Chapter 1 Introduction
1.3 Organization of this thesis
This thesis is organized as follows: the first chapter briefly introduces 802.11n wireless LAN system and the channel model used for simulation. In chapter 2, the algorithms of CFO mitigation, channel estimation, phase error tracking, and MIMO detection will be described. Simulation results will be analyzed in Chapter 3. The chapter 4 will show the architecture and the techniques of tri-mode hardware implementation. Finally, a brief conclusion and future work will be presented in chapter 5.
Chapter 2
Equalizer Design for WLAN
In this chapter, a tri-mode equalizer design for wireless LAN is proposed. The proposed equalizer includes CFO mitigation, channel estimation, phase error tracking (PET) and MIMO detection. Data distortion caused by multi-path fading, residual CFO and SCO can be eliminated together with equalization.
2.1 System Platform Description
IEEE 802.11n is an OFDM-based indoor WLAN system. We assume there are two transmitted antennas and two received antennas, the block diagrams of the baseband transceiver can be illustrated in Fig 2.1. The transmitted data are coded, MIMO signal processed, interleaved, mapped and modulated by IFFT. Then cyclic prefixes are inserted and OFDM symbols are windowed before upsampling and transmitting through channels.
The MIMO signal processing has two types. SDM is a spatial multiplexing transmission so it can raise the symbol rate to N times by N parallel transmitted antennas. STBC codes the signal at different time and different antennas to achieve transmit diversity. SDM can achieve high speed transmission, and STBC can get excellent system performance on the other hand. These two 2x2 MIMO signal processing are illustrated in Fig 2.2. The techniques of MIMO symbol detection for both MIMO signal will be described in section 2.5.
Mapping IFFT
Figure 2.1 System block diagram.
...
Figure 2.2 2x2 MIMO signal processing.
While receiving, we assume perfect synchronization. Then cyclic prefixes are removed, and signals are transferred to frequency domain by FFT. The following step is equalization. The tri-mode equalizer consists of CFO mitigation, channel estimation, phase error tracking and MIMO detection. The equalizer not only deals
with the channel effect but also compensates the CFO and SCO effects. The algorithms of equalization will be described in detail in the following sections. After equalization, de-mapping, de-interleaving and decoding are processed to recover data.
2.2 CFO Mitigation
To enhance the accuracy of channel estimation, CFO mitigation is utilized to reduce phase errors in the training fields which are used to estimate channels in the mixed-mode of 802.11n.
In 802.11n, the preamble and the header have a Compatibility portion and a High throughput portion for mixed-mode operation [12]. The Compatibility portion of the mixed mode header consists of legacy signal field (L-SIG) can be decoded by non-HT devices, as well as HT devices. What has been observed is that the pilots of the L-SIG, HT-SIG and values in pilot locations in L-LFT in this preamble structure can be utilized for CFO mitigation in HT mixed-mode operation. The training symbols of 802.11n are shown as Fig 2.3.
L-STF L-LTF L-SIG HT-SIG
HT-STF
HT-LTFs Data
8u 8u 4u 8u 4u 4u per
LTF
Compatibility portion High-Throughput portion Figure 2.3 Training symbols of 802.11n.
We utilize the concept of the D-symbol estimation [14]. When the remained CFO and SCO are relatively smaller or the Noise is very large, the differences of the rotated phases between two adjacent symbols are very small, as illustrated in Fig.
2.4(a). This may result in poor estimation accuracy and in some cases may give estimation results of the opposite sign. If we compare the phase rotation of the current symbol with the next D symbol that delays D-symbol-interval, demonstrated as Fig.
2.4(b) and (c). the effects of noise may be reduced to some extent. From above conclusions, the proposed CFO mitigation uses 2-symbol estimation to avoid this problem thus gets better performance.
