Under the proposed channel equalizer, multipath fading, residual CFO and SCO can be eliminated with channel equalization simultaneously. No additional compensators or buffering registers are required; therefore, low cost can be achieved. Moreover, both the tracking accuracy of DDCE and PET can be enhanced through such a feedback compensation loop.
For low power consideration, tracking operations of DDCE and PET can be stopped after a certain symbol of evaluation, compensation can be continued by prediction.
Chapter 4 .
A High Speed and Low Complexity Channel Equalizer for UWB System
In chapter 3, we proposed a channel equalizer for general OFDM-based wireless access systems. Based on this design, modifications can be made when dealing with different applications with particular requirements and specifications. In this chapter, a high-speed and low-complexity version channel equalizer is proposed for high-speed UWB systems.
4.1 Motivation
The trend of wireless communication is towards low power and high speed. UWB is the new generation wireless access system, which is designed for short-range personal area networks. The specified data rate is up to 480Mbits/s, which are almost ten times of the supported data rate in general WLAN systems. In the design of UWB systems, the concern of high speed and low complexity becomes extraordinarily important. In chapter 3, we proposed a high performance channel equalizer with a relatively low cost compensation scheme for general wireless access systems. However, the speed is limited by the complex divider (complex inverse + complex multiplier) for channel equalization; and the complexity reduction will be bounded in the different operation domains of DDCE and PET. Table 4.1 shows the gate count of the proposed channel equalizer and the 802.11a baseband processor for example.
Table 4-1 Gate count statistics of the 802.11a baseband transceiver Logic gate count Memory (Byte)
802.11a transceiver 370K 3.3K
Channel equalizer 120K 0.56K
From Table 4.1, the channel equalizer occupied almost 1/3 of the total gate count, which will be the primary problem in UWB system. Therefore, the architecture of the proposed channel equalizer in chapter 3 must be improved based on the special specifications in the UWB standard draft to meet the high speed and low complexity requirement.
4.2 Coordinate Conversion
In Chapter 2, we have already introduced the UWB system. Unlike IEEE 802.11a PHY, only M-PSK is used for constellation. PSK is a digital modulation scheme, which has constant amplitude with various phase shifts for different possible signals. That is, phase information determines the constellation result, magnitude information can be neglected. Based on this idea, data can be converted from a complex value to a phase value only after FFT for later channel equalizer design and FEC. The coordinate conversion can be listed as
θ
ej
M B j A k
X( )= + ⋅ = ⋅ (4-1)
2
2 B
A
M = + (4-2)
A
1B tan−
θ = (4-3)
Where θ is the phase information for later designs, M is the magnitude information which can be neglected. A complex division in the Real-Imaginary coordinate will become a phase subtraction in the Magnitude-Phase domain. That is, the critical path can be reduced from the
complex division in the channel equalizer proposed in chapter 3, to a TLU-based arc-tangent for coordinate conversion. Moreover, the computation complexity of the proposed channel equalizer will be significantly reduced in the Magnitude-Phase domain. The detail algorithm will be explained in the next section.
For a complex value A+ j⋅B, the relationship between the phase result and the quadrant can be shown in Figure 4.2.1.
I Q
I: A>=0 B>=0 II: A<0 b>=0
III: A<0 B<0 IV: A>=0 B<0
: |A| > |B|
: |A| < |B|
Figure 4.2.1 The phase result of different quadrants
⎪⎪ instead of the whole phase range form −π ~π . The architecture of the conventional arc-tangent approaches can be divided into a direct-TLU method and a division-based TLU method [19]. In the direct-TLU design, all the phase results of A>=B are established in the
table. The table size will be significantly increased with the wordlength of the input value. In order to reduce the table size, a division-based TLU is applied to reduce the possible input pattern. The phase results of B/A are established as a look-up table instead of the results of A, B directly. However, a real divider is required in this method.
To achieve the high-speed and low-cost requirements of UWB system, a logarithm-based TLU method is proposed. The architecture can be shown in Figure 4.2.2. Based on the logarithm property in equation (4-6), the table size can be reduced and the real divider can be removed by a simple subtraction.
