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Control PC Interface TE Port RRC PDCP RLC MAC PHY Control PC Interface TE Port RRC 36.331 PDCP 36.323 CpdcpXXXXX() 36.322 CrlcXXXXX() RLC 36.321 CmacXXXXX() MAC CphyXXXXX() 36.104,36.211,36.212 36.213,36.214,36.302 PHY CteXXXXX() Protocol CT RF CT 36.523 36.521-1, 36.521-3 23.401,24.301,29.274, 32.426,33.102,33.401, 33.402 NAS 36.331 RRC 36.323 PDCP 36.322 RLC 36.321 MAC 36.104,36.211,36.212 36.213,36.214,36.302 PHY SGSN PCRF HSS MME IP eNodeB UE SGW (Serving Gateway) PGW (PDN Gateway) MSC Voice Call Traffic Path Registration to CS Network Path BSC BTS (GSM) Paging Path SGSN SGs RNC UE NodeB (UMTS) MME IP eNodeB (LTE) SGW (Serving Gateway) PGW (PDN Gateway) SGSN PCRF HSS MME IP eNodeB SGW (Serving Gateway) PGW (PDN Gateway) UE EPS Bearer External Bearer UE Internet EPC E-UTRAN eNodeB S-GW Peer Entity P-GW End-to-End Service EPS Bearer E-RAB External Bearer S5/S8 Bearer Radio Bearer S1 Bearer Radio S1 S5/S8 Gi ON Duration DRX Cycle DRX Cycle PDCCH Reception Here DRX Inactivity Time ON Duration DRX Cycle DRX Cycle PDCCH Reception Here DRX Inactivity Time ON Duration DRX Cycle DRX Command MAC CE Reception Here (Both DRX Inactivity timer and OnDuration Timer stops here) ON Duration Short DRX Cycle Short DRX Cycle Short DRX Cycle Timer Long DRX Cycle http://lteworld.org/blog/measurements-lte-e-utran High frequency Current Cell UE Current Cell UE Center frequency Low frequency High frequency Center frequency Low frequency Target Cell High frequency Current Cell UE Target Cell Center frequency Low frequency Target Cell High frequency Current Cell Center frequency Low frequency UE High frequency Current Cell UE Target Cell Center frequency Low frequency High frequency Current Cell UE Target Cell Center frequency Low frequency High frequency Current Cell UE Target Cell Center frequency Low frequency High frequency Current Cell UE Center frequency Target Cell Low frequency IMS SIP H.323 H.263 RTP etc SMS Voice (VoIP) Video SIP Application Servers SGSN IMS (CSCF) HSS PCRF MME eNodeB UE Other IP Network SGW (Serving Gateway) PGW (PDN Gateway) SIP Register Server Clients B A INVITE REGISTER (Contact Address) AUTHENTICATION REQUEST 100 Trying 180 Ringing 200 OK REGISTER (Credentials) Media Transfer OK BYE 200 OK PC1 – UE PC PC2 Server PC Ethernet Cable TE Port RF Port LTE Network Simulator UE PC Wireshark Wireshark Dummy Hub IP Network Data Server Router TE Port RF Port LTE Network Simulator Wireshark IP Monitoring PC for troubleshot UE PC Wireshark Bit Stream Bit Stream 36.211 6.3.1 I/Q 36.211 6.3.2 I/Q 36.211 6.3.3 I/Q 36.211 6.3.4 36.211 6.5 Cell Specific Reference Signal PDCCH PA PB PDSCH : in the same symbol as reference signal PDSCH : in the symbol with no reference signal In some subframe, there can be no SRS depending on SRS Scheduling parameter settings 1 subframe Attach Request EPS attach type value Old GUTI or IMSI PDN Connectivity Request PDN type Access point name UE network capability NAS : Security Mode Command Replayed UE security capabilities Attah Accept Activate Default EPS Bearer Setup Request GUTI PDN type EPS attach result value Access point name SIB1 TAC (Tracking Area Code) Tracking Area Update Request Old GUTI EPS Bearer Context Status Old Location Area Identification Tracking Area Update Accept GUTI TAI List EPS Bearer Context Status Location Area Identification RRC DedicatedInfoNAS NAS