D
(a) (b)
(c)
Figure 2.4 The principle of D-symbol estimation [14]
The signal is compensated by CFO and the guard interval is removed before FFT. Under consideration of residual CFO as fD , SCO as d=(Ts’-Ts)/Ts, where Ts
is the sampling time and Ts’ is the offset sampling time. The post-FFT data stream
Y
l,k,n at the k-th sub-carrier and the n-th receive antenna during l-th OFDM symbol duration can be expressed as:1
2 ( ) /
, , , , , , , ,
sts
l u g u
sts sts
sts
j l m T T T N
l k n k l i k i n k l n
i
Y e
p fd H w
=
D +
= å +
(2.1)where , ,
d is the complex signal that is transmitted through the
k-th sub-carrier and the i
sts-th transmitted antenna during l-th OFDM symbol duration.W
k,l,n is the noise caused from Additive White Gaussian Noise (AWGN), ICI, phase noise and other non-ideal parameters. Leta = D × f T
u be the phase shift caused from the residual CFO in an OFDM symbol. There (2.1) can be re-written as1 L-SIG and HT-SIG can be rewritten as
1 convenient because SCO value is relative small compared with CFO at the beginning of a packet. Assume that the channel response is almost static in the duration of a packet which holds true for most indoor scenarios because the duration of a packet is relatively shorter than the coherence time of indoor channel. The pilot patterns in the L-SIG and HT-SIG are defined as the same as pilot patterns in 802.11a standard [15].
The pilot patterns in L-SIG and HT-SIG totally three symbols are exactly identical, so we can directly compute the phase differences between any of the two consecutive symbols. On the other hand, the phase differences between the first L-LTF symbol and L-SIG need to be multiplied by an additional correct vector η . Define the first
received L-LTF symbol as Yl. The 2-symbol phase difference ˆ ,1 CFO mitigation are illustrated as Fig 2.5.
Figure 2.5 Training symbols required for proposed CFO mitigation.
The value of residual CFO is very small after coarse and fine CFO estimation and compensation. To translate the complex-valued signals to phase, arctangent can be approximated by a real divider. The double residual CFO value
a¢ is obtained by
averaging over ˆ ,1In proposed design, the phase error of HT-LTFs can be compensated by counter rotating the estimated phase in frequency domain with CORDIC modules.
2.3 Channel Estimation
Multipath fading is one of the data distortion issues in OFDM systems. The wideband signal is transmitted over frequency-selective fading channel. The preamble-based channel estimation is generally used under indoor channel because the duration of a packet is relatively shorter than the coherent time, i.e. the channel is assumed to be constant during a packet period. After obtaining the estimated channels, equalization is applied to remove the multipath influence.
(1) SISO mode
In OFDM-based wireless LAN systems, preamble-based Zero Forcing channel estimation is generally applied to estimate the channel frequency response for SISO mode due to its advantage of low complexity. The pre-known signal is defined as
a
l k, in the preamble with l = λ,λ+1. Using the feature of the repeated structure in of long preamble in frequency domain, we can average the result of twice Zero Forcing estimations to suppress noise. The estimate of k-th sub-channel is generally given by, 1, Equation 2.8 can be modified as
, , 1,
ˆ
k0.5
k(
k k)
H = ´ a
l´ Y
l+ Y
l + (2.9)The estimated channels can be improved further by passing them through a smooth filter. We use a three taps [0.25 0.5 0.25] FIR filter based on the correlative property between adjacent sub-carriers. The smoothed channels are compared with the results of the per tone estimation only in Fig 2.6.
Figure 2.6 Smooth the estimated channels with a 3 taps fir filter
(2) 2x2 MIMO modes (SDM-MIMO/ STBC-MIMO)
H22
Figure 2.7 2x2 MIMO Channel Estimation for 802.11n
For 2x2 MIMO transmissions for 802.11n, there are two symbol durations for HT-LTF. The relationship between the transmitted preambles and the combinations of
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0
the signals in receiver are illustrated as Fig. 2.7. We note that the HT-LTF is transmitted in Alamouti form for 2x2 MIMO. The pre-known signal is defined as ak in the preamble, and the received preamble signals of k-th sub-channel can be expressed as: frequency responses can be obtained by simple linear combinations.
After linear combination, the 2x2 MIMO channel estimates of k-th sub-channel are given by: equation 2.12 can be modified as
1, 6, 1, 7, 1, 6, 1, 7,
Carrier Frequency offset (CFO) and sampling clock offset (SCO) are the other two major data distortion issues in OFDM systems. Though CFO has been mitigated
in data portion still can not be neglected. Residual CFO and SCO rotating the received data in constellation diagrams cause great data errors while receiving. Phase error tracking (PET) is generally applied to trace the phase rotation caused by residual CFO and SCO; Fig. 2.8 shows the 64QAM constellation with and without PET.