A
Figure 4.2.2 The architecture of the proposed logarithm-based TLU arc-tangent
4.3 The Proposed High-speed and Low-complexity Channel Equalizer Design
The block diagram of the channel equalizer proposed in chapter 3, and the channel
equalizer with coordinate conversion for the high-speed and low complexity requirement can be shown in Figure 4.3.1.
Channel
Figure 4.3.1 Block diagram of the proposed channel: (a) channel equalizer for general OFDM system (b) channel equalizer for PSK based OFDM system
All the complex number computations can be replaced by simple real number additions and subtractions by coordinate conversion. A soft de-mapping with phase variations is supported.
This design can be used for PSK based OFDM wireless systems. For QAM systems such as IEEE 802.11a, the completely equivalent constellation map conversion from I-Q to magnitude-phase cannot be achieved. That is, another coordinate conversion from phase to complex number is applied after the channel equalizer for later de-mapping, which is even more complicated. The detail algorithm of the DDCE and PET with phase information only
can be discussed as follows.
In the original DDCE, which includes the basic ZF scheme and the data-aided decision-directed tracking loop, the estimated CFR is estimated by the division between the received training sequence and the defined sequence and is updated by the tracking loop. With coordinate conversion, the complex division can be replaced by a subtraction.
(
( ( ) ( )))
The decision-directed tracking loop can be modified as below
) is the CFR error of the present OFDM symbol. After the applied loop filter, θHA,N is then feedback to the channel equalization to update the estimated CFR.
The algorithm of the PET is the same as the design proposed in chapter 3. From the equations listed above, both DDCE and PET operate in the phase coordinate. The complexity of DDCE is significantly reduced by the coordinate conversion. The phase error calculated by PET can be directly combined with the updated CFR and feedback to the channel equalization without any redundant conversion. The modified channel equalization which removes multipath fading, residual CFO and SCO all together can be listed as
PET
In the 55Mbits/s ~ 200Mbits/s transmission modes, data are duplicated within an OFDM symbol, the data format can be shown in Figure 4.3.2.
d0 d1 d2
···
d24 d0 d1 d2···
d24* d23* d22*···
d0* d24* d23* d22*···
d0*d0 d1 d2
···
d24 d25···
d49* d48* d47*···
d25*d24*···
d24
d49 d0* (a)
(b)
Figure 4.3.2 Date format of a OFDM symbol in (a) 55Mbits~88Mbits/s (b) 110Mbits/s~200Mbits/s transmission modes
An average method with the concern in deep fading subcarreirs is applied to reduce the additive noise in data subcarriers base on the duplicate property. In data transmission, some subcarriers may be seriously distorted by the deep fading problem in a frequency-selective-fading channel. The noise level of deep fading subcarreirs is much higher, resulting in affecting the correctness of other subcarriers in such an average method. Figure 4.3.3 shows the deep fading problem in CFR.
CFR1 CFR2
deep fading
Figure 4.3.3 Deep fading subcarriers in frequency-selective-fading channel
Take 110Mbits/s~200Mbits/s for example, data are repeated in CFR1 and CFR2. If the power ratio of CFR1 and CFR2 is much smaller or bigger than “1”, one of the subcarriers of the duplicated data is seriously distorted, which cannot be averaged. In order to keep the operation in phase domain, the geometric average method with the deep fading detect scheme is applied. The algorithm can be derived as follow.
2
With the coordinate conversion from complex number to phase information only, a high-speed and low-complexity channel equalizer can be achieved. The critical path can be reduced from a complex division to a TLU-based arctangent. The computation complexity of the channel equalizer can be significantly reduced in the phase coordinate. The detail performance and complexity analysis will be discussed in the next chapter.
Chapter 5 .
Simulation Result and Performance Analysis
In order to verify the proposed design, complete system platforms are established complaint to the IEEE 802.11a and the UWB proposal on Matlab. The platform has been introduced in chapter 2. CE accuracy, PET performance and the system PER of the proposed design will be simulated and compared with conventional approaches in the following performance analysis.
