2.5 I NTERPOLATION PROCESS
2.5.2 Interpolation in frequency domain
After interpolation in time domain between scattered pilots, we can get estimated CFR every three subcarriers. Then, we use these sampled CFR to interpolate the whole CFR at the rest data subcarriers. Since the interpolation in time domain is done, the sample interval in frequency domain is from 12 fc to 3fc, where fc is the subcarrier spacing. Here, we use Linear, Parabolic, Second-order, and Cubic, four methods for interpolation in frequency domain, where Ĥ(k) is the result of the interpolation in frequency domain, k is the sub-carrier index.
Hp(m) = H(3* <3(m+1), and
=k/3-m.
nomial int oint base-poin x(i)} can be
range form . 2.15.
m) is the CFR after interpolation in time domain, where 3m<k μ
Classical poly erpolation of an N-p t set {ti, performed by the Lag ulas [18-19]. It shows in Fig
0( ) '( ) k 0 k k
Fig. 2.15 Polynomial interpolation in frequency domain
A. Linear interpolation
2
is only 1/3 or 2/3 two kinds of values, so the taps can be calculated in advance,
E between these interpolation methods. As we know, high order tter performance than low order interpolation. But if we concern the noise effects, the MSE of high order interpola r than low order interpolation. The criteria are MSE, and the fo n in following equation (2-21).
2
and save in the registers.
Next we discuss the MS
interpolation will use more samples to get smother curves, and gets be
tion will not be always bette rmulation detail is show
| ( ( )) k | }2
MSE=
∑
Cj× Hj Nj+ −H(2-21)
ferent coefficients. The coefficients are listed on table 2-2, and the
ferent in each interpolation curve, so the higher order can get better
[ ])Hj Hk
In the same channel conditions, we can find that different interpolation methods which MSE will depend on dif
relationship is listed on table 2-3.
We can find that the first term in (2-21) will enhance the noise effect with high order interpolation in comparison of ( 2)
j
∑
Cj . In table 2-3 we can find the enhance term of each method. In the formulation, the other terms effects will be difmethod. In fact the CFR would be a smooth performance without noise effects.
(ex: 2 [ 2] (2 [ ] [ ]) (2
However, the noise effect term ( Cj E Nj2) [ 2]
∑
j will be worse with higher order interpolation. So there will be a crossover in simulation with different SNR noise. We can use the equation (2-21) to determine the crossover point with different channels.ssover po
e coefficients list
C2 C3
The noise term will be dominant at low SNR< crossover point, but the other term effect will be dominant at high SNR> cro int. Then we can choose the better interpolation method for different channel cases.
Table 2-2 th
C0 C1
Average 0 0.5 0.5 0
Linear 0 0.3333 0.6666 0
Lagrange (2 order) -0.1111 0.8889 0.2222 0 Lagrange (3 order) -0.0617 0.7407 0.3704 -0.0494
Table 2-3 the coefficients relationship
Average Linear Lagrange (2 order) Lagrange (3 order)
(Cj2)
∑
0.5 0.5555 0.8519 0.69212CiCj
∑
0.5 0.4444 0.1481 0.3078∑
2Cj 2.0 2.0 2.0 2.0Chapter 3
Channel Equalization Algorithms
, we in lization algorithms, and we w how the
ritical path is the complex division operation. The division model is dominant hardware cost nd power consumption in channel equalizer. So we can simplify this division model and
ow the results of saving hardware cost and power consumption in later sections.
to channel equalization
e the bandwidth into many ding. Therefore, the equalization for each subcarrier becomes simple in frequency domain, ly a one-tap equalizer to compensate the channel fading effects. In OFDM–based
.
