Chapter 2 System Platform
2.3 CW Jamming Model
When signals ( )s t are transferred from transmitters through channels, they are interfered by white Gaussian noise n t . Furthermore, before receivers receive ( ) signals, they are interfered by other intentional or an unintentional CW jamming ( )i t which experiences a fading channel h tj( ), the received signals are expressed as the
following:
( ) ( ) ( ) ( ) j( ) .
r t =s t +n t +i t ⊗h t (6) where the symbol ⊗ represents convolution.
When jammers are delivered by a stable carrier, they are called as continuous-wave (CW) jamming. The jamming has their own changing rate (CR) which is denoted as how long transmitted data bit changes per second. Generally speaking, if the ratio of changing rate and system bandwidth is not greater than 1
30, CW jamming is called as narrowband interference. Changing rate will decide
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change its value and keep its value for a period of time. Depending on different values of amplitude rate and phase rate will directly the amplitude and the phase of the jamming in the time domain and indirectly change the waveform of the jamming in the frequency domain which makes their fractional power containment bandwidth adopted by FCC become rougher and interfere with more subcarriers of MIMO-OFDM systems.
In this paper, both single-tone continuous-wave jamming and multi-tone continuous-wave jamming with QPSK modulation are introduced.
1. Single-Tone Continuous-Wave Jamming The mathematical equation is expressed as
( ) cos(2 I) sin(2 Q) ,
i t =A⋅ π ft+θ +B j⋅ π ft+θ (7)
where A 、 B represent the amplitude of in-phase and quadrature-phase path of a jammer, f represents the carrier frequency of a jammer, θ θI, Q represent the phase offset of in-phase and quadrature-phase path of a jammer respectively.
2. Multi-Tone Continuous-Wave Jamming The mathematical equation is expressed as
, ,
where A 、n Bn represent the amplitude of in-phase and quadrature-phase path of the nth jammer, fn represents the carrier frequency of the nth jammer, θI n, ,θQ n, represent the nth phase offset of in-phase and quadrature-phase path of the nth jammer.
For single-tone continuous-wave jamming and multi-tone continuous-wave jamming, parameters of them, frequency, amplitude and phase, satisfy with the following below:
random frequency: 0MHz≤ fc ≤20MHz. random amplitude A: 2+B2=1.
random phase: 10− ° ≤θ θI, Q≤10 .°
Figure 2-8 presents that CW jamming changes in time domain according to different changing rates (CR). Figure 2-8 CW jamming in Time Domain. (a)CR=133k. (b)CR=667k.
Figure 2-9 shows that MATLAB is used to simulate single-tone continuous-wave Jamming. It illustrates that the change of main lobe of the jamming in frequency domain depends on the condition of amplitude rate and phase rate. The main bandwidth occupied by the main power of CW jamming is about the quarter of 20 MHz. For 20MHz OFDM systems, CW jamming is narrowband interference.
The simulation environment is the following: Modulation：4X4, 64QAM, signal to jamming ratio (SJR)：-10 dB, CW tone number：1, changing rate：33k bps. Figure 2-10 represents the 2D floor plan of the first, fifth and thirty-five symbols of Figure 2-9 and it clearly shows that the bandwidth range occupied by their main lobes are different.
Figure 2-11 shows the effect of CW jamming on OFDM systems.
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Figure 2-9 X axis : frequency , Y axis : # of symbol , Z axis :magnitude. CW jamming in Frequency Domain (3D).
Figure 2-10 CW jamming in Frequency Domain (2D).
-1.5 -1 -0.5 0 0.5 1 1.5
Figure 2-11 16QAM constellation, SNR=25dB, with TGN E. (a)Without CW Jamming. (b)With CW Jamming, SJR=-10dB.
Chapter 3
Analysis and Methods
In this chapter, FD-IQME is proposed to solve I/Q mismatch by using short preamble based on the IEEE 802.11n standard. Then, some analysis for CW jamming form different aspects are presented; some methods for IQM under CW jamming are suggested.