5.1 Performance Analysis of the Proposed Channel Equalizer for OFDM-based Wireless Systems
The proposed channel equalizer for general OFDM-based wireless systems is simulated in the system platform compliant to the IEEE 802.11a PHY. The PER analysis will focus on the 10% PER, which is the requirement in IEEE 802.11a standard.
5.1.1 Channel Estimation Accuracy Analysis
To analyze the CE accuracy of the proposed channel equalizer, mean-square-error (MSE) between the estimated CFR and the real CFR is measured. An exponentially decayed Rayleigh fading channel model with 50ns RMS delay spread is applied. The detail information of the applied channel model is in chapter 2. The MSE value of CE can be derived as equation (5-1), where H(k,n,p) is the real CFR and He(k,n,p)is the estimated CFR updated each OFDM symbol n.
( )
k is the number of data subcarriers, n is the total OFDM symbol number per packet, and p is the packet number per SNR conditions.
MSE Analysis with Packet-invariant multipath channel
The MSE curves of different CE designs measured in BPSK transmission with a packet-invariant multipath channel are shown in Figure 5.1.1.
Figure 5.1.1 MSE analysis of the proposed design
The proposed DDCE achieves 9.0~13.0dB and 6.0~10.0dB gain in MSE compared with ZF CE and pilot-tracking CE [11] respectively. Compared with the fixed-coefficient LMMSE in [10], the proposed design achieves 2.0~13.9dB gain in MSE when SNR is higher than 0 dB.
Applying the smoothed filter in low SNR region and the decision-directed tracking with data subcarriers in high SNR region, the proposed channel equalizer is robust to reduce CE error in
[11]
all SNR regions.
MSE Analysis with Packet-variant multipath channel
In order to verify the proposed design in a practical time-variant indoor wireless channel model, 50Hz Doppler frequency caused by 10 KM/hr opposite speed in 5GHz band is modeled. The MSE result under a packet-variant multipath channel with 50Hz Doppler frequency can be illustrated in Figure 5.1.2.
Figure 5.1.2 MSE analysis with packet-variant CFR
As Doppler frequency equals 0Hz, the MSE of ZF approach decreases as SNR increases.
However, as Doppler frequency rose to 50Hz, the MSE of ZF approach is saturated since only CFR estimation in the initial preamble will lose the time-variant information of CFR. Appling the moving average algorithm to trace the channel variation, the proposed DDCE achieves better 8 ~ 20dB gain in MSE estimation than ZF approach. It also achieves better 5 ~ 17 dB gain in MSE estimation than the conventional channel interpolator [11], which only achieves better 2.5 ~ 3dB gain in MSE estimation than the ZF approach in the concern of a
time-variant CFR.
PER Analysis with Different compensation scheme
For system performance analysis of the proposed DDCE with feedback compensation scheme, PER with different CE approaches in 54 Mbits/s transmission mode is simulated and illustrated in Figure 5.1.3. A feedforward compensation scheme [19] is compared with the proposed feedback compensation scheme. In the feedforward scheme, data subcarriers are compensated with the estimated equalization error instead of using a feedback loop to update the estimated CFR. The feedforward compensation can be shown as follows
) ( )
(
) ( ) ) (
( H k H k
k H k k X
X
e
e e
∆
−
= ⋅ (5-2)
Figure 5.1.3 PER analysis of different CE approaches (54Mbits/s)
The proposed DDCE with feedback compensation scheme reduces 50% design SNR loss (0.9dB) compared with ZF CE, and reduces 25% design SNR loss (0.3dB) compared with a feedforward compensation scheme. The accuracy of such a decision-directed tracking
algorithm highly depends on the correctness of input data. That is, a feedback compensation scheme can reduce the CE error, which enhances the tracking accuracy. Compared with the feedforward scheme, the proposed feedback scheme enhances the CE accuracy and reduces compensation complexity by using the original equalization.
