Chapter 3 The Proposed Digital Beamforming Algorithm
3.2 Introduction to Detect Algorithm
When sub-frame detection is detected the signal and boundary detection is determined the starting of the symbol, the front end algorithms are complete the timing and frequency synchronization. The assumption is that the best timing and frequency are reached after the front end algorithms. The idea reference signals (RS), primary synchronization signals (PSS), second synchronization signals (SSS) of received signals is used to calculating the correlation value. The correlation value can examine the relative signal level. If the correlation value is large, it cans be expressed that the signal is coming which can decoded at the known sub-carries.
For example, the received signals are combined the all of transmitter signals that come from the difference transmitters. Due to each signals suffers interference by others, the dirty signal after interference cannot recognized rapidly and accurately.
When beam pattern has been weighted to steer desired signal and to minimize
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multipath effect, the receiver adjusts the higher gain for interest signal to receive the large power and better qualities signal. The correlation values are used to quantize the received power level that indicates the signal come from. According the correlation property, the maximum correlation value means the arrival of angle of the largest received power. Finally, the beam pattern is adjusted to this arrival of angle.
In Fig. 3.2, the example is that the tape of multipath is six and AOA of main tap is 180o. Using the switch beam with different angle, the correlation values of different angle are calculated. After the calculating the correlation value, the angle of beam pattern is 180o that the signal receives the largest power, so we can estimate AOA of the signal is 180o.
Number of Tap 1 2 3 4 5 6
AOA of Tap 180 0 69 0 107 0 54 0 102 0 15 0
Energy Factor 1 0.3 0.4 0.6 0.6 0.8
Fig. 3.2 All transmitter signals on receiver end on digital beamforming system
3.3 Detection Algorithm
The proposed algorithm has three steps to estimate AOA of signal:
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0 90 135 180 270
Correlation value
Angle of beam pattern
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1. Using SSS calculate the cross-correlation value to find CIR, and then find 2 taps of maximal and second largest power.
2. Initiation of the beam pattern steers 0 , 0 180 , 0 90 and 0 270 , the PSS is used to 0 calculate four auto-correlation values which determine the possible region of received signal AOA. Finally, the RS calculates auto-correlation value to find AOA accurately as well.
3. In order to get clearly received signal, the two 2 taps of maximal power and second largest use the formula to find possible AOA of signal.
Step1: Use SSS to calculate cross-correlation value to find CIR
Assume that the signals from every transmitter that these arrive the received end at the same time are distorted by channel effect. The channel impulse response can simply detected to know the channel variation. The cross-correlation achieve to detect the channel variation.
Correlation, a mathematical tool, is used in signal processing for analyzing the series of values, such as time domain signals. Correlation is one of the most common function and the most useful statistics. The cross-correlation is used to find the relation of two different signals.
The correlation matrix is represented by calculating the parallel cross-correlation of the received signal R ki( ) and the known PSS training sequence ( )Q k to be reference. Fig. 3.3 describes the correlation value how to generate by proposed cross-correlation architecture. These parameters are illustrated in later.
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Fig. 3.3 Cross-correlation structure
1
The parallel cross-correlation with each Q kL( ) indicates the correlation power is
, ( )
The cross-correlation value of receiver is used to find CIR. In Fig. 3.4, fining largst value and second largest value register as Tap1 and Tap2, and these are used later.
regi
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auto-correlation value is calculated of four different AOAs, and finding largest and second largest power values determine the regions. Fig. 3.7 is represented the four regions: region1, region2, region3 and region4.
0
Angle of beam pattern
Fig. 3.6 Determine region to estimate AOA
0
Angle of beam pattern
00
1800
900
2700
1350
Fig. 3.7 Estimate AOA in the region
After determining the best region, Fig. 3.7 shows that the beam pattern is adjusted the AOA at the half of best region. The RS is used to calculate two partition of auto-correlation value, and then the searching region can reduce half region.
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Step3: By two taps of maximal power and second largest, find possible AOA of signal Finally, the pervious step find the AOA of maximal power, it has the limited improve the system performance. Although the AOA of half the best region that is between AOA of maximal tap and AOA of second largest tap is found, the received signal is not purely clear. It might be restrict the region of improvement. Therefore, the goal is that the AOA of pure signal is searched in the last step. The receiver of system performance can get the maximum gain.
In Step1, find two taps of maximal and second largest power (Tap1, Tap2).