Message(EMM) NAS(ESM) Message Type (8 bits) Message Type (8 bits) Protocol Discriminator + Message Authentication Code + Sequence Number (44 bits) Security Header Type (4 bits) Length of DedicatedInfoNAS C1 (RRC Message Type Identifier : 4 bits) 1 frame 1 subframe 1 slot PUCCH Region Subband 3 Subband 2 Subband 1 Subband 0 PUCCH Region PUCCH Region Subband 3 Subband 2 Subband 1 Subband 0 PUCCH Region PUCCH Region Subband 3 Subband 2 Subband 1 Subband 0 PUCCH Region PUCCH Region Subband 3 Subband 2 Subband 1 Subband 0 PUCCH Region PUCCH Region Subband 3 Subband 2 Subband 1 Subband 0 PUCCH Region PUCCH Region Subband 3 Subband 2 Subband 1 Subband 0 PUCCH Region (a) (b) (c) (d) (e) 1 subframe LTE CDMA WCDMA Voice Comm Voice Comm CSFB Packet Comm CSFB HO Packet Comm HO RD HO Packet Comm RD RD Idle Packet Comm RD CR CR Idle CS CR Idle CS CS CS Power On CS : Cell Selection CR : Cell Reselection RD : Cell Redirection HO : Handover CSFB : CS Fallback Idle NW UE RRC Connection Request T300 RRC Connection Setup NW UE RRC Connection Request T300 RRC Connection Reject UE Higher Layer UE Lower Layer Out of Sync Indication Out of Sync Indication N310 Times Out of Sync Indication In Sync Indication T310 In Sync Indication N311 Times In Sync Indication UE Higher Layer UE Lower Layer Out of Sync Indication Out of Sync Indication N310 Times Out of Sync Indication T310 Triggering Handover Procedure UE Higher Layer UE Lower Layer Out of Sync Indication Out of Sync Indication N310 Times Out of Sync Indication T310 Initiating Connection Reestablishment op 0 + 0 op + 0 0 -1 ip 0 Z 0 0 0 Z 0 -1 ip 0 + -1 Z 0 Z 0 -1 + 0 1 + op op op op 1 + 0 0 -1 ip 1 Z 0 1 1 + Z 0 -1 ip 0 -1 Z 1 Z 0 -1 + 1 op op op 1 + 0 op + 1 0 -1 ip 0 Z 0 0 0 Z 1 -1 ip 1 + -1 Z 0 Z 0 -1 + 1 op op op 1 + op 0 + 1 0 -1 ip 1 Z 0 1 1 + Z 1 -1 ip 1 -1 Z 1 Z 0 -1 + 0 op op op 0 + op 1 + 0 1 -1 ip 0 Z 1 0 0 + Z 0 -1 ip 0 -1 Z 0 Z 1 -1 + 0 1 + op op op op 0 + 0 1 -1 ip 1 Z 1 1 1 + Z 0 -1 ip 0 -1 Z 1 Z 1 -1 + 1 op op op 0 + op 0 + 1 1 -1 ip 0 Z 1 0 0 + Z 1 -1 ip 1 -1 Z 0 Z 1 -1 + 1 1 + op op op op 1 + 1 1 -1 ip 1 Z 1 1 1 + Z 1 -1 ip 1 -1 Z 1 Z 1 -1 + 0 op op GPS Signal Frame Structure Telemetry and handover words (TLM and HOW) Satellite clock, GPS time relationship Telemetry and handover words (TLM and HOW) Ephemeris (precise satellite orbit) Telemetry and handover words (TLM and HOW) Almanac component (satellite network synopsys, error correction) Word Subframe 1-2 3-10 1 1-2 3-10 2 1-2 3 Frame 300 bits 1500 bits 3-10 4 5 n x y i 0 i i x(n) y(n) x(n) y(n) x(n)y(n) Sum of Times (Sum of Multiplication) Correlation r n xy ( x)( y) n( x ) ( x ) 2 Inner Product Discrete Fourier Transform Convolution 2 n( y ) ( y ) 2 2 N 1 X k xn e i 2 k n N n 0 yi xi Sum of Times (Sum of Multiplication) n x y i 0 i i |X| N 1 X 1 xn e n 0 i 2 1 n N N 1 X 2 xn e n 0 i 2 2 n N N 1 X 3 xn e n 0 i 2 3 n N N 1 X N xn e n 0 i 2 N n N FIR IIR This means the result of convolution is an array (vector) with the size = n This means that each element (each value) of the convolution comes from “Sum of Multiplication” 1. 2. 3. 