Message passing is to calculate a marginal probability given a structure of information model (a graph).
[Factor graph]: A factor graph is a bi-partile graph. One type of nodes is random variable (unknown we would like to know). The other type of nodes is factor, which represents the interaction between random variables, or evidences. The global probability must be able to be represented by the multiplication of local factors, i.e.,
p[x1,x2,...,xn] = f1[xv1]f2[xv2]...fm[xvm], where each xv is a list of x (partial set of xn).
The interpretation of the world (the guessing of the random variables) depends on the factors. So if we accumulate the factors,
p = f1*f2*...*fn,
we can calculate the marginal probability by probability propagation.
[Baysian Network]:
The joint probability of a network can be represented as multiplication of local conditional probability. The basic concept is built on sufficient statistics (also conditional independence.)
[e.g.] Three random variables,
x->y->z, p(z x, y) = p(z y). Given y, knowing x has no use. That means, knowing y is sufficient to predict z. (Look wiki for sufficient statistics).
The upshot is that we can factorize the distribution.
If we know p(x,y,z), we can calculate all the marginal distributions such as p(x), p(y), p(xz). If we want to calculate p[z,x=x'], we can start with
p[z,x= x'] = sum_{y}p[x=x',y,z]/sum_{z,y}p[x=x',y,z].
p[z,y,x=x'] = p[z,y,x=x']p[y,x'] = p[z,y]p[y,x']p[x'].
A Baysian network can therefore factorize into localized factors, f1, f2, ...fn.
A Baysian network is a special case of a factor graph.
A random markov field is also a special case of a factor graph.
[Probability Propagation]
To calculate the marginal probability of a factor graph, an algorithm of probability propagation can be adopted.
z-->
y-->f-->x: the edge from a factor node to a variable node.
2007年11月20日 星期二
2007年11月6日 星期二
coding
[Symbol]
x[n] = the nth transmitted symbol.
y[n] = the nth received symbol.
n[n] = the nth received noise.
y[n] = x[n] + n[n].
T: a time interval.
N: number of symbols in an interval (or orthogonal function for better definition).
W: bandwidth.
W = N/2T, by Nuquist sampling theorem.
N0 : noise spectral density.
n[n] = Normal(0, N0/2). From conservation of energy, total energy = N0*W = E[n[n]^2] * N/T. So the variance is linear proportion to noise spectral density. n[n] is the amplitude in time domain, whereas N0 is the amplitude^2 in the spectrum domain.
R : bit rate.
Eb = x[n]^2/R. Power per source bit. Eb is the symbol power spectral density. Eb*W = E[x[n]]*N/T.
SNR: Eb/N0 is dimensionless, reported in decibels.
x[n] = the nth transmitted symbol.
y[n] = the nth received symbol.
n[n] = the nth received noise.
y[n] = x[n] + n[n].
T: a time interval.
N: number of symbols in an interval (or orthogonal function for better definition).
W: bandwidth.
W = N/2T, by Nuquist sampling theorem.
N0 : noise spectral density.
n[n] = Normal(0, N0/2). From conservation of energy, total energy = N0*W = E[n[n]^2] * N/T. So the variance is linear proportion to noise spectral density. n[n] is the amplitude in time domain, whereas N0 is the amplitude^2 in the spectrum domain.
R : bit rate.
Eb = x[n]^2/R. Power per source bit. Eb is the symbol power spectral density. Eb*W = E[x[n]]*N/T.
SNR: Eb/N0 is dimensionless, reported in decibels.
2007年10月31日 星期三
Channel Fading
[Glossary]
+ Channel Fading: There can be multiple paths between the transmitter and the receiver. The major component can be the line of sight (LOS). Other components can vary with time either because the device is moving or because there are moving objects (cars) in the channel. Using deterministic model is non-realistic. Stochastic model (fading) is constructed to represent the channel property.
+ Delay spread: The time difference between LOS and the last received signal.
+ Resolvable: When the delay is less than the inverse of bandwidth (minimum sampling time), the delayed component and the major component is non-resolvable. If the delay is larger than that, the delay is resolvable. Unresolvable component is merged into the major component and expressed as the mean of the two components (or multiple components if there are multiple unresolvable delays). The merged representative component undergoes constructive and destructive interference.
+ Outage: As the device moves, the signal amplitude may stay below a certain level. This phenomena is called outage. Often at certain locations, the signals are too weak to be clear.
[Model]
Generally, fading models can be categorized into narrow band fading and broad band model.
