% PER is 25 dB, lost about 1.6 dB when compare with the ideal sampling. Take the SCO effect into consideration, the required SNR for 10% PER with SCO 200 ppm is about 27dB, lost about 2 dB when compare with no SCO effect.

Figure 4-8-(b) shows the proposed algorithm can tolerance SCO effect about 200 ppm.

In Figure 4-8-(b) the required SNR for 10% PER with SCO 200 ppm is about 26dB, instead of 27 dB in Figure 4-8-(a). It could be cause by not enough packets since the curve is not smooth Figure 4-8-(a) or specific initial phase errors.

Then, consider with the 4*4 MIMO-OFDM system with 64 QAM modulation and TGn channel D (RMS=50ns, Tap=8). The performances are shown in Figure 4-9.

Figure 4-9-(a) shows the required SNR for 10% PER is about 20.5 dB, lost about 0.8 dB when compare with the ideal sampling. Take the SCO effect into consideration, the required SNR for 10% PER with SCO 200 ppm is about 22dB, lost about 1.5 dB when compare with no SCO effect. Figure 4-9-(b) shows the proposed algorithm can

Figure 4-9-(a) shows the required SNR for 10% PER is about 20.5 dB, lost about 0.8 dB when compare with the ideal sampling. Take the SCO effect into consideration, the required SNR for 10% PER with SCO 200 ppm is about 22dB, lost about 1.5 dB when compare with no SCO effect. Figure 4-9-(b) shows the proposed algorithm can

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