This thesis is organized as follows. In Chapter 2, the simulation platform and detail specifications of the IEEE 802.11a WLAN and the multi-band OFDM-based Ultra-Wideband system will be introduced. Algorithms of the proposed channel equalizers for different requirements will be described in Chapter 3 and Chapter 4 respectively. The simulation result and performance analysis will be discussed in Chapter 5. Chapter 6 will introduce the design methodology, hardware architecture, and the chip summary of the proposed design.
Conclusion and future work will be given in Chapter 7.
Chapter 2 .
System Platform
In this chapter, we introduce the two system platforms for design analysis and performance simulation. The first one is developed complaint to IEEE 802.11a physical layer (PHY) [1].
The second is complaint to the Ultra-Wideband (UWB) with multi-band OFDM modulation proposed by Texas Instrument (TI) [2]. The detail block diagrams and system specification will be described as follows.
2.1 Introduction to IEEE 802.11a System
IEEE 802.11a is an OFDM-based indoor WLAN system. The block diagram of the baseband transceiver can be illustrated in Figure 2.1.1.
Data out
acquisition Guard-interval FFTFFT reduction
de-mapping Viterbi De-scramblerDe-scrambler
decoder
encoder InterleaverInterleaver Constellation mapping
Figure 2.1.1 System platform of IEEE 802.11a PHY
The system platform includes a COFDM modem and an indoor radio channel model. The COFDM modem comprises a 64-point DFT-based QAM-OFDM modem and a forward-error correction (FEC) coding. The supported data rate is from 6Mbits/s to 54 Mbits/s with coding rate equals 1/2, 2/3 and 3/4. The system parameters can be listed in Table 2.1
Table 2-1 System parameters of IEEE 802.11a PHY Constellation mapping method BPSK, QPSK, 16QAM, 64QAM Date rate (Mbits/s) 6, 9, 12, 18, 24, 32, 48, 54 FEC coding rate (R) 1/2, 2/3, 3/4
FFT size (N) 64
Number of used subcarriers (NST) 52 Number of data carriers (NSP) 48 Number of pilot carriers (NSD) 4
IFFT/FFT period (TFFT) 3.2us
GI duration (TGI) 0.8us (TFFT/4) PLCP preamble duration 16us (TSHORT + TLONG)
The PLCP preamble is a training sequence used for synchronization. It comprises ten short symbols and two long symbols. The two long symbols are used for zero forcing CE. The training structure can be shown in Figure 2.1.2.
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 GI2 T1 T2 GI SIGNAL GI Data 1
Short preamble 10*0.8 = 8us Long preamble 2*0.8 + 2*3.2 = 8us 8+8 = 16us
0.8 + 3.2 = 4us 0.8 + 3.2 = 4us
Figure 2.1.2 Training structure
The indoor radio channel model comprises a time-variant Rayleigh fading channel, CFO,
SCO and AWGN. The detail channel model blocks will be discussed in the later section. In the baseband receiver, first, time-domain synchronization estimates and compensates signal distortion from AGC error, symbol-timing drift, and CFO. And then FFT is applied to make signal transformation from time domain to frequency domain. After FFT, the proposed channel equalizer is applied to remove frequency domain data distortion issues, such as multipath fading, residual CFO and SCO. Later, the data subcarriers are de-mapped and decoded by the FEC design. Finally, the received system parameters and data bits are sent to MAC.
2.2 Introduction to Ultra WideBand System
UWB is a new generation wireless communication systems, which is used for high-speed, short-range data access. It will be wildly used in the future digital home electronics appliance industry. UWB has not been standardized; we focus on the multi-band OFDM UWB in this thesis [2]. The block diagram of the UWB PHY is similar to the IEEE 802.11a WLAN system.
The key differences between these two systems can be listed as follow,
OFDM symbols are interleaved across both frequency and time. An example of the time-frequency interleaving (TFI) can be shown in Figure 2.2.1.
Channel #1
Figure 2.2.1 TFI example of the UWB PHY [2]
The supported data rate is up to 480Mbits/s, which is almost ten times of the data rate in IEEE 802.11a systems. A 128-point FFT is applied and only PSK (BPSK, QPSK) is used in the UWB system.