The received signal is the summation of multiple components as,
r(t) = sum(A_n(t) u(t-t_n) exp^j(w(t-t_n)+phi_n(t))), where
A_n(t): amplitude of the nth component (nth multiple path).
t_n: the time delay of the n_th component.
phi_n(t): the phase change from Doppler frequency shift.
phi_n(t) = Integrate(fd(t) dt), where
fd(t) is the Instant Doppler frequency shift = v cos(th(t))/lambda. th(t) is the angle of motion to the direction of arrival.
The equivalent impulse response function is
c_n(t, tau) = A_n(t)exp^(-j*phi_n(t)) delta(tau-tau_n(t))
To get the received signal, the receiver needs to integrate over the arrival components with different delay time tau.
+ Gaussian In-phase fading: when there is no major component in the multiple path, the fading process is like a zero-mean Gaussian process. It's characterized by the standard deviation and the correlation time. The std represents the amplitude fluctuation. Autocorrelation can show the correlation time.
[example]: In an environment of a uniform circular reflector and a moving car, the autocorrelation function is Bessel. There waveform is periodical.
+ Rayleigh fading: both the in-phase and quadrature fading components are Gaussian, the joint amplitude is Z = sqrt(X^2+ Y^2) is a Rayleigh fading,
p(Z=z) = z/c Exp(-z^2/std^2).
The power spectrum distribution is exponential,
p(Z^2 = x) = c1 exp(-x/x0).
+ Rician fading: there is a major component (like LOS) in the multiple paths.
The amplitude distribution is p(z;s,std) = z exp(-(z^2+ s^2)/s) I0(zs/std).\
One important parameter is s, the strength of LOS.
+ Nakagami fading: a function in between Rayleigh and Rician.
+ Level crossing rate: below a certain level of the signal, the system is difficult to demodulate. This period is called outage.
+ Finite state Markov Model: use finite random walk markov process to model the fading.
+ Flat fading: the fading amplitude for different frequency component is equal.
[Wide band model]
Wide band channels causes the delay symbols to have ISI. For narrow band, the delay spread is localized within symbol time. There can be constructive and destructive interference within a symbol, but the ISI is small. On the other hand, wide band channel has shorter symbol time. The delay spread tends to be larger than the symbol time. The upshot is ISI from delay spread.
+ Frequency selective fading: the fading at different frequencies are varying. Multi-carrier modulation is also subjected to frequency selecting fading.
+ Channel Fading: There can be multiple paths between the transmitter and the receiver. The major component can be the line of sight (LOS). Other components can vary with time either because the device is moving or because there are moving objects (cars) in the channel. Using deterministic model is non-realistic. Stochastic model (fading) is constructed to represent the channel property.
+ Delay spread: The time difference between LOS and the last received signal.
+ Resolvable: When the delay is less than the inverse of bandwidth (minimum sampling time), the delayed component and the major component is non-resolvable. If the delay is larger than that, the delay is resolvable. Unresolvable component is merged into the major component and expressed as the mean of the two components (or multiple components if there are multiple unresolvable delays). The merged representative component undergoes constructive and destructive interference.
+ Outage: As the device moves, the signal amplitude may stay below a certain level. This phenomena is called outage. Often at certain locations, the signals are too weak to be clear.
[Model]
Generally, fading models can be categorized into narrow band fading and broad band model.
The received signal is the summation of multiple components as,
r(t) = sum(A_n(t) u(t-t_n) exp^j(w(t-t_n)+phi_n(t))), where
A_n(t): amplitude of the nth component (nth multiple path).
t_n: the time delay of the n_th component.
phi_n(t): the phase change from Doppler frequency shift.
phi_n(t) = Integrate(fd(t) dt), where
fd(t) is the Instant Doppler frequency shift = v cos(th(t))/lambda. th(t) is the angle of motion to the direction of arrival.
The equivalent impulse response function is
c_n(t, tau) = A_n(t)exp^(-j*phi_n(t)) delta(tau-tau_n(t))
To get the received signal, the receiver needs to integrate over the arrival components with different delay time tau.
+ Gaussian In-phase fading: when there is no major component in the multiple path, the fading process is like a zero-mean Gaussian process. It's characterized by the standard deviation and the correlation time. The std represents the amplitude fluctuation. Autocorrelation can show the correlation time.
[example]: In an environment of a uniform circular reflector and a moving car, the autocorrelation function is Bessel. There waveform is periodical.
+ Rayleigh fading: both the in-phase and quadrature fading components are Gaussian, the joint amplitude is Z = sqrt(X^2+ Y^2) is a Rayleigh fading,
p(Z=z) = z/c Exp(-z^2/std^2).