In this chapter troduce the channel equa ill s
c a sh
3.1 Introduction
It is mentioned in Chapter 2. In OFDM system, it will divid
subcarriers, so the channel frequency response of each subcarrier can be considered as flat fa
and it is on
communication systems, the received signal R[k] can be expressed by [ ] [ ] [ ] [ ]
R k =S k H k⋅ +N k
Where S[k] is the transmitted signal, H[k] is the CFR, and N[k] is AWGN noise. The , (3-1)
estimated signal Ŝ[k] can be obtained by dividing the estimated CFR, Ĥ[k] from channel stimation.
propose one new method to simplify divider complexity without
transferring receiving data by
, (3-2)
In related research, there was other approach via changing receiving data format to achieve divider-free method [20]. Here, we keep up the full-time complex dividing operation with new approach. We
format. In the same time, we replace the division operation
re
and a few registers to implement.
3.2
In channel equalizer, it contains a complex number division. One complex division operation includes two real number divisions. As we know, the division hardware cost is proportional to square of word-lengths, but the signal bus needs sufficient digits to represent receiving signals in order to get enough accuracy. In DVB-T/H system, it will provide higher clock rate for 64Qam and Viterbi decoder. So we can reuse the hardware by raising clock rate.
Furthermore, we can optimize the saturation cases and don’t need to add word-length to get enough decimal fractions of the quotient. Then according to multi-cycles division, we can use the shift-subtraction structure to simplify the hardware efficiently.
In addition, the division gate count is about 62.8% of equalizer, and the cycle time of DVB
3.3 Proposed division scheme
First, we introduce the format notations. In complex divider, the equation can be expressed by:
currence step based algorithm [21]. In recurrence step algorithm, it only requires an adder (substracter)
Motivation
-T/H systems for 8Mhz channels is about 109ns. Due to the long cycle time and the high hardware cost of long digits dividers, we propose a low cost architecture to implement the equivalent divider.
s and n is at structure is show
are (m1, n1 ll produce some
intermediate 1, 2n1).
α. When
the output da α. The complex
division includes two real ore, in order
to get n2 bits in decimal ac t n2 bits left. The dividend beco
igh.
Fig. 3.1 The format (m, n) structure
First, we define the format (m, n) of the signed number, where m is the total bit
the bits of decimal. The form n in Fig.3.1. The formats of inputs a, b, c, d, ), and the formats of outputs e, f, are (m2, n2). In this process, it wi
values like (ac + bd), (bc - ad), and (c2 + d2), which formats are (2m Since the output can only present in dynamic range P, we define saturation point
ta is out of the range P, it will be saturated at saturation point number divisions with 2m1 bits word-length. Furtherm
curacy, so the dividend should shif
mes (2m1 + n2) bits and the divisor is (2m1) bits. And we can find in Fig.3.2, we can find the output of single cycle division is 2m1+n2 bits which is bigger than m2 bits. These bits present the saturation cases and over design here. It needs (2m1+n2) bits subtractor. So if we implement the divider by single cycle division model directly, the hardware will be cost h
Fig. 3.2 The bits presentation of division
In proposed separate one cycle
into many cy lify the divider to
subtraction by hardware reus
it will detect if state 3, else goes to
state 2. In state 2, it will do m ration and getting the
quotient by iterations. At last, it ate 3.The state diagram is shown in Fig.3.3.
design, the multi-cycle division,
t
he basic concept is to cles and get quotient by iterative subtraction. So we can simpe and raising clock rate.
First, the procedure of proposed division scheme consists of three states [21]. In state 1, the result is saturated or not. If saturation occurs, it goes to
ain function including subtraction ope will output the result of division in st
detect saturation
output the result do main function
Next operation Not saturated
Saturation
Fig. 3.3 The state diagram
As mention before, because of the format (m , n ) of output so we can detect that if the
so it will not be affected. In this method, the relative position of dividend and divisor is
2 2
turated in the beginning. If the result is saturated, we can get the diately. In that case, other logics will be idle for power saving.