Section 3.1 describes I/Q mismatch estimation in frequency domain. CW jamming will be analyzed from different aspects, including the amplitude, phase, power, and the ratio between CW jamming and preamble patterns in section 3.2. CW jamming detection is described in section 3.3. In section 3.4, one anti-jamming method is suggested to solve I/Q mismatch and CW jamming under some assumptions, but it is impractical enough. Peak-Avoidance Method (PEAM) and Averaging Method in Time Domain (TD-AVM) are introduces in section 3.5 and section 3.7; a smooth filter is proposed for getting accurate CFR in section 3.6. Finally, the Proposed Algorithm of I/Q Estimation with CW Jamming is depicted step by step in section 3.8.
3.1 I/Q Mismatch Estimation in Frequency Domain (FD-IQME)
In MIMO-OFDM system, the packet format based on the IEEE 802.11n is shown as Figure 2-5. The legacy short training (L-STF) and legacy long training OFDM symbol (L-LTF) are identical to the 802.11a short training and long training OFDM symbol. The high-throughput long training OFDM symbols (HT-LTF) are transmitted after one high-throughput short training OFDM symbol (HT-STF). For any PPDU, the number of HT-LTF is the same as spatial streams in the HT Data portion of the PPDU.
Each HT-LTF consists of one legacy Long Training Symbols (LTS) of 3.2 µs as in 802.11a/g and a regular guard interval of 0.8 µs, giving a total length of 4µs. The cyclic shift (CSD) is applied to each OFDM symbol. Therefore, the L-STF, the L-LTF, the HT-STF and the HT-LTF are shifted according to different cyclic shift values of each antenna in time domain.
By making use of the received HT-LTF, the channel frequency response can be roughly estimated. Taking 2x2 system for example, these channel frequency responses
ˆRT( )
H f , which means the estimating channel frequency response of Tth transmitter antenna to Rth receiver antenna, can be obtained as follows:
*
20 The received L-STF in receiver one is expressed as
* *
Equation (13) can be rewritten as
* (10) are used, equation (14) can be rewritten as
1 1 11 1 11 1 11
After some rearrangement and making the new equation conjugate, equation (15) can be derived as
By the same method, equation (14) can be rewritten another form as follows:
*
After some rearrangement and making the new equation conjugate, equation (17) can be derived as
* estimated IQM coefficient will be obtained as follows:
1 1 1 11 2 12 equal to and equation (9) and (10) are used, equation (14) can be rewritten as
1 1 11 1 11 1 11
After some rearrangement and making the new equation conjugate, equation (20) can be derived as
By the same method, equation (14) can be rewritten another form as follows:
*
After some rearrangement and making the new equation conjugate, equation (22) can be derived as
22 Based on legacy short training OFDM symbol, there are 12 ratios of 1*
1
β
α in the receiver one in MIMO-OFDM 2x2 systems. By averaging the 12 ratios, a final ratio of IQM coefficient will be determined for compensating data distorted by I/Q mismatch. Thus, the IQM coefficient is solved from the equation below.
1 1 1 11 2 12
In the Receiver two, the same methods are also taken to obtain the 12 ratios of 2*
2
β α to compensate for the frequency dependent I/Q mismatch in receiver two. Above equation from (9) to (26) is the case of 2x2 MIMO-OFDM systems in 20 MHz, these methods can also be applied to solve I/Q mismatch in MIMO-OFDM 4x4 systems.
3.2 Analysis of CW Jamming
In this section, CW jamming will be analyzed from different aspects, including the amplitude, phase, power. The ratio of the transmitted signal and CW jamming is presented latter. The analysis of CW jamming is based on different SJR and changing rate.
3.2.1 Amplitude, Phase, Power of CW Jamming
SJR=-10dB and changing rate= 33kbps is assumed. In time domain, the amplitude of sampled CW jamming varies according to changing rate. Compared CW jamming with preamble patterns (STF/LTF), the amplitude of CW jamming is much larger than the amplitude of preamble patterns due to SJR=-10dB, as can be seen from Figure 3-1. If only 64 sample of CW jamming are taken to observe, the CW jamming almost covers the transmitted signal, as can be seen from Figure 3-2. Figure 3-3 shows that power of CW jamming completely dominate OFDM systems and phase of CW jamming changes randomly. However, something interesting can be found after CW jamming is transferred from time domain into frequency domain by FFT. When one symbol (80 samples) gets rid of cyclic prefix (16 samples) first and then the remainder are taken into FFT, the frequency spectrum of the remainder shows two high peaks at the symmetric subcarrier index. The position of subcarrier index, which is far away from peaks, suffers from less attack of CW jamming. These subcarrier indexes can be used to estimate IQM coefficients. By the same way, the phase of the transmitted signal and CW jamming is shown as figure 3-4. The variation of phase of CW jamming is uncontrollable and unpredictable. Once CW jamming is added to the transmitted signal, the phase of the transmitted signal is hard to recover, not only in time domain but also in frequency domain. The same phenomenon can be discovered from the power of view.