In the 55Mbits/s and 80Mbits/s transmission mode, data subcarriers are duplicated four times within an OFDM symbol. In the 110Mbits/s, 160Mbits/s and 200Mbits/s mode, data subcarriers are duplicated twice within a OFDM symbol
The detail specifications of the multi-band OFDM UWB PHY can be listed in Table 2.2.
Table 2-2 System parameters of the multi-band OFDM UWB PHY Constellation mapping method BPSK, QPSK
Date rate (Mbits/s) 55, 80, 110, 160, 200, 320, 480 FEC coding rate (R) 1/2, 3/4, 5/8, 11/32
FFT size (N) 128
Number of used subcarriers (NST) 112 Number of data carriers (NSP) 100 Number of pilot carriers (NSD) 12 Data bytes per packet 1024
IFFT/FFT period (TFFT) 242.42ns
Cyclic prefix duration (TCP) 60.61ns (TFFT/4) Guard interval duration (TGI) 9.47ns
PLCP preamble duration 9.375us (TSHORT + TLONG)
Because of the time interleaving, the data format is a little different from the format in 802.11a system. The preamble and data format can be shown in Figure 2.2.2. In IEEE 802.11a system, GI is the cyclic prefix of each OFDM symbols, which is used for the concern of
multipath spreading. In UWB system, cyclic prefix (CP) is for multipath concern and the GI is particularly referred to the time between band switching. Because of the time interleaving, six OFDM symbols are used for basic channel estimation. For example, CE0, CE4 is for channel #1; CE1, CE5 are for channel #2; and so on.
PS20 21 OFDM symbol*312.5ns
9.375us
PS0 PS1 FS0 FS1 FS2 CE0 CE1 CE5
3 OFDM symbol*312.5ns 6 OFDM symbol*312.5ns
Packet Sync Sequence Frame Sync Sequence Cannel Estimation Sequence
• • • • • • • • •
OFDM Symbol
CP GI
242.42ns
60.61ns 9.47ns
312.5ns
(a)
(b)
Figure 2.2.2 UWB PHY (a) OFDM symbol format (b) training structure
Although the signal flow of UWB is very similar to the flow in 802.11a system. There are some particulars that can be used for design modification and algorithm improvement to achieve the very high-speed and low-cost requirements of UWB system. This part will be discussed in chapter 4.
2.3 The Indoor Wireless Channel Model
In order to simulate the data transmission in the real environment, an indoor wireless channel model is established, which includes a time-variant multipath fading [14-15], CFO, SCO, and AWGN. The detailed are introduced individually below
2.3.1 Multipath Fading Channel Model
In wireless transmission, transmitted signal arrives at receiver through several paths with different time delay and power decay, which is called multipath interference. The received signal can be modeled as
) (
) ( )
( N N
N
t x t
x t
y = +
∑
β ⋅ −τ (2-1)ISI and a frequency-selective fading occur when the maximum delay spread is larger than the symbol period or the channel coherent bandwidth is smaller than the data bandwidth. The applied multipath fading channel is established according to the IEEE specification. The applied multipath fading channel consists of 13 independent taps, which has Rayleigh distributed magnitude, exponentially decayed power and random uniformly distributed phase [14]. The channel impulse response (CIR) and the channel frequency response (CFR) with RMS delay equals 50ns are shown in Figure 2.3.1.
(a) (b)
Figure 2.3.1 (a) CIR (b) CFR example of the multipath fading channel
In order to bring the practical time-variant characteristic to the applied channel model, the Doppler effect is modeled according to Jake’s Doppler spectrum [15]. 50Hz Doppler frequency caused by 10 KM/hr opposite speed in 5GHz band is modeled for indoor
environments.
2.3.2 Carrier Frequency Offset Model
The sensitivity to carrier frequency offset (CFO) is one of the main drawbacks of the OFDM system. The orthogonal property of OFDM system is based on the perfect frequency carrier sampling. When transmission with CFO, the received data will be influenced by the data in other subcarriers, which is referred as ICI. The subcarriers spectrum can be shown in Figure 2.3.2.
