Continuous Inter-Planetary Communication

Aronee Dasgupta & Danny PaulSelf Study Seminar

Radiating Systems and Digital Modulation and CodingPresented to Mr. Nagendra N and Mrs. P Shanti

Introduction• What is interplanetary communication ?

• Digitally connecting planets together

• What is continuous communication??• Uninterrupted connection

• So what is continuous communication??• Uninterrupted communication between planet

• How is continuous interplanetary communication achieved?• Achieved using three satellites in orbits that are 120 degrees apart

The Solar System Information Highway

• Geosynchronous satellites in planetary orbits to form planetary communication networks to support planetary communications.

• Three polar orbiting satellites operating in the solar polar plane.

• The three solar polar planes are evenly separated by 120 degrees and have a semi-major axis distance and eccentricity such that they could be easily launched from Earth and maintain a constant distance from the Earth.

• The satellites would be interconnected with satellite cross -links and would find the shortest paths back to earth.

The Solar System Information Highway

• Why this solar information highway is required?

• The weight of all non communication satellites will be reduced

• Excellent replacement to NASAs Deep Space Network (DSN) wherein every satellite directly communicates to the base station on earth, because of which it consumes large amounts of power, this causes frequent power outages in the satellites whenever there is a solar or planetary obstruction

Low Density Parity Check Codes (LDPC)

• LDPC ( Low Density Parity Check ) codes are a class of linear bock code.

• The term “Low Density” refers to the characteristic of the parity check matrix which contains only few ‘1’s in comparison to ‘0’s.

• LDPC codes are arguably the best error correction codes in existence at present.

• LDPC codes were first introduced by R. Galager in his PhD thesis in 1960 and soon forgotten due to introduction of Reed-Solomon codes and the implementation issues with limited technological knowhow at that time.

• The LDPC codes were rediscovered in mid 90s by R. Neal and D. Mackay at the Cambridge University.

We can define N bit long LDPC code in terms of M number of parity check equations and describing those parity check equations with a M x N parity check matrix H.

Where, M – Number of parity check equationsN – Number of bits in the code word

Low Density Parity Check Codes (continued)

0521 ccc0641 ccc

06321 cccc

Consider the 6 bit long codeword in the form

which satisfies 3 parity check equations as shown below.

654321 ,,,,, ccccccc

We can now define 3x6 parity check matrix as,

100111101001010011

H

521 ccc

The density of ‘1’s in LDPC code parity check matrix is very low

Column weight - number of ‘1’s in a columnNumber of times a symbol taking part in parity checks

cw

Row weight - number of ‘1’s in a row Number of Number of symbols taking part in a parity check

cw

If the parity check matrix has uniform row weight and uniform column weight (same number of ‘1’ in a column and same number of ‘1’ in a row) we call that a regular parity check matrix.

and changes, therefore this is an irregular parity check matrix

rw cw

Low Density Parity Check Codes (continued)

100111101001010011

HThe parity check matrix defines a rate , code where

NKR KN ,MNK

NMH

Codeword is said to be valid if it satisfies the syndrome calculation

0. THcz

We can generate the code word in by multiplying message with generator matrixm GGmc .

We can obtain the generator matrix from parity check matrix by, G H

1.) Arranging the parity check matrix in systematic form using row and column operations

2.) Rearranging the systematic parity check matrix

3.) We can verify our results as

110100111010101001

sysH KMMsys PIH

KT

MK IPG

100111010110001011

G

0. THG

Low Density Parity Check Codes (continued)

100111101001010011

H Tanner graph is a graphical representation of parity check matrix specifying parity check equations.