First, we define A is the minuend, B is the subtrahend, and sub is the result of subtraction.
ine the quotient by subtracting B from A. In this algorithm, the quotient can only or ‘0’, so if A is larger than two times of B, the quotient can’t represent.
reason, we must make sure that A can not be larger than two times of B in state 2.
t normalize to saturation poin
ting (m2-n2-1) bits right, and let B be the divisor. The quotient will shift back at last,
exactly to get the MSB of the quotient, and we can detect the saturation case easily. We only take one cycle for saturation detection, and we can save (2m1+n2-m2) cycles.
Here, A is the dividend >> (m2-n2-1), and B is the divisor. If A is larger than B, it will represent that the quotient is saturation, and the quotient will be the saturation point α. If A is smaller than B, it will make sure that A can not be larger than two times of B, and it will go to state 2 to get the quotient. The flow of state 1 is shown in Fig.4.
Fig. 3.4 The flow of the state 1
In state 2, we can use subtraction to determine the quotient q[k] is ‘1’
akes sure A can not be larger than two times of B e can determine it by the sign bit of the subtraction and q[k] is ‘1’, A < B, the sign bit of sub is ‘1’
sub. Then, we update A depends on the sign bit of sub to get the next bit of quotient. We can get
2-1) cycles in state 2. The flow
between parameters is listed in
or ‘0’ by binary
property. Because it m . When A ≥ B, the q[k]
will be ‘1’ else not, w result. If A ≥ B, the
sign bit of sub is ‘0’ and q[k] is ‘0’. We can
find q[k] is the inverse of the sign bit of by (sub<<1) or (A<<1) the quotient of format (m2, n2) one by one bit through (m of the main function in state 2 is shown in Fig.3.5, and the relationship table 3-1.
Fig. 3.5 The flow of the main function in state 2 Table 3-1 the parameter relationship in state2
Sub>=0 Sub<0
Sign bit of sub “0” “1”
q[k] “1” “0”
Remainder (A) Sub<<1 A<<1
In state 3, it is output stage. e last cycle of state 2, and goes to next new division operation.
Furthermore, we should determine the clock rate of this architecture which depends on
the cycles of one operati e is for state 1 to detect
if it is saturation. The following (m2-1) cycles are for compu (m2-1) bits of quotient excluding sign bit. The sign bit can be dete before state 2 will output the complete quotient stably in the last . So there are cles needed in operation, in other word the ratio between mbol : m2}. Th g diagram is shown in Fig.3
It can output the whole quotient at th
on. It will take m2 cycles totally. The first cycl ting the
rmine . It
cycle m2 cy one
clock rate and sy rate is {1 e timin .6. The hardware implementation will mention in section 5.3.2.
Fig. 3.6 Timing diagram
Chapter 4 .
imulation and Performance Analysis
ter, the overall simulation platform built for DVB-T/H system will be illustrated odel and some other distortion source such as Doppler delay spread and iscussed later. Finally, the performance analysis of the proposed channel ualizer scheme and comparison with state of the art will be performed.
In order to verify the performance of the proposed channel equalizer scheme, a complete VB-T/H baseband simulation platform is constructed in Matlab. The block diagram of the
S
In this chap
first. The channel m SCO model will be d eq
4.1 Simulation Platform
D
overall simulation platform is shown as Fig. 4.1.
Fig. 4.1 Overall DVB-T/H platform
As shown in Fig. 4.1, the blocks with dotted line is the specific function blocks for DVB-H
system. By adding support of 4k IFFT/FFT, in-depth interleaving, and additional TPS information, the developed DVB-T system platform can share most of the function blocks with DVB-H system at the same time. The platform is composed of transmitter, channel, and receiver. A typical transmitter that receives data from MPEG2 encoder or IP datagram is completely established. The transmitter consist the full function of FEC blocks and OFDM modulation blocks. The coding rate, interleaving mode, constellation mapping mode, IFFT length, and guard-interval length are all parameterized and able to be selected while simulation. An oversampling and pulse shaping filter is added before data entering channel to simulate discrete signal as far as continuously. The oversampling rate is also parameterized and can be chosen according to the simulation accuracy. The roll-off factor of the pulse-shaping filter is chosen as a normal value α =0.15 because it is not defined in the DVB-T/H standard.