Perfect carrier sampling Carrier sampling with CFO
frequency frequency
(a) (b)
Figure 2.3.2 The received data (a) without CFO (b) with CFO (ICI)
CFO is caused by the radio frequency mismatch and the relative speed between a single transmitter and a receiver. The received data y(t) can be modeled as
(
j f f f t)
t x t
y( )= ( )⋅exp− 2π( 1+ ξ − 2)⋅ (2-2)
Where f1 is the transmitter carrier frequency, f2 is the receiver carrier frequency and fξ is the frequency shift caused by Doppler effect. From equation (2-2), CFO causes a linear phase shift in time-domain. From Moose’s law [16], the linear phase shift in time-domain converts to the ICI in frequency-domain. The received data after FFT with CFO can be
derived as
)) , ( )
, ( ( )
,
(N k e 2 ( )( ) X N k ICI N k
Y = −j π N⋅ls ⋅ ∆f T ⋅ + (2-3)
When CFO is smaller than 2ppm of the 5GHz, the ICI in frequency-domain can be neglected.
The mean phase error will dominate the signal error. Figure 2.3.3 shows the frequency-domain signal distortion with CFO equal to 20ppm and 0.4ppm respectively.
dominant by ICI dominant by the linear mean phase error
Phase [rad] Phase [rad]
Phase [rad] Phase [rad]Magnitude [dB]Magnitude [dB]
Magnitude [dB]Magnitude [dB]
Figure 2.3.3 Signal distortions with CFO equal to 20ppm and 0.4ppm respectively.
2.3.3 Sampling Clock Offset Model
SCO is the sampling clock rate mismatch between the digital to analog converter (DAC) in transmitter and the analog to digital converter (ADC) in receiver. Because of the SCO, even if the initial sampling point is optimized, the following sampling points will slowly shift with
time. This shift in time-domain becomes a phase rotation in frequency-domain. The SCO model is established by the concept of oversampling with interpolation. Figure 2.3.4 shows the time-domain oversampled received data and the frequency-domain linear phase shift caused by SCO.
(a)
(b)
Figure 2.3.4 (a) the time-domain sampling offset (b) the frequency-domain linear phase shift
2.3.4 AWGN Model
The AWGN channel model is established by the random generator in Matlab. The output random signal is normally distributed with zero mean and variance equal to 1. The complex AWGN noise can be modeled as
[ ]
2 ) 10 randn(1, j
) randn(1,
)
( 20
SNR PS
t w
−
⋅
⋅ +
= l l (2-4)
Where PS is the data signal power, SNR is the signal to noise power ratio, and l is the data signal length.
Chapter 3 .
A Channel Equalizer Design for OFDM WLAN Systems
In this chapter, a high performance channel equalizer design for general OFDM WLAN systems is proposed. It includes a data-aided decision-directed channel estimation (DDCE) and a pilot-aided phase error tracking (PET). Data distortion caused by multipath fading, residual CFO, and SCO can be eliminated together with channel equalization.
3.1 Decision-Directed Channel Estimation
Multipath fading is one of the data distortion issues in OFDM systems. ISI occurs due to the multiple transmission paths between a single transmitter and a receiver. The channel frequency response (CFR) of the multipath environment is so called as a frequency-selective fading. In OFDM WLAN systems, zero forcing CE with known training sequence is generally applied to estimate the CFR and equalization is applied to remove the multipath influence.
The zero forcing (ZF) channel estimation [9] and equalization can be derived as
) (
) ) (
( X k
k k Y
H
L L
A = (3-1)
) (
) ) (
( H k
k k Y
X
A D
e = (3-2)
In equation (3-1), YL is the received training sequence, XL indicates the defined (transmitted) training sequence and HA is the estimated CFR. After CE, received data YD is
then divided by the estimated CFR to eliminate multipath fading as equation (3-2). Under the assumption of a packet-time invariant CFR in WLAN systems, CE is applied in the beginning of every packet and never updated until the next packet. However, CE error exists since the additive noise in training sequence and the time-variant characteristic in a practical wireless environment. The example of CE error between the estimated CFR and the real CFR can be shown in Figure 3.1.1.