The power spectrum distribution is exponential,
p(Z^2 = x) = c1 exp(-x/x0).
+ Rician fading: there is a major component (like LOS) in the multiple paths.
The amplitude distribution is p(z;s,std) = z exp(-(z^2+ s^2)/s) I0(zs/std).\
One important parameter is s, the strength of LOS.
+ Nakagami fading: a function in between Rayleigh and Rician.
+ Level crossing rate: below a certain level of the signal, the system is difficult to demodulate. This period is called outage.
+ Finite state Markov Model: use finite random walk markov process to model the fading.
+ Flat fading: the fading amplitude for different frequency component is equal.
[Wide band model]
Wide band channels causes the delay symbols to have ISI. For narrow band, the delay spread is localized within symbol time. There can be constructive and destructive interference within a symbol, but the ISI is small. On the other hand, wide band channel has shorter symbol time. The delay spread tends to be larger than the symbol time. The upshot is ISI from delay spread.
+ Frequency selective fading: the fading at different frequencies are varying. Multi-carrier modulation is also subjected to frequency selecting fading.
phpMyAdmin
Installation of phpMyAdmin is quite simple. Just upload the entire directory to your host and then it works.
Some advanced features need more tuning. The advanced features include, {bookmark, history retreival, schema designer, PDF-generation, field contents transformation}. Designer allows graphical designs of schema. Later the graphical designs can be output as pdf files.
To activate those features, some remarks need to be unremarked. Check the line after pmadb directive. Whenever you see pma words, you need to unmark them.
If you have multiple databases, you should think of use a central control user and password to work on pmadb. Otherwise you only need to create tables in scripts/create_tables_xxx.sql into your database and keep pmadb commented.
Create tables in pmadb (multi-database mode) or in your database (single database mode). The features will be stored in those tables. You can find the history of your sql command. You can design the relation links in your database. It can be much fun to use them to coordinate your project.
Some advanced features need more tuning. The advanced features include, {bookmark, history retreival, schema designer, PDF-generation, field contents transformation}. Designer allows graphical designs of schema. Later the graphical designs can be output as pdf files.
To activate those features, some remarks need to be unremarked. Check the line after pmadb directive. Whenever you see pma words, you need to unmark them.
If you have multiple databases, you should think of use a central control user and password to work on pmadb. Otherwise you only need to create tables in scripts/create_tables_xxx.sql into your database and keep pmadb commented.
Create tables in pmadb (multi-database mode) or in your database (single database mode). The features will be stored in those tables. You can find the history of your sql command. You can design the relation links in your database. It can be much fun to use them to coordinate your project.
2007年10月24日 星期三
GMSK overview
[Glossary]
+ FSK: Frequency shift keying. Use M frequencies (carriers) to represent M symbols.
+ MSK: Minimum frequency Shift Keying. In a M-FSK, choose the phase of each carrier such that switching the carriers does not cause phase shift, which broadens the spectrum and reduces spectral efficiency.
+ CPFSK: Continuous Phase FSK. The phase is the integration of M-PAM. The integration guarantees the phase is continuous. M-PAM is the differentiation of the phase, which is the instantaneous frequency. So the instantaneous frequency fluctuates with M-PAM modulation.
+ GMSK: Gaussian Minimum Shift Keying. Choosing the shape function of the M-PAM by Gaussian to reach the best spectral efficiency is called Gaussian-MSK (GMSK).
+ PAM: Pulse Amplitude Modulation. Each symbol is represented by a distinct amplitude of a shape function. si(t) = Aig(t), where g(t) is the shape function valid within a symbol time.[Example 1]
The above example is an example of symbol time Ts = 50us, strong ISI case (sigma = 20). In the M-PAM figure, Gaussian-shape signals overlap. Phi(t) is the integration of the phase and s(t) is the real baseband. For the first symbol = 10, the corresponding frequency is 5 cycles per Ts. It's roughly true. The slight deviation (the real cycle is around 4) is the Gaussian tail not integrated in the phase (A Gaussian has infinite long tail).
[Example 2]
The following example is the same case with different sigma. The ISI is weaker. Each Gaussian is distinct in M-PAM figure. The required bandwidth is larger. The frequency is more precise (see signal s(t)).
[Advantages of GMSK]
+ High Spectral Efficiency.
+ Constant envelop--> non-linear amplifier is OK (cheaper).
+ Use simple non-coherent detection for demodulation (no good PLL is required). Use M-non-coherent IQ components and add them by square root. The carrier with the maximum frequency is the estimated symbol.