4. g[-m] This is same as g[-m + n] g[-m + n] is same as g[-(m-n)] g[-(m-n)] is same as g[-m] shifted by n g[-m] is the reflection of g[m] around y axis g[-(m-n)] =g[n-m] n g[m] Control System Model Control System Model Simultaneous Equations Simultaneous Equations Matrix Statistics Operation / Manipulation Result Of Operation Graph Theory Statistics Graph Theory Computer Graphics Presentation Computer Graphics Linear Algegra Interpretation (x2,y2) (x1,y1) 1.0 0.0 x1 x2 0.0 1.0 y1 y2 (x2,y2) (x1,y1) -1.0 0.0 x1 x2 0.0 1.0 y1 y2 1.0 0.0 x1 x2 0.0 -1.0 y1 y2 (x1,y1) (x2,y2) (x1,y1) -1.0 0.0 x1 x2 0.0 -1.0 y1 y2 (x2,y2) (x2,y2) (x1,y1) 1.0 0.3 x1 x2 0.0 1.0 y1 y2 (x1,y1) (x2,y2) cos(pi/4) -sin(pi/4) x1 x2 sin(pi/4) y1 y2 cos(pi/4) pi/4 0.2 1 0.8 0.0 0.4 0.5 0.35 2 3 0.15 0.6 To From 1 2 3 1 0.2 0.8 0.0 2 0.4 0.15 0.6 3 0.5 0.35 0.0 0.0 (a) (a_f) (b) (b_f) (c) Location, Size of the peak does not change, but graph gets smoother (c_f) (d) (d_f) Length of signal is same but lengh of Zero Pad gets longer Signal Zero Pad Total number of data points is same but number of periods gets larger (a) (a_f) (b) (c) (b_f) Location of the peak does not change, but height of the peak gets higher and width of the peak (c_f) gets narrower (d) (d_f) (a) (b) (c) (d) (a_f) (b_f) (c_f) (d_f) A B C s(t) Abs(fft(s(t)) Arg(fft(s(t)) Abs(fft(s(t)) : Expanded Arg(fft(s(t)) : Expanded a b c d e f g h i a = 1.0; b = 1.0; p1 = 0.0; p2 = 0.0; A B C (a) (b) p (i) (ii) (iii) (c) (v) (d) (iv) Figure 1 a = 1.0; b = 1.0; p1 = 0.0; p2 = 0.2*pi; A B C (a) (b) p (i) (ii) (iii) (c) (v) (d) (iv) Figure 2 a = 1.0; b = 0.8; p1 = 0.0; p2 = 0.0; A B C (a) (b) p (i) (ii) (iii) (c) (v) (d) (iv) Figure 3 m1 m2 a = 1.0; b = 0.8; p1 = 0.0; p2 = 0.2*pi; A B C (a) (b) p (i) (ii) (iii) (c) (v) (d) (iv) Figure 4 m1 m2 (a) (b) (c) Discontinuity of Phase Due to phase calculation software algorithm (d) A a = 1.0; b = 1.0; p1 = 0.0; p2 = 0.0; (a) (b) (c) (d) B a = 1.0; b = 1.0; p1 = 0.0; p2 = 0.2*pi; C a = 1.0; b = 0.7; p1 = 0.0; p2 = 0.0; D a = 1.0; b = 0.7; p1 = 0.0; p2 = 0.2*pi; Time Domain Fourier Series Expansion A combination of infinite number (sin() + cos()) Time Domain Time domain Data Sequence Freq Domain Fourier Transform Frequency Domain Data This is a differential equation because it has ‘derivative’ components in it derivative form differential form y ' ' y '2 y 3 This is a differential equation because it has ‘differential’ components in it d 2 y dy 2y 3 2 dx dx y 2 y 1 2 y 3 y ' ' y '2 y This is NOT a differential equation because it does not have ‘differential’ nor ‘derivative’ components in it This is NOT a differential equation because it is not a form of equation (no ‘equal’ sign) even though it has ‘derivative’ component in it Algebraic Equation y2 2 y 2 0 Solution Algebraic Equation Solver In this case, Variable y is a number In this case, variable y is a function (e.g, y(x), y(t) etc)) y 1 i In this case, Solution y is a value Differential Equation y ' '2 y '2 y 0 y 1 i Solution Differential Equation Solver y D1e( 1i ) x D2e( 1i ) x In this case, Solution y is a function (e.g, y(x), y(t) etc)) As you see here, the dependent variable in differential equation is a ‘Function’, not a value. This is a key characteristics that defines ‘Differential Equation’ The highest order among all terms becomes the order of the differential equation. In this case, the highest Order is 3. So we call this equation as a ‘3rd order differential equation’ Dependent Variable Independent Variable Order (=3) Order (=2) y (x) implies 3 2 d y d y dy 3 2y 3 3 2 dx dx dx Independent Variable Dependent Variable y (x) Independent Variable implies d3y d 2 y dy 3 2 2y 3 3 dx dx dx There are only one type of independent variable. This kind of differential equation is called