0 10 20 30 40 50 60
0 0.5 1 1.5 2 2.5
#subcarrier Magnitude
estimated CFR real CFR
Figure 3.1.1 Channel estimation (CE) error
(a) (b)
Figure 3.1.2 64QAM data constellation：(a)without CE (b)with CE
CE error makes equalization imperfect and degrades the system performance. Figure 3.1.2 shows the 64QAM data constellation distribution. Data is seriously distorted without CE or without an accurate CE.
A data-aided DDCE is proposed to enhance system performance. CE accuracy can be improved and equalization error can be reduced through this scheme. The block diagram of the proposed DDCE can be illustrated in Figure 3.1.3.
From FFT
Figure 3.1.3 Block diagram of the proposed DDCE
This proposed DDCE consists of a basic ZF scheme, smoothed filter and a data-aided decision-directed error-tracking scheme. In the initial training sequence, CFR is estimated by the ZF scheme. The estimated CFR can be derived as equation (3-1). Based on the continuity of the real CFR, large variations between adjacent subcarriers can be taken as the influence of noise. Therefore, a smoothed filter is proposed to reduce additive noise. The estimated CFR is smoothed by a low pass filter after ZF. This smoothed filter is realized by a 5-tap bit-selection
and adder (BSA) without any multiplier in the concern of low complexity. The impulse response of this 5-tap BSA can be derived as
∑
After BSA, the smoothed CFR is inversed and stored to do later data equalization. If the data subcarriers are perfectly equalized, that is, multipath influence is completely removed and only additive noise influence left in the data constellation as shown in figure 3.1.4, the mean of data subcarriers should be exactly at the defined constellation point due to the zero mean additive noise. However, CE error exists and causes equalized data drift.
I Q
E
Data distribution with AWGN only
Data distribution with CE error
Defined constellation point
1 -1
-1 1
Figure 3.1.4 Data constellation distribution with and without CE error
Based on the idea mentioned above, a data-aided decision-directed error tracking is proposed to eliminate CE error further. The equalized subcarriers Xe(k) with estimated CFR HA(k) can be shown as
[ ]
frequency-domain additive noise in data subcarriers. The estimated CFR error ΔH(k) causes the de-mapping error vector between the equalized carrier Xe(k) and the predicted de-mapping result XD(k). This error vector can be derived asFor CE error estimation, the mean of normalized constellation error vectors is evaluated to eliminate the zero-mean additive noise Wi(k). The mean of the normalized constellation error vectors during l OFDM symbols is listed as packet-invariant CFR, such an infinite average method can reduce the zero-mean noise efficiently. However, for a practical time-variant wireless channel, this method will eliminate channel variations as noise. Therefore, the tracking length β depends on the applied channel condition of different system specifications. The estimated channel error can be derived as
∑
− +This loop filter can be realized as equation (3-8) to reduce computation complexity. Since XD(k) is the predicted de-mapping result, XD-1(k) can be implemented by table-look-up (TLU) method with an inversed-defined-constellation-point table. N-1 and (N-1)‧N-1 terms can
also be generated by look-up tables to avoid using high cost dividers.
The estimated CE error is then feedback to the channel equalization; update the estimated CFR in memory. The updated CFR can be listed as
)
Because of HA(k) is updated every OFDM symbol, equation (3-8) can be modified as follows
N
Under this feedback loop, CE error can be compensated with the original channel equalization multiplier without any additional compensation scheme. Moreover, the accuracy of such a decision-directed based algorithm highly depends on the correctness of input data. That is, CE error is decreased before the decision-directed error tracking and later pilot-based PET in each data OFDM symbol; both tracking scheme accuracy can be enhanced under the proposed feedback scheme.
3.2 Phase Error Tracking
CFO and SCO are the other two data distortion issues in OFDM systems, which are mainly induced by crystal oscillator frequency mismatch and relative motion between transmitter and receiver. ICI occurs and causes received data distortion. Time-domain acquisition is generally applied to mitigate CFO, however, the residual CFO and SCO still cause data rotation in frequency-domain and make received data incorrect. PET is generally applied to trace the phase rotation; the constellation distortion can be recovered after PET compensation. Figure 3.2.1 shows the 64QAM data constellation with and without PET.