Although the position of subcarrier index far away peaks may be useful to estimate IQM coefficients, the condition is actually more complicated because CW jamming is time-variant for OFDM systems. Different SJR are analyzed here and 1000 packets are used to get a statistics. On different SJR, the power distribution of
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Figure 3-1 (a)The real part of preambles in time domain. (b)The real part of CW jamming in time domain. (c)The image part of preambles in time domain. (c)The image part of CW jamming in time
domain.
Figure 3-2 64 samples taken from preamble and CW jamming.
0 50 100 150 200 250 300 350 400
Figure 3-3 Power and phase of preambles and CW jamming in time domain.
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Figure 3-4 Power and phase of preambles and CW jamming in frequency domain.
STF
Figure 3-5 Power Distribution on Each Subcarrier Index.
3.2.2 Ratio of CW Jamming and Preamble Patterns in Aspect of Power
From figure 3-5, STF only has its value on 12 positions of subcarrier index.
These 12 values are collected to calculate the ratio of CW jamming of short preamble.
The statistics of figure 3-6 (a) is shown as power distribution on 12 positions.
Compared with the ratio of index 4~9, he ratio of index 1~3 and index 10~12 is higher due to two peaks of CW jamming, as can be seen in figure 3-6 (b).
Even if the position suffered from less attack, the power of CW jamming on these positions still cannot be ignored when SJR=-10 dB. Under this circumstance, reducing the power may be the way to solve the effect of CW jamming.
CW/STF ,SJR=-10dB
Ratio of CW jamming and STF
CW/STF ,SJR=-10dB CW/STF ,SJR=-5dB CW/STF ,SJR=0dB (a)
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Ratio of CW jamming and STF
CW/STF ,SJR=0dB CW/STF ,SJR=-5dB CW/STF ,SJR=-10dB
(b)
Figure 3-6 Power Distribution on 12 Subcarrier Indexes.
3.3 CW Jamming Detection
The desired signal is mixed with CW jamming over transmission. When the desired signal is received at receiver, it is actually hard to get the information about CW jamming, such as its amplitude, phase, carrier frequency, and power. However, some phenomenon is observed after taking CW jamming into FFT. The frequency spectrum of CW jamming will display two high peaks. If they exceed some threshold which is given by one reasonable value, CW jamming does interfere with the transmitted signal. Therefore, some methods for resisting CW jamming should be
turned on.
3.4 Anti-Jamming Method
When modulation of CW jamming is ASK or BPSK and CW jamming close to the receiver is assumed. The CW jamming is simplified as [21]:
( ) cos(2 ),
i t = A⋅ π ft+θ (27)
where represents the amplitude of a jammer, f represents the carrier frequency of a jammer, θ represents the phase offset of a jammer. Because ( )i t is a real number,
By using this property of conjugate symmetric (28) and digital signal processing, CW jamming can be cancelled totally and then has no effects on estimating IQ mismatch. The received signal can be written as:
1( ) ˆ11( ) - 1( ) ˆ11( ) - 1( ) ( ) ( ).
R k =αH k L STF k +βH∗ −k L STF∗ −k + α+β I k (29) Equation (29) can be rewritten as
1( ) ˆ11( ) - 1( ) ˆ11( ) - 1 ( )
And symmetric position of subcarrier index is used to cancel CW jamming, i.e. index k and index N-k, index k+1 and index N-k-1.
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coefficient which will be used to estimate a new CFR. After that, these step last iteratively and an accurate IQ value will be obtained.
However, the modulation of information cannot usually be obtained and so the above method is impractical. By observing the behavior of CW jamming in frequency domain, the variation of CW jamming is not large between two training symbols is assumed. A new idea is proposed that short training field is subtracted from long training field after FFT. Expectedly, the influence on CW jamming could be mostly reduced.