(a) (b)
Figure 2.8 64QAM data constellation: (a) without PET (b) with PET
2.4.1 Carrier Frequency Offset Tracking
In this section, an Least Mean Square (LMS) based adaptive CFO tracker is proposed. Considering the integration of the three modes, different but similar algorithms are used here in order to get a good trade-off between performance and computational complexity. The proposed CFO tracking has three steps to complete the adaptive recursion.
Step 1. Pilot Pre-compensation
When the packet length is long, the phase error caused by residual CFO may exceed the ±π range. This will cause large estimation error while tracking residual CFO using conventional PET. The pilot pre-compensation concept [16] is utilized to solve this problem. The received data after pilot pre-compensation is written as:
ˆ 1,
After pilot pre-compensation, the detected pilot phase is the difference between two adjacent OFDM symbols. The detected pilot phases in complex form can be
P
l + is the transmitted pilot value of k-th sub-carrier of ists-th transmitted antenna during (l+m)-th OFDM symbol duration. The pilots occupies at k = -21, -7, 7, 21 in each OFDM symbol.To average the phases over receiving streams and pilot sub-carriers, We use two different methods to obtain mean phase error in the three modes. Linear Least Square (LLS) [14] is utilized in SDM-MIMO and STBC-MIMO modes, and Weighted Least Square (WLS) [17] is utilized in SISO mode on the other hand. LLS has the advantage of low computational complexity, but has bad performance in the condition of few pilot numbers, especially in low SNR conditions. WLS has better performance than LLS by using the information of signal’s power but pays the price of more complexity in hardware. In the 2x2 SDM-MIMO and STBC-MIMO modes, there are eight pilots from two data streams totally, but there are only four pilots for PET utilization in SISO mode. For these reasons, we use WLS and LLS to estimate the phase rotations from residual CFO in SISO mode and SDM-MIMO/STBC-MIMO
modes, respectively.
Linear Least Square for SDM-MIMO/STBC-MIMO modes:
, , Weighted Least Square for SISO mode:
2
where wl+m,k is the weighted coefficients of k-th sub-carrier during (l+m)-th OFDM symbol duration and it is calculated from the power of received data,
a
l¢ is the +m estimated phase shift from residual CFO between (l+m-1)-th and (l+m)-th symbols.To get the pilot phase difference between two adjacent symbols from complex value ˆu , the arctangent operation can be approximated by a real divider because the phase difference values are very small between two adjacent symbols.
Step 3. Recursive Adjustment
ˆ (ˆ ˆ ) ( )
The first estimate of residual CFO for SISO mode can be obtained by
1, ,
2.4.2 Sampling Clock Offset Tracking
Assume that carrier frequency and sampling time are generated by the same reference oscillator in receiver as suggestion of 802.11n specification [13]. The phase shifts caused from CFO e and SCO d have the following relationship:
(
f T
c FFT)e
= × × (2.26)d
where fc is carrier frequency and TFFT is the duration of FFT.
2.5 MIMO Detection
In this section, one tap channel equalizer for SISO mode and two types of 2x2 MIMO symbol detectors for SDM-MIMO and STBC-MIMO are introduced respectively. The complexity in hardware is important considering implementation.
Zero Forcing (ZF) having low complexity is generally used in SISO mode for wireless LAN. The optimal SDM-MIMO symbol detector is the maximal likelihood (ML) detector, but its complexity increases exponentially with number of transmit antennas and modulation order [18]. Sphere decoding scheme has the main disadvantage of lots delay. Vertical Bell Labs Layered Space-Time (V-BLAST) is a sub-optimal solution also requires lots of computational complexity on ordered-successive-interference cancellation (OSIC). On the other hand, minimal mean square error (MMSE) provides a good trade-off between performance and complexity for SDM-MIMO detection. The data encoded by STBC has an advantage of low complexity in receiver. The data is transmitted in Alamouti form for 2x2 STBC-MIMO mode, so maximal likelihood (ML) symbol detection can be utilized to decode STBC-MIMO signals.