Various distortion models are adopted in the channel model to simulate real mobile environment such as multipath fading, Doppler spread, AWGN, CFO, and SCO. In practically, there are still some imperfect effects which contain co-channel interference, adjacent-channel interference, phase noise, and common phase error caused by imperfect front-end receiving.
However, the distortion of these imperfect effects is relatively smaller compared with effective time-varying channel response caused by Doppler spread, CFO, and SCO. Therefore these effects are neglected in our simulation platform.
The baseband receiver in our system platform can be divided into inner receiver and outer receiver as Fig. 4.2 shows. The inner receiver includes all of the timing and frequency synchronization function, FFT demodulation, ch ation, equalization, and pilot remove blocks. The outer receiver consists of
annel estim
other functional blocks that following the de-mapping. The transmission parameters extracted by TPS decoder such as constellation mapping mode and Viterbi code rate will be sent the relative blocks as control parameters.
Besides, the extracted TPS parameter such as guard interval length and IFFT/FFT mode
should be checked all the time during online receiving to prevent synchronization error. Once TPS check fail occurs, the acquisition and tracking of inner receiver must be shut down and then restart all the synchronization schemes. As for bit-error-rate (BER) measurement, the DVB-T standard defines quasi error-free condition, which means less than one uncorrelated error event per hour, while the BER of the output of the Viterbi decoder is equal to 2 10× −4. Therefore, in order to verify the overall system performance, the BER after Viterbi decoder should be measured.
Fig. 4.2 The baseband receiver design
ζ^
^
εF
^
εI ε^R δ^
Fig. 4.3 Functional blocks of inner receiver
Fig. 4.3 shows the detail functional blocks of the inner receiver. The main functional blocks consists of symbol timing offset synchronization, carrier frequency offset synchronization, SCO synchronization, channel estimation, and equalizer, respectively. Th acquisition parts (gray color) only operate in the beginning of the receiving and then are turned off when the tracking parts work, and the tracking parts works all the time until th receiver is turned off or TPS check error occurs. In this thesis, we only focus on the performance analysis of the channel estimation and equalization scheme. The detailed discussion of other functional blocks such as timing synchronization and CFO synchronization will be neglected in this work and can be found in [22].
e
e
4.2 Channel Model
The typical baseband equivalent channel model for DVB-T/H system platform is shown as in Fig. 4.4. The transmitted data will pass through multipath fading, Doppler delay spread, CFO, SCO, and AWGN in turn. The effects of co-channel interference, adjacent-channel interference, phase noise, and common phase error are neglected in our simulation. In the following sections, the detailed effect of each channel distortion will be illustrated.
⊕
⊗
2 j ft
e πΔ (1+ζ)fs
.4 Channel model of DVB-T/H system Fig. 4
4.2.1 Multipath Fading Channel Model
In wireless communication transmission, the multipath fading is caused by the reception through different paths with different time delay and power decay. In DVB-T standard, two
types of multipath fading channel model are specified [3]. The fixed reception condition is modeled
by Rayleigh floating
the
following equations whe pectively
modeled by Ricean channel (Ricean factor = 10dB) while the portable reception is channel. The full 20-tap Ricean and Rayleigh channel was used with
point tap magnitude and phase values with tap delay accuracies rounded to within 1/2 of duration for practical discrete simulation. The channel models can be generated from
re x(t) and y(t) are input and output signals res
Rayleigh: path, and τi is the relatively delay of the i-th path, respectively. The detailed value of these parameters is listed in table B.1 of [3]. The rms delay of Rayleigh and Ricean channel is 1.4426 sμ (about 13 samples) and 0.4491 sμ (about 4 samples). From the above two equations, we can find that the major difference between Ricean and Rayleigh channel is the ma
(the ratio of the power of the direct path to the reflected path) and can be expressed as
in path (the sight way). In Ricean channel, a main path is defined with the Ricean factor K
2
ain path in Rayleigh ch
(4-3)
However, there is no m annel. Hence the received signals consist of several reflected signals with similar power d bring serious synchronization error. The impulse response and frequency response of the two types of channel when K=10dB are shown in Fig. 4.5. As we can see there is a significant direct path in the impulse response of the Ricean channel. In the impulse response of the Rayleigh channel, there is no any direct
an
path and all the paths have similar magnitude. Therefore, the frequency selective fading effect in the frequency response of the Rayleigh channel is more serious than that of the Ricean channel.