3.5 Peak-Avoidance Method (PEAM)
From frequency spectrum view, the magnitude of the jamming displays two peaks on the positive subcarrier index and the corresponding negative subcarrier index. Figure 3-7 illustrates that legacy short training fields (L-STF) which are far away from the peak suffer from less power of the jamming. These L-STFs which are corrupted by less power are used to estimate IQ mismatch and theoretically should show more accurate estimated values. Furthermore, one estimated result is obtained from each STF. By making use of statistical techniques, mean and variance of these data are calculated. When data which have bigger variances are discarded and then the remainders are averaged, the estimated value is more correct. This concept can also apply to high-throughput short training fields (HT-STF).
0 10 20 30 40 50 60 70
Figure 3-7 CW Jamming and L-STF in Frequency Domain.
3.6 Smooth Filter
Based on equation (25), multipath fading channels need to be estimated first to acquire a rough channel frequency response (CFR) in the frequency domain. However, the estimation of the CFR is destroyed totally by CW jamming and then the estimation of IQ mismatch becomes very inaccurate. Therefore, a smooth filter which has five taps is designed to lower the peak value of CFR. Figure 3-8 represents a block diagram of a smooth filter and its mathematical equation expressed as:
4
Figure 3-9 illustrates that the magnitude of CFR becomes more approximate to the original channel through smooth filter, and although it is unequal to the original, it can make the estimation of IQ mismatch more correct.
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Figure 3-8 Smooth Filter block diagram.
0 10 20 30 40 50 60
0 5 10 15
Channel Frequency Response
Subcarrier index
amplitude
TGN E with Jamming
TGN E with Jamming, compensated TGN E
Figure 3-9 Channel Frequency Response.
3.7 Averaging Method in Time Domain (TD-AVM)
In this paper, the cyclic prefix (CP) length greater than the rms delay spread of multipath fading channel is assumed. And when the transmitted signal only suffers from AWGN, multipath fading channel and I/Q mismatch without being interfered with CW jamming, the received legacy short training (L-STF) and the high-throughput short training symbol (HT-STF) repeat every sixteen samples in time domain. By exploiting the periodicity of patterns, power of CW jamming can be reduced to obtain better IRR. The concept of averaging method is to average five L-STFs to get one new L-STF and then make three copies of this new one to form four L-STFs. Transforming four L-STFs from time domain into frequency domain by
FFT, the distribution of power of CW jamming is lower than before averaging.
Therefore, a more precise IQM coefficient can be estimated.
The concept of this method is to make CW jamming become periodical signal in one FFT interval without changing short preamble at the same time. When SJR=-10dB and 1000 packets are used to get a statistics. Figure 3-10 shows that power of CW jamming on each subcarrier index declines after TD-AM, excluding the index which two peaks occupy. From statistical view, index 17 is taken for example;
after TD-AM, its probability density function (PDF) moves left, as can be seen from figure 3-11. Moving left presents that the averaging power of CW jamming is reduced by TD-AVM.
-5 0 5 10 15 20 25 30
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61
power(dB)
subcarrier index jamming after averaging method jamming
Figure 3-10 Comparison of power of CW jamming between before and after TD-AVM.
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Figure 3-11Probability density function (PDF) of power of Subcarrier index 17. (a)Before TD-AVM.
(b)After TD-AVM.
3.8 The Proposed Algorithm of I/Q Estimation with CW Jamming
The proposed algorithm can be summarized as follows:
1) Detect whether CW jamming exist or not. If not, execute the FD-IQME algorithm described in section 3.1; otherwise, go to 2).
2) Use smooth filter to improve the estimation of a rough CFR.
3) Execute the averaging method (TD-AVM) described in section 3.7.
4) After FFT, perform the FD-IQME algorithm and then the peak-avoidance
method (PEAM) described in section 3.5.
Figure 3-12 shows the proposed algorithm structure in the receiver; Figure 3-13 shows the flow char of the proposed algorithm.
Figure 3-12 The proposed algorithm structure in Rx.
Figure 3-13 The flow chart of the proposed algorithm.