2.5.1 Zero Forcing channel equalizer for SISO mode
The ZF channel equalizer can be expressed as ˆ ( ) ( )ˆ
k
X k Y k
=
H
(2.27) where ˆX is the equalized signal of k-th subcarrier. In Equation (2.27), received data
k Yk is divided by the estimated Channel Frequency Response to eliminate multipath fading.2.5.2 Minimal Mean Square Error SDM-MIMO Symbol Detection The channel matrix coefficients of the k-th subcarrier are given by:
1, 3,
Equation (2.28) can be re-written as:
1 3
The receiving signals can be modeled as:
Y(k)=H X(k)+N(k)× (2.30) where Y(k) and X(k) are the received and transmitted signals of k-th subcarrier respectively, and N(k) is the noise term.
We define an error vector e(k) which is the difference between the transmitted signals and the received signals which have passed through MMSE filter. e(k) is defined as :
e(k)=X(k)-G Y(k) (2.31) H
where G is the MMSE filter. We define the cost function J as:
J=E{e (k)e(k)} (2.32) H
Because J is a scalar value, it can be re-written as:
J=tr[E{e(k)e (k)}] (2.33) H
To minimize cost function J, we set zeros to the complex gradient vector JÑ , then Wiener-Hopf equation is obtain as:
H
where RYY is the covariance of the received signals and RXY is the cross-correlation of the transmitted and received signals.
From Equation (2.34), we can obtain MMSE filter as:
1 1
and Equation (2.36) can be re-written as:
1 1
The noise power can be calculated as:
1 2 1 2 2 Finally, we can obtain the decoding signal as:
ˆ ( ) H ( )
X k
=G Y k
× (2.40)The constellations after MMSE detection are shown as Fig. 2.9.
(a) SNR=14 (b) SNR=28
Figure 2.9 Constellation diagram of MMSE detection under different SNR.
2.5.2 Maximal Likelihood STBC-MIMO Symbol Detection Example of the 2x2 STBC-MIMO transmissions:
Table 2.1 Transmitted signals for 2x2 STBC-MIMO
TX1 TX2
Symbol 1 S0 S1
Symbol 2 -S1* S0*
The receiving signal for 2x2 STBC-MIMO can be express as:
0 0
where yij represents the receiving signal of i-th receiving antenna at j-th symbol.
Equations (2.41) and (2.42) can be transferred as:
0 0
(a) SNR=10 (b) SNR=18
Figure 2.10 Constellation diagram of ML detection under different SNR.
Chapter 3
System Simulation and Performance Analysis
In this chapter, we will discuss the design flow, system platform and performance for the proposed design. A complete baseband system platform on MATLAB is established complaint to 802.11n draft to verify the proposed design.
Channel estimation accuracy, PET performance and PER for overall system will be simulated and be compared with conventional approaches.
3.1 Design and Verification Flow
In design and verification flow as shown in Fig 3.1, we first have to understand the design requirements. Second, appropriate algorithms can be determined for proposed design, and then be simulated in float point on MATALB to evaluate whether it meets the specification requirements. Next, word length in each operation will be determined to compromise between performance and complexity in fixed point simulation. The simulation on MATLAB is completed here if the performance of fixed point simulation meets specification requirements. The RTL code is developed according to the fixed point simulation and then is synthesized by XST Synthesizer built in Xilinx ISE. Finally the flow is completed after FPGA verification.
Figure 3.1 Design and verification flow
Figure 3.2 The system platform on MATLAB
3.2 System Platform on MATLAB
Our system platform on MATLAB is illustrated as Fig 3.2. The platform is built
chapter 1. The parameters of the system environment are set according to IEEE 802.11 TGn Comparison Criteria 67 [6]:
n Trace-back length of Viterbi decoder is 128.
n No smoothing filter for channel estimation, i.e., per tone estimation n PPDU length is 1000 bytes.
n SNR is calculated as ensemble averaged SNR.
n When the number of packet error reaches to 100, then quit from this loop.
n 20,000 seeds of channel realization are used Physical layer impairments added in our platform include
n IM2 (Carrier frequency offset) Offset value is -20ppm, and sampling clock offset is also added.
n IM6 (Antenna Configuration) Antenna configuration is linear array and distance between adjacent
two antennas is a half wavelength.