5.1.2 Phase Error Tracking Performance
In order to verify the PET performance, the design is simulated under 40ppm (200KHz) CFO and 40ppm (800Hz) SCO, which is the standard requirement. After the time-domain acquisition, the amount of the residual CFO is lower than 10KHz. This residual CFO and SCO cause the phase rotation in frequency-domain.
Phase Rotation Analysis of the Proposed PET
Mean phase error grow with OFDM symbol index
Figure 5.1.4 The phase deviation caused by residual CFO and SCO
The frequency-domain phase rotation can be divided into a mean phase error caused by residual CFO and a linear phase error caused by SCO. In Figure 5.1.4, both the mean phase
error and the increase rate of linear phase error grow with the OFDM symbol indexes. The phase error can be eliminated after the proposed PET. Figure 5.1.5 shows the frequency-domain phase rotation in the 6Mbits/s transmission mode. This phase deviation grows with the increasing of OFDM symbol indexes, which exceeds ± within a packet. π With the pilot pre-compensation in the proposed PET, the tracking range can be extended.
That is, the proposed PET achieves a high accuracy in the full-phase range.
(a) (b)
Figure 5.1.5 The phase deviation of (a) residual CFO (b) residual CFO and SCO
PER Performance of the Proposed PET
For performance analysis of the propose PET, PER is simulated with AWGN channel, 40ppm CFO, and 40ppm SCO. The applied CFO model includes the practical phase-noise effect. The PER curves of 6Mbits/s and 54Mbit/s with different PET approaches can be shown in Figure 5.1.6.
In the 54Mbits/s mode, the transmission time of one packet is 147.78us with maximum pilot error equals to 0.373π. The feedfoward PET without pre-compensation will have a better PET accuracy compared with feedback scheme. However, in 6Mbits/s mode, the transmission time of one packet is 1.33ms, which is much longer than the 54Mbits/s mode.
Since the phase error increases with time, the phase rotation will exceed π that causes phase
evaluation failed in the feedforward PET. With the proposed pilot pre-compensation which increases the tracking range, the fixed-coefficient loop filter which enhances tracking accuracy, and a predication scheme in data subcarriers, the proposed PET achieves a better 1.9~2.3dB gain in SNR compared with feedback PET.
(a) (b)
Figure 5.1.6 PER of PET approaches in (a) 6Mbit/s (b) 54Mbits/s transmission mode
5.1.3 System Performance
To verify the complete system performance of the proposed channel equalizer, PER of a complete IEEE802.11a baseband processor are measured with the typical indoor wireless channel model that contains 50ns multipath RMS delay spread, 40ppm CFO and 40ppm SCO.
The PER curves of different transmission mode can be shown in Figure 5.1.7.
The design SNR for 10% PER is listed in Table 5-1. The proposed baseband system achieves 1.35~7.16dB average gain in SNR compared with standard requirement and current approaches [12] [13]. High performance can be achieved by the proposed channel equalizer with the combination of DDCE and PET. Both the tracking accuracy can be enhanced by the proposed feedback compensation loop with channel equalization.
Figure 5.1.7 PER performance of the proposed baseband processor
Table 5-1 Required SNR for 10% PER of the proposed baseband processor Data Rate
(Mbits/s)
The Proposed Design SNR
(dB)
Design SNR [12]
(dB)
Design SNR [13]
(dB)
IEEE 802.11a Requirement
6 2.5 4.9 5.4 9.7
9 4.0 5.8 5.8 10.7
12 5.2 8.6 7.0 12.7
18 7.4 9.9 9.5 14.7
24 10.1 12.4 11.3 17.7
36 14.2 15.9 14.9 21.7
48 18.6 20.3 18.6 25.7
54 20.3 21.7 20.6 26.7
Average gain 2.15 1.35 7.16
5.2 Performance Analysis of the Proposed Channel Equalizer for UWB System
To verify the proposed high-speed and low-complexity channel equalizer for PSK-based OFDM systems, a system platform complaint to the multi-band OFDM UWB PHY is established. System performance will focus on the 8% PER which is the requirement of the UWB system. Computation analysis with the proposed two channel equalizers will also be discussed.