Chapter 4
Simulation Results and Performance
4.1 Simulation Results of Only I/Q-Mismatch
A typical MIMO-OFDM system with FD-IQME algorithm is simulated to evaluate and compare the performance. The length of OFDM symbol is 64 samples and cyclic prefix is 16 samples. The parameters used in the simulation are as follows:
4X4 MIMO-OFDM systems in 20 MHz.
PSDU is 1024 bytes
1000 packets
Multipath Mode: TGn E.
Modulation:64 QAM, coding rate:2/3
SJR=-10dB each receiver
I/Q Mismatch :
gain error :1dB, phase error:20° in receiver one gain error :2dB, phase error:13° in receiver two gain error :2dB, phase error:18° in receiver three gain error :1dB, phase error:19° in receiver four
Figure 4-1 shows that the performance of FD-IQME algorithm is acceptable.
Without CW jamming, packet error rate (PER) converges to 0.01 as signal-to-noise
IQ w/o jamming, IQ compensated IQ with jamming, IQ compensated
(a)
IQ w/o jamming, IQ compensated IQ with jamming, IQ compensated
(b)
Figure 4-1 The Compensation Result.
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4.2 Performance Index
The aim of this paper is to estimate IQM coefficients correctly under the attack of CW jamming. Accurate IQM coefficients, which are obtained from FD-IQME once, can be used to compute CFR again and compensate data. Due to huge simulation time, the system performance is based on the image rejection ratio (IRR). The image rejection ratio as a function of the mismatch is denoted as [22]:
10
Figure 4-2 IRR values corresponding to different phases and gains.
4.3 Simulation Results of I/Q-Mismatch with CW Jamming
For convenience of representation, the abbreviation is used for the proposed methods as below.
FD-IQME : I/Q-Mismatch Estimation in Frequency Domain.
SF : Smooth filter.
SP-LP : Short preamble subtracted from long preamble.
PEAM : Peak-Avoidance Method.
TD-AVM : Averaging Method in Time Domain.
The estimated IQM coefficients on Receiver one is taken to analyze the performance of each method. Because PER and BER converge on SNR=20dB, SNR will be fixed on 20dB when these proposed methods above are discussed. And SJR=-10dB.
4.3.1 Evaluate FD-IQME
While FD-IQME is used to estimate IQM coefficients without dealing with CW jamming, IRR approximates 12 dB from Table 4-1. However, IRR approximates 36 dB when there is no CW jamming. The gap is about 24 dB, which means that CW jamming must be considered when estimating IQM coefficients; this result can correspond to Figure 4-1.
Actually, the IRR value, which is calculated, is only a point. However, it is convenient to observe so that the point is expanded to one plane; the yellow plane is expanded form the point of 35.96 dB and the green plane is expanded form the point of 11.93 dB, as can be seen from Figure 4-3.
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Figure 4-3 IRR, comparison of FD-IQME w/o jamming and FD-IQME with CW jamming.
Table 4-1 IRR, comparison of FD-IQME w/o jamming and FD-IQME with CW jamming.
FD_IQME ∆εεεε(dB) ∆θθθθ(degree) IRR (dB)
w/o jamming 0.032 0.798 35.96
With jamming 1.046 22.972 11.93
4.3.2 Evaluate SF & SP-LP
From Figure 4-4, using smooth filter, which makes IRR reduced to 9 dB, is worse than using no smooth filter. The result shows that this method SF is not robust enough. The main reason is that smooth filter does not assure that the estimated CFR can approximate the real CFR but rather that the two peak which are caused by CW jamming can be suppressed. Nevertheless, the estimated CFR, which is adjusted by the smooth filter, is still not available, even worse.
Figure 4-4 IRR, comparison of FD-IQME w/o jamming, FD-IQME with CW jamming, and FD-IQME+SF with jamming.
When SP-LP is evaluated, the ideal CFR is assumed. From Figure 4-5, using the
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changing rate (CR). Two adjacent CW jammings are always different, which makes SP-LP fail to eliminate CW jamming.
Figure 4-5 IRR, comparison of FD-IQME w/o jamming, FD-IQME with CW jamming, and
Figure 4-5 IRR, comparison of FD-IQME w/o jamming, FD-IQME with CW jamming, and