In our simulations, we have one FEC encoder and two spatial streams. Rate 1/2 convolutional coding is employed. Also, 800 ns Guard interval is used. The IEEE indoor MIMO WLAN channel model ‘D’ [5] in the condition of non line of sight (NLOS) is applied. No beamforming is considering in our system.
3.3 Performance Analysis
The performance of the tri-mode equalizer for 802.11n will be simulated and analyzed in this section. We will focus on the 10% PER in system performance, which is the requirement of IEEE 802.11n standard.
3.3.1 Channel Estimation Accuracy Analysis
Channel estimation accuracy is highly related to the effects of residual CFO in preamble portion for 802.11n as introduced in chapter 2. HT-LTFs are use to estimate MIMO channels in preamble based channel estimation, and the residual CFO in HT-LTFs can be suppressed by CFO mitigation. So channel estimation accuracy is used to analyze the performance of CFO mitigation. We first define the mean channel estimation error as subcarrier and M×N is the dimension of
H . Fig. 3.3 shows the residual CFO effects
k on channel estimation error under different CFO mitigation algorithms for 802.11n (2x2 system) on a TGn D channel.10 12 14 16 18 20 22 24 26 28 30
10-2 10-1 100
Mean channel estimation errors at different SNR
SNR per receive antenna, dB
Mean Channel estimation errors per sample
proposed w/o mitigation
ref [4]
ideal cfo esti.
Figure 3.3 Mean channel estimation errors vs. SNR under different
The proposed CFO mitigation achieves 1.0~4.0dB SNR gain in mean channel error compared with conventional one which is without CFO mitigation. Compared with the method used in [4], there are still 0.5~2.0dB SNR improvement in mean channel error, so the proposed CFO mitigation algorithm increases the accuracy of channel estimation effectively.
3.3.2 Phase Error Tracking Performance Analysis
CFO is one of the main factors to degrade system Packet Error Rate (PER) performance. In order to verify the PET performance, the design is simulated under 40ppm CFO, which is standard requirement. The transmission is under QPSK and 1/2 coding rate. Fig 3.4 shows that different PET algorithms are compared for 802.11n (2x2 system) on PER performance. We notice that conventional weighted average method [14] can not get good performance and mean average method [16] is even worse. As mentioned in chapter 1, the pilot-based PET can not suppress noise enough to get a satisfied PER performance due to few pilot numbers in WLAN systems,
Figure 3.4 Compare PET Algorithms at 2x2 MIMO, QPSK, ½ Code rate.
4 6 8 10 12 14 16 18 20
10-2 10-1 100 101
Compare PER
SNR
mean average proposed method weighted average
Ideal CFO Estimation PER = 10%
especially in low SNR region. There are only 4 pilots can be utilized per data symbol in one data stream for wireless LAN systems. On the other hand, the proposed adaptive CFO tracking algorithm suppresses the PER loss due to residual CFO within 0.2 dB for 802.11n (2x2 system) compared with ideal CFO estimation. From Fig. 3.4, the proposed adaptive PET achieves 3.0 dB gains than weighted average one at 10%
PER requirement. We can conclude the proposed PET increases the system 40ppm CFO and 40ppm SCO in receiver.
The required SNR for SISO and SDM-MIMO modes to achieve 10% PER are listed in Table 3.1. The proposed baseband system can achieve 0.2~3.8dB and 0.2~1.2dB SNR gain compared with TGn proposed results [19] and [20], respectively.
Table 3.1 PER Performance Comparison on SISO/SDM
35.5
Required SNR, This Work 21.8
33.3 24.4
Required SNR, Ideal 21
33.5 25
Required SNR, PLL Based [2] 23
130
Required SNR, This Work 21.8
33.3 24.4
Required SNR, Ideal 21
33.5 25
Required SNR, PLL Based [2] 23
130
Higher performance can be obtained in the proposed baseband receiver because
Higher performance can be obtained in the proposed baseband receiver because