Tap is value of maximal tap and 1 Tap is value of second largest tap. Using 2 Tap1 and Tap2 value of impulse response, the substitution formula (2) can be written as:
1* _ 2* _
_ 2
Tap Angle X Tap Angle Y
temp AOA= +
………..(2)
where temp AOA_ is last step to estimate AOA, Angle_ X is angle of Tap1, _
Angle Y is angle of Tap2.
In order to finding the all possible AOAs, the binary search is used to find _
Angle Y and to estimate Angle_X . TABLE II describes an example. The search AOA is 130o after step two in Fig.3.8. Using the formula (2) find all possible of
_
Angle X and Angle Y_ . TABLE III illustrates this situation. According the auto-correlation value of Angle_ X , the maximum value is used to decide the best angle of beam pattern, called Angle_X .
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TABLE II It is an example that a path has 6 taps in channel
Number of Tap 1 2 3 4 5 6
AOA of Tap 69 0 188 0 107 0 54 0 102 0 95 0
Energy Factor 0.3 1 0.4 0.6 0.6 0.8
TABLE III Possible Angle_X and Angle_Y _
Fig. 3.8 The example which showed searching region (AOA of last step = 130 ) o
3.4 Weighting Vector
3.4.1 Weighting CalculateWeighting vector is combined gain and steer vector (Fig. 3.9). The Kaiser-Bessel function (formula (3) ) is used to calculate gain which can enhance strength of desired signal. The formula (4) is Steer vector, it will adjust beam pattern to steer estimate AOA and minimize unwanted signal.
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N is number of receiver antenna, d is element distance and θ is estimate AOA .
Fig. 3.9 the description of weighting vector
3.4.2 Update Weighting
According the weighting vector, the receiver signals can multiple the weighting and combine it to create the new signals. Fig. 3.10 is the architecture of the weighting calculating. It uses a weighting vector to update the signals. Fig. 3.11 describes that the proposed algorithm found the large energy of interest tap signal and the less energy of others.
If the weighting vector can minimize multipath signal, it can improve the system performance. In section 4, the BER, PER and other performance are indicated.
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Fig. 3.10 Weighting calculate
0
Fig. 3.11 Multipath is minimized
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Chapter 4 Simulation
Matlab is used to simulate language. The MIMO-OFDM system based on 3GPP Long-term Evolution (LTE), Spatial Channel Model (SCM) Specification, is used as the reference simulation platform. The major parameters are shown in TABLE IV
TABLE IV Simulation Parameter
Parameter Value
Number of antennas 4Tx and 4Rx
Signal bandwidth 20 MHz
Carrier frequency 2.4 GHz
Number of subcarrier 168
Subcarier modulation 64 QAM
Subframe size 1 ms
Channel Model SCM model_C
Number of taps 6
Equalization Zero-Forcing
FFT size 1024
The proposed algorithm is that estimate AOA and using weighting vector to emphasize interesting signal, minimizing multipath signals. In this simulation platform, all simulation results compared with the worst performance without using digital beamforming technique. If using the proposed algorithm, the beam pattern can be to steer desired estimation of AOA and to diminish multipath. It can improve the performance. The best case is beam pattern to steer perfect AOA.
The criterion of AOA estimation algorithm is that the accuracy of AOA estimation angle. The proposed algorithm of estimation AOA approximates to the acute angle around 2o~5o error. To compare AOA of estimation and idea AOA, it loses few values.
The reason is that the power of signal is spreading by 5± , the estimation error of o
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proposed algorithm has less than 5± of ideal AOA. In the 5° ± range, the power of ° interference signal has been degraded. The AOA of estimation can updating the weighting vector, changing beamforming pattern to receive desired signal and suppress multipath. It can improve the performance and get the clearly and largest power signal. In this thesis, the BER and PER shows the system performance.
In Fig. 4.1, there shows comparison of three cases, idea case, the proposed case and worst case. All of these are simulated in 4 transmit antennas and 4 receive antennas. In this figure, the without beamforming technique, it has worst performance because the received-end gets less energy of signal and suffer from serious multipath effect. By using proposed algorithm, performance has improved obviously. The curves of BER on Fig. 4.2, the proposed algorithm with digital beamforming has to approach the best method within 2 dB. But the result shows that the digital beamforming system has 16 dB better than without digital beamforming system.