Ordinary Differential Equation (ODE) Independent Variable Dependent Variable Independent Variable u ( x, y ) implies u u u 2 2 0 2 x y xy 2 2 2 Independent Variable There are more than one types of independent variables. (In this example, we have two different type of independent variable). This kind of differential equation is called Partial Differential Equation (PDE) Calculus Differential Equation (Continous) Modeling Algebra Laplace Transform F(s) (Laplace Form) Solving Solving Solution Real World Problem Inverse Transform Solution Modeling Solving Solving Difference Equation (Discrete) Solution F(z) (z Form) z Transform y (t ) Laplace Transform Y ( s) e y(t )dt st 0 Symbols for original function Symbols for Laplace Transformed Function Definition of Laplace Transformed Function y ' (t ) sY ( s ) y (0) y ' ' (t ) s 2Y ( s) sy (0) y' (0) (t ) 1 d (t ) dt s u (t ) 1 s : Unit Step u (t ) 1 s e s t 1 s2 e t te t 1 (s ) 1 (s )2 1 1 s Differential Equation e.g, f(y’’,y’,t) Any Solution Process Differential Equation e.g, f(y’’,y’,t) Laplace Transform y(t) = ?????? Y(s) = ?????? Inverse Laplace Transform y(t) = ?????? Derive a differential equation that tells you the velocity of a falling body at any given time. (Assume the condition where you should not ignore the air resistance) Governing Law : Total Force applied to a body = Motion of the body F ma Q. Can I convert this into a term related to velocity ? A. Q . What kind of Force is there ? i) Force to helps movement = Pulling force by gravity = a mg ii) Force to hinder movement = air resistance = Yes. Acceleration (a) is the derivative of velocity (v) dv ma m dt kv mg kv F ma dv dt Why negative sign here ? : It is because this fource act in opposite direction to the other Force (Gravity). : We assumed that Pulling Force by Gravity is ‘Positive Force’ mg kv m dv dt m dv mg kv dt A B C Force trying to get to the spring’s resting position = -k s p4 p1 -x s x=0 p2 +x p3 Force being pulled down by gravity =mg If you hand a mass to the spring, it would try to fall down and length of the spring would increase, but soon the mass would not fall down anymore because of the restoration force of the spring. This is the point where the springs restoration force and pulling force by gravity become same. We call this point as “Equilibrium Point”. At this point, the mass does not move in any direction. So it is the same situation where there is no force being applied to the body (in reality, the two force with the same amount is continuously being applied in opposite direction) It is very important to know where is the reference point, the point where we define x = 0. It is totally up to you how to define the reference point. You can set any point as a reference point but the final mathematical equation may differ depending on where you take as a reference point. So usually, we set the point where we can get a simplest mathematical model. In vertical spring model, we set the Equilibrium Point as the reference point because we can remove the term –k s and mg since they cancel each other at this point C Governing Law : Total Force applied to a body = Motion of the body F ma Q . What kind of Force is there ? i) -x x=0 +x Force to makes movement = Restoration force of the spring trying to get back to the equilibrium position = ii) We can set this part to be ‘0’ by setting ‘the equilibrium point’ as the reference point of the