(a) (b)
Figure 3.2.1 64QAM data constellation：(a)without PET (b)with PET
The time domain received data after preamble-aided synchronization can be listed as
T sampling clock period of transmitter and receiver individually,λ is the relative SCO defined in [17]. The frequency domain received data subcarriers can be indicated as
)) is the influence caused by ICI and can be neglected if the remaining CFO is small enough.
However, the remaining CFO and SCO will also bring the problem of increasing phase rotation with symbol index, which cannot be neglected even with a slight residual CFO and SCO. The phase rotation of the Nth OFDM symbol and kth subcarrier can be derived as
The first term is caused by residual CFO, which is a constant phase rotation within an OFDM symbol. This constant phase increases with OFDM symbol index. The second term is caused by SCO, which is a linear phase rotation with subcarrier index. The slope of this linear phase increases with OFDM symbol index. The phase rotation of subcarriers and OFDM symbol can be shown in Figure 3.2.2.
Figure 3.2.2 Phase rotation caused by residual CFO and SCO
The data flows of conventional PET approaches are shown in Figure 3.2.3. The conventional feedforward PET traces the pilot rotations without any pre-compensation. Data subcarriers are compensated with the present tracking information which has a high accuracy.
However, the tracking value will be seriously miscalculated if the phase rotation exceeds ±π.
In IEEE 802.11a 6Mbits/s and 1Kbytes/packet transmission, the transmission time of one packet is 1.33ms. In general condition, residual CFO is more than 0.2ppm of the 5GHz RF frequency, maximum SCO is 40ppm, and the pilot phase error will arrive at ±3.4π in such a 1.33ms transmission time. In this transmission process, the phase evaluation of this feedforward PET failed and seriously degraded the system performance. Moreover, data subcarriers have to be buffered under this feedforward scheme which costs additional registers. Different from the feedforward design, the conventional feedback PET traces pilot rotations with a pre-compensation in pilot which increases the phase tracking range. Data
subcarriers are compensated with the phase rotation of the previous symbol [12]. Tracking accuracy becomes very important in such a feedback scheme.
Pilot Phase
Figure 3.2.3 conventional (a) feedforward PET (b) feedback PET
To avoid phase evaluation failure and keep high accuracy in the full phase error range, a high accuracy PET with feedback compensation scheme is proposed. It comprises a tracking scheme and a prediction scheme. The block diagram can be illustrated in Figure 3.2.4. Pilot subcarriers are pre-compensated with the phase rotation of the previous OFDM symbol to increase the tracking range. The pilot pre-compensation can be derived as
( )
by SCO. After pilot pre-compensation, the detected pilot phase is the difference between two adjacent OFDM symbols. The tracking scheme with fixed-coefficient loop filters can be listed asMean
Figure 3.2.4 Block diagram of the proposed PET
1 symbol. The first term of equation (3-16) is the linear regression method to find the slope of the curve, which has a minimum mean-square-error (MMSE) from it to the phase samples. A linear interpolation is then used to find the phase error of all subcarriers. The fixed-coefficient loop filters are applied to enhance tracking accuracy [18].
A prediction scheme is applied to estimate the increase rate C0 of the mean phase error and the increase rate C1 of the linear phase slope. With the prediction scheme, data subcarriers are compensated with the present phase rotation completely. The joint phase rotation caused
by residual CFO and SCO can be modeled as a linear equation
It can predict the phase rotation of the present data subcarriers by the previous tracking information. Moreover, since the two coefficients will saturate to a stable value after a certain number of OFDM symbol (S), the tracking scheme of the PET can be stopped and compensation can be continued by this prediction scheme. The feedback compensation loop can be listed as
Pilot subcarriers may be seriously distorted by additive noise and cause wrong estimations, especially in low SNR region. These wrong estimations will be accumulated in such a feedback loop. We proposed two check schemes to reduce the probability of making wrong estimations. First, compensation is conducted after getting a stable estimation by observing through a certain number of symbols. Moreover, we check the validity of estimations and
Pilot subcarriers may be seriously distorted by additive noise and cause wrong estimations, especially in low SNR region. These wrong estimations will be accumulated in such a feedback loop. We proposed two check schemes to reduce the probability of making wrong estimations. First, compensation is conducted after getting a stable estimation by observing through a certain number of symbols. Moreover, we check the validity of estimations and