Fig. 4.1 SER of digital beamforming technique for 64QAM modulated 4×4 MIMO OFDM systems
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Fig. 4.2 BER of digital beamforming technique for 64QAM modulated 4×4 MIMO OFDM systems
In Fig 4.3, if energy factor of largest power and second largest power closed, idea beamforming possible doesn’t have better performance. Because the 1st largest power of AOA is similar to 2nd largest power of AOA, the attenuation of multipath is unobvious. For example, assume the ideal beam angle is 93 degree, the 90 degree beam angle after proposed algorithm decision. In some case the proposed algorithm has better performance than ideal beam angle. Fig. 4.4 shows that the BER under the difference of 1st and 2nd is 4o. Fig. 4.5 indicates that the 1st and 2nd have ≤7o interval.
The summary is that the difference of 1st and 2nd is 10≤ o which might the proposed algorithm has well enough to estimation the best AOA under the serious multipath condition. In Fig. 4.6, if the interval between the 1st of AOA and 2nd of AOA is 10≥ o, it is normally case which ideal performance is better than the proposed beamforming .
Tap1
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Tap1 Tap2 Tap3 Tap4 Tap5 Tap6
93 71 100 237 1 116
1 0.6 0.8 0.5 0.3 0.2
Fig. 4.5 Difference of tap1 and tap2 AOA is 7o, BER of digital beamforming technique for 64QAM modulated 4×4 MIMO OFDM system
Tap1 Tap2 Tap3 Tap4 Tap5 Tap6
93 71 100 237 1 116
1 0.6 0.8 0.5 0.3 0.2
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Fig. 4.6 Difference of tap1 and tap2 AOA is 10o, BER of digital beamforming technique for 64QAM modulated 4×4 MIMO OFDM system
TABLE V Comparison with other algorithms
Ref [4] Ref[5] Ref[6] Proposed arrive of channel Numbers of
SCM channel SCM channel (6 taps) Performance
loss 3 dB < 1 dB 4 dB 2 dB
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Chapter 5 System Architecture
The received signals pass through the FFT window to acquire the frequency response of training signal. The major component is the register-based correlation at frequency domain in the proposed algorithm architecture. This component is hugely used in the AOA estimation. In Fig. 5.1, the architecture includes three modules;
region divider and correlation, coarse search of AOA estimation, fine search of AOA estimation. The function of first module consists of the correlation to find channel impulse response and four values of auto-correlation to determine region. In the second block, the functionality finds AOA of largest power by two auto-correlation values. The future of the third module is that the night values of auto-correlation is used to estimation the best AOA of clear signal. Fig. 5.2 and Fig. 5.3 are detail architecture of cross-correlation and auto-correlation. In Fig. 5.4, the weighting vector is calculated by formula (2) to adjust beam pattern. The proposed algorithm keeps update to find perfect beam angle. TABLE VI lists the cost of the computing architecture complexity. The major component of the computing architecture is the multiplier. The gate count of multiplier is 3.605K by Taiwan Semiconductor Manufacturing Company (TSMC) 0.18-μm one-poly six-metal layer (1P6M) CMOS
library.
TABLE VI Computing architecture complexity Number of computing architecture Multiplier 868 Accumulator 16
MUX 5 Divider 1
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Comparison(Find largest value and second large value)
Antenna Array Multiplier . . . .
AOA of possible region 2
AOA of possible region 1
Multiplier Auto-correlation
Divider
AOA of largest power
Register 10
Cross-correlation Comparison(Find largest value )
Fig. 5.1 Architecture of proposed algorithm
Q1
Fig. 5.2 Cross-correlation
32 R1
R2
R3
RL Reg_r1
Reg_r2
Reg_r3
Reg_rL
Fig. 5.3 Auto-correlation
W1
W2
W4 W3
Fig. 5.4 Antenna array
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Chapter 6 Conclusions
In this paper, the proposed digital beamforming technique is use to improve performance in MIMO-OFDM system. Digital beamforming technique is similar with smart antenna system. The digital beamforming is used to suppress the interference signal for the purpose of degrading multipath effect and promoting the desired signal.
Otherwise, the smart system needs higher cost than digital beamforming technique, because it acquires the direction antenna in place of the original architecture.
Accordingly, the proposed algorithm calculates the weighting vector to change the beam pattern toward the best received angle; as a result, the method can improve performance.
The future issues are that modifies the proposed algorithm and reduces the complexity. The most important is that the complexity of calculating correlation has needed to reducing, so the hardware implementation issue might be easy and rapid.
On the other hand, the accuracy of AOA estimation is another problem that it needs to avoid the effect of channel variance.
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