model. (Refer to previous figure and comments on it) Yes. Acceleration (a) is the 2nd derivative of distance (x) mg Force to oppose the pulling force by gravity = Restoration force of the spring just to oppose the pulling force by gravity = iv) A. Force created by Gravity = Force pulling the object down to the ground = iii) kx Q. Can I convert this into a term related to position of the mass (x = distance from the reference point) ? ks Force to prevent movement = damping force dx = dt dx kx mg ks dt dx kx dt d 2x a 2 dt d 2x ma m 2 dt dx d 2x kx m 2 dt dt d 2x dx m 2 kx 0 dt dt Governing Law : Population Growth Rate per Individual = Rate of Factors increasing the Population – Rate of Factoring decreasing the Population dP /P dt Q . What kind of Factors are there ? i) Increasing Factors a) Birth Rate 1 dP P dt ? = bP b) Rate of immigration = ki P ii) Decreasing Factors a) Death Rate = dP b) Rate of emigration = ke P (bP ki P) (dP ke P) (b ki d ke ) P Governing Law : Kirchhoff's voltage law The directed sum of the electrical potential differences (voltage) around any closed circuit is zero The sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop Voltage Drop Ri EMFS : Voltage Generator di L dt E 1 q C Voltage Drop Voltage Drop Voltage Generator(positive sign) Differentiate both sides Voltage Drop (negative sign) di 1 ( E ) ( Ri ) ( L ) ( q) 0 dt C di 1 E Ri L q 0 dt C di 1 E Ri L q dt C dq i dt dE di d di 1 dq R L dt dt dt dt C dt dq Simplify the equation i dt dq d dq 1 ER L ( ) q dt dt dt C dE di d 2i 1 R L 2 i dt dt dt C dq d 2q 1 ER L 2 q dt dt C Simplify the equation Mathematical Operation Modeling Interpretation Other Models Differential Equation Real World Problem Matrix Statistics Probability (Stocastics) Other Models Mathematical Solution Real World Solution amp1 CH1 x amp2 CH2 I x I+jQ + amp1 CH3 x amp2 CH4 x Q x j x1 amplitude = 1 x2 amplitued = 0.5 x1 amplitude = 1 x2 amplitued = 0.25 How do we get this kind of constellation ? + + e2 e1 x1 e3 e4 EVM_x1 = min{e1, e2, e3, e4}; assuming DPCCH {1,1} DPDCH {1,1} Is this constellation correct ? c 15 d 15 Chip Rate Signal a bi 1 a bi Real part Imaginary part Imaginary axis | (a bi) | =abs(a+b i) a bi b Real axis a (a bi ) =arg(a+b i) =angle of (a+b i) c3 = c1 + c2 c1 c3 c1 plot(y) Horizontal axis is automatically set, because it is not specified in plot() function plot(x,y) Total horizontal range is automatically set, because it is not specified in plot() function plot(x,y); xlim([-8 8]); ylim([-1.5 1.5]); plot(x,y); axis([-8 8 -1.5 1.5]); plot(x,y); axis([-8 8 -1.5 1.5]); title('y=sin(x)'); xlabel('x'); ylabel('sin(x)'); color : ‘red’ format: ‘dashed line graph’ plot(x,y,’r--’); axis([-8 8 -1.5 1.5]); title('y=sin(x)'); xlabel('x'); ylabel('sin(x)'); plot(x,y1,'r-',x,y2,'b-');axis([-8 8 -1.5 1.5]); col1 row1 row2 1 N+1 row M Subplot(M, N, 1); plot() Subplot(M, N, 2); plot() Subplot(M, N, 3); plot() Subplot(M, N, M x N); plot() col2 col3 col N 2 3 N N+2 N+3 N+N NxN subplot(2,2,1); plot(x,y1,'r-');axis([-8 8 -1.5 1.5]); subplot(2,2,2); plot(x,y2,'g-');axis([-8 8 -1.5 1.5]); subplot(2,2,3); plot(x,y3,'b-');axis([-8 8 -1.5 1.5]); subplot(2,2,4); plot(x,y4,'m-');axis([-8 8 -1.5 1.5]); Plot curve along imaginary axis (absolute value of the expression) (the line where real value = 0) = This represents ‘Frequency Response’ pole Plot curve along imaginary axis (arg of the expression) (the line where real value = 0)