+ Good for voice (LOW BER 10^(-3) is OK).
[Disadvantages of GMSK]
+ Large ISI. Gaussian waveform extents to infinity and inevitably causes ISS. Gaussian waveform does not satisfy Nyquist criterion. Increasing spectral efficiency (smaller bandwidth) also increasing ISI (larger temporal extend) according to Uncertainty Principle.
+ Bad for data (require high BER).
+ FSK: Frequency shift keying. Use M frequencies (carriers) to represent M symbols.
+ MSK: Minimum frequency Shift Keying. In a M-FSK, choose the phase of each carrier such that switching the carriers does not cause phase shift, which broadens the spectrum and reduces spectral efficiency.
+ CPFSK: Continuous Phase FSK. The phase is the integration of M-PAM. The integration guarantees the phase is continuous. M-PAM is the differentiation of the phase, which is the instantaneous frequency. So the instantaneous frequency fluctuates with M-PAM modulation.
+ GMSK: Gaussian Minimum Shift Keying. Choosing the shape function of the M-PAM by Gaussian to reach the best spectral efficiency is called Gaussian-MSK (GMSK).
+ PAM: Pulse Amplitude Modulation. Each symbol is represented by a distinct amplitude of a shape function. si(t) = Aig(t), where g(t) is the shape function valid within a symbol time.[Example 1]
The above example is an example of symbol time Ts = 50us, strong ISI case (sigma = 20). In the M-PAM figure, Gaussian-shape signals overlap. Phi(t) is the integration of the phase and s(t) is the real baseband. For the first symbol = 10, the corresponding frequency is 5 cycles per Ts. It's roughly true. The slight deviation (the real cycle is around 4) is the Gaussian tail not integrated in the phase (A Gaussian has infinite long tail).
[Example 2]
The following example is the same case with different sigma. The ISI is weaker. Each Gaussian is distinct in M-PAM figure. The required bandwidth is larger. The frequency is more precise (see signal s(t)).
[Advantages of GMSK]
+ High Spectral Efficiency.
+ Constant envelop--> non-linear amplifier is OK (cheaper).
+ Use simple non-coherent detection for demodulation (no good PLL is required). Use M-non-coherent IQ components and add them by square root. The carrier with the maximum frequency is the estimated symbol.
+ Good for voice (LOW BER 10^(-3) is OK).
[Disadvantages of GMSK]
+ Large ISI. Gaussian waveform extents to infinity and inevitably causes ISS. Gaussian waveform does not satisfy Nyquist criterion. Increasing spectral efficiency (smaller bandwidth) also increasing ISI (larger temporal extend) according to Uncertainty Principle.
+ Bad for data (require high BER).
2007年10月18日 星期四
Hong Kong trip
(A) TAKA provides waterproof LCD TV. Not known the gaurantee.
(B) Shenzhen Vogue Industry designs better GPS.
(C) Linkstar.com.cn 吉祥星有多款GPS.
(D) Self-Power Radio by Shining time Industry (shinningtime.com)
(E) EMS top gun (http://www.hkems.com//product/xbox/LCDTopGun.html) a game controller with a gun shape.
(F) IP cam:
(a) Tungson (www.tungson.cn) has fixed wi-fi ip cam.
(b) Telebahn (www.telebahn.cn) is another IP camera company. The model IPC 500 seems a copy from other companies.
(c) Shenzhen Jiameikang (www.jmk.hk) has a similar ip cam model UP-009, which is identical to Telebahn's IPC 500. But it has a new model UP-010 which seems an improvement with different outlook. Both are not wi-fi enable.
(d) jc-cctc.com has primary products on traditional CCTV. Only two unattractive ip cams.
(B) Shenzhen Vogue Industry designs better GPS.
(C) Linkstar.com.cn 吉祥星有多款GPS.
(D) Self-Power Radio by Shining time Industry (shinningtime.com)
(E) EMS top gun (http://www.hkems.com//product/xbox/LCDTopGun.html) a game controller with a gun shape.
(F) IP cam:
(a) Tungson (www.tungson.cn) has fixed wi-fi ip cam.
(b) Telebahn (www.telebahn.cn) is another IP camera company. The model IPC 500 seems a copy from other companies.
(c) Shenzhen Jiameikang (www.jmk.hk) has a similar ip cam model UP-009, which is identical to Telebahn's IPC 500. But it has a new model UP-010 which seems an improvement with different outlook. Both are not wi-fi enable.
(d) jc-cctc.com has primary products on traditional CCTV. Only two unattractive ip cams.
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