5.2.1 PER performance of Different CE approaches
The PER performance of different CE approaches can be shown in Figure 5.2.1. The PER curves are simulated under a multipath fading channel with 5ns RMS delay spread.
Figure 5.2.1 PER curves of different CE approaches in 480Mbit/s mode
The five different CE approaches are listed below.
Phase ZF CE：Basic channel estimation with known training sequence, only phase
subtraction in equalization.
Phase DDCE：The proposed high-speed and low-complexity DDCE, phase subtraction with updated CFR phase by the proposed tracking scheme.
)))
Phase DDCE with complex ZF：Basic equalization with both magnitude and phase, only CFR phase updated by the tracking scheme.
)))
Complex ZF CE：Basic channel estimation with known training sequence, complex division for equalization.
)
Complex DDCE：The proposed DDCE for general OFDM systems, with updated complex CFR to reduce CE error.
)
From Figure 5.2.1, we can discover that the proposed phase DDCE has a slightly better performance than the complex ZF CE. Performance can be maintained with the reduction in critical path and computation complexity under the proposed design.
5.2.2 Computation Analysis
In this thesis, we propose two channel equalizers. The first one is the high-performance
version for general OFDM system, the second one is the high-speed version for UWB system.
The detail computation analysis of the proposed two channel equalizer versions with an 18Mbits/s packet (QPSK, coding rate = 3/4) in IEEE 802.11a system can be listed in Table 5-2. We can change the complex operations to equivalent number of real operations and calculate the reduced percentage of each operation.
1 complex division = 6*real multiplication + 2* real division + 4*real add/sub 1 complex multiplication = 4*real multiplication + 2*real add/sub
Table 5-2 The computation analysis of the proposed two channel equalizers Proposed
High-speed version
Proposed High-performance
version
Complex ZF CE &
PET
Complex multiplication 0 22200 5772
Complex division 0 5876 5876
Real multiplication 11544 11544 888
Real add/sub 27188 11988 444
Table 5-3 The computation reduced percentage analysis Reduce % from Proposed
High-performance version
Reduce % from complex ZF
& PET
Real division 100% 100%
Real multiplication 91.5% 80.5%
Real add/sub 65.97% 23.4%
Form Table 5-3, the proposed high-speed and low-complexity channel equalizer reduces 100% of the real divisions, 80.5% of the real multiplications and 23.4% of the real add/subs compared with conventional complex ZF CE and PET.
5.2.3 Deep Fading Analysis
The deep fading subcarriers are seriously distorted by additive noise. A geometric average method with a deep fading detection scheme is applied to enhance system performance. The CFR power ratio (CFRsmall CFRbig ) of the duplicated subcarriers is measured. In figure 5.2.2, we can discover that the power ratios are close to “1” in correct packets. In error packets, the amount of small power ratios increase, deep fading may occur.
Figure 5.2.2 The power ratio distribution
We can decide the threshold value of deep fading subcarriers by the power ratio distribution.
From figure 5.2.3, the proposed geometric average method with deep fading detection achieves a better 1.3dB gain in SNR than the general average method without deep fading detection.
Figure 5.2.3 PER of the proposed deep fading detection (th=0.7)
5.2.4 System Performance
Figure 5.2.4 PER performance of the proposed UWB PHY
To verify the complete system performance of the proposed channel equalizer, a complete TFI-OFDM UWB PHY with a Low-Density Parity Check code (LDPC) in FEC is
established. LDPC achieves a better 2.0dB gain in SNR compared with the Viterbi encoder.
There is no puncturing in the LDPC scheme, only a fixed coding rate (3/4) can be supported.
Therefore, the supported data rates of the proposed UWB PHY are 120, 240, and 480Mbits/s.
PER curves are simulated under Intel channel model with 5ns RMS delay spread, 40ppm CFO, and 40ppm SCO. The simulation result can be shown in Figure 5.2.4
PER curves are simulated under Intel channel model with 5ns RMS delay spread, 40ppm CFO, and 40ppm SCO. The simulation result can be shown in Figure 5.2.4