0 200 400 600 800 1000 1200 1400 1600 1800 0
(a) Impulse response of Rayleigh channel (b) Frequency response of Rayleigh channel
ud
200 400 600 800 1000 1200 1400 1600 1800 Subcarrier index
Amplitude
(c) Impulse response of Ricean channel (d) Frequency response of Ricean channel Fig. 4.5 Channel response of Rayleigh and Ricean (K=10dB) channel
4.2.2 Mobile channel model
In DVB-T standard, it only provides two static channel models which is described in section 4.2.1. However, the applications in DVB-T/H systems are not only fir fix reception, but also for mobile reception. Therefore, we refer to the channel models Typical Urban 6 (TU6) and Rural Area 6 (RA6) in GSM COST 207 project [23]. The two single-transmitter
profiles come from the set defined by the COST 207 project (GSM transmission). The technical specification of COST207 describes the equipment and techniques used to measure the channel characteristics over typical bandwidths of 10~20 MHz at near 900MHz. Therefore, the COST207 profiles are applicable to the DVB-T transmission situations. The detailed value of these parameters is listed in table 4-1 and table 4-2. The Fig4.6 shows the TU6 model, the Doppler spectrum filter will introduce in next section.
Fig. 4.6 TU6 model
Table 4-1 Typical Urban Reception (TU6) channel model
Tap number Delay(us) Power(dB) Doppler spectrum
1 0 -3 Rayleigh 2 0.2 0 Rayleigh 3 0.5 -2 Rayleigh 4 1.6 -6 Rayleigh 5 2.3 -8 Rayleigh 6 5.0 -10 Rayleigh
Table 4-2 Rural Area Reception (RA6) channel model
Tap number Delay(us) Power(dB) Doppler spectrum
1 0 0 Rice
oppler spec types
Doppler
In DVB-T/H system, the reception ability in mobile environment is necessary. Hence a mobile radio channel including Doppler spread must be constructed. A simplified Doppler spread model is shown in Fig. 4.7 [24]. In the beginning, we assume a channel with a known and fixed number of paths P such as Rayleigh or Ricean with a Doppler frequency d( )k
Fig. 4.7 Doppler spread model
f ,
attenuation ρ(k)ejθ( )k , and time delay τ( )k . All the parameters are fixed as described in section 4.2.1 except the Doppler frequency. Since each path has its own Doppler frequency, the decision of the statistic distribution of f is very important. There are two commonly d sed Doppler frequency PDFs, uniform and classical, where the former exploits uniform d, and the later uses Jake’s Doppler spectrum [25],
respectively e Jak s essed as
u
distribution to model Doppler sprea
. The PDF of th e’s Doppler pread can be expr
2
After transformation of random variable, each f can be obtained by the following equation d cos(2 (1)) max
d d
f = π⋅rand ⋅f (4-5) The type of Doppler spread (uniform or Jake’s) affects the system performance enormously.
Because each path gets different f in each simulation case with different d fdmax, the value of fdmax should be fixed for each simulation and comparison.
B. Rayleigh fading
In wireless communication, the multi path effect will cause the frequency selective fading problems. If the transmitting environment is without the main direct path, according to central
In wireless communication, the multi path effect will cause the frequency selective fading problems. If the transmitting environment is without the main direct path, according to central