Tanner graph consists of N number of variable nodes and M number of check nodes

In Tanner graph mth check node is connected to nth variable node if and only if nth element in mth row in parity check matrix is a ‘1’.mnh H

1c 3c2c 4c 5c 6c

1z 3z2z

The marked path z2 → c1 → z3 → c6 → z2 is an example for short cycle of 4

The number of steps needed to return to the original position is known as the girth of the code

Low Density Parity Check Codes (continued)

1. Suppose we have codeword as follows: where each is either ‘0’ or ‘1’ and codeword now has three parity-check

equations.ic

654321 ,,,,, ccccccc c

a.) Determine the parity check matrix H by using the above equation

b.) Show the systematic form of H by applying Gauss Jordan elimination

c.) Determine Generator matrix G from H and prove G * HT = 0

d.) Find out the dimension of the H, G

e.) State whether the matrix is regular or irregular

0521 ccc0641 ccc

06321 cccc

Low Density Parity Check Codes (continued)

0521 ccc0641 ccc

06321 cccc

100111101001010011

H6 columns and 3 rows

Convert into systematic form using basic row and operations (try to avoid column operations)H sysH

101001100111010011

100111101001010011

32 RRH

101001001110010011

101001100111010011

232 RRRH

110100001110010011

101001001110010011

1233 RRRRH

110100001110101001

110100001110010011

3211 RRRRH

110100111010101001

110100001110101001

322 RRRH

110100111010101001

sysH KMMsys PIH

K

TMK IPG

100111010110001011

G

000000000

110001010100101111

.100111010110001011

. THG

Dimensions of H = 3x6

Dimensions of G = 3x6Since the column weight and row weight changes, this is an irregular parity check matrix

Low Density Parity Check Codes (continued)

Low Density Parity Check Codes (continued)

2. Consider parity check matrix H generated in the example in the previous slides

a.) Determine message bits length K, parity bits length M, codeword length N

b.) Use the generator matrix G obtained in the example to generate all possible

codewords c.

100111101001010011

H

100111010110001011

G Dimensions of the matrix = 3x6,3M ,6N 3 MNK

H

All possible message set

111110101100011010001000

msg_8msg_7msg_6msg_5msg_4msg_3msg_2

1msg_

m

All possible codeword set

010111101110001101110100100011011010111001000000

.msg_8

.msg_7

.msg_6

.msg_5

.msg_4

.msg_3

.msg_2

.1msg_

codeword_8codeword_7codeword_6codeword_5codeword_4codeword_3codeword_2codeword_1

GGGGGGGG

c

Radiating System

• Traditionally satellite antennas have been a the parabolic reflector with a horn antenna at its center.

• However they suffer from a flaw: interference due to solar radiation.• Our antenna of interest is the Adaptive Array Antenna.• The adaptive antenna array automatically steers the beam in the direction of

desired signal (Signal of Interest).• Adaptive antenna arrays have ability to adapt changing environment conditions to

maximize signal strength of signal of interest.

Radiating System (continued)

• The overall radiation pattern of an antenna array is obtained by the radiation pattern of the individual elements, their positions, orientation in space and relative phase and amplitudes of the feeding currents to the elements .

• The overall array pattern can be steered in direction of desired user without physically moving any of individual elements by varying amplitude and phase of individual elements

• Using LMS algorithm to arrive at the antenna architecture.• This algorithm is useful when the interference contains some spectral correlation

with the SOI.

Array Design Architecture

• Vary amplitude and phase of individual elements to obtain the array pattern in desired pattern

• The overall radiation pattern of an array is obtained by radiation pattern of individual elements, their positions, orientation in space and the relative amplitude and phase of feeding currents to the elements .

• The antenna array is a linear array in which centers of antenna elements are placed along straight line. The signals incident on all the antenna elements are of different phases due to the difference in distance traveled by the wave between two antenna elements.

Array Design Architecture (continued)

• The signal present at element 1 has Dsin(x) more than signal at element 2. The phase of element 1 lags behind that of 2 by βDsin(x) where β = 2π /λ.

• The receiver down converts the signal s(t) to IF. The A/D down converts the signal to base band equivalent.

• As they reach the antenna elements, the waves are converted to electrical signals x(t). We define them as x1(t), x2(t)…xn(t). These signals are then weighted by w1, w2…wn .

• Then the output signal is weighted sum of the input signals- y(t) =

• e(k) represents the error between the summed output y(k) and reference signal r(k). The error processor calculates the required weight adjustment to null out the undesired signal. This process is iterative and will continues till all weights in the array converge.

Array Design Architecture (continued)

• By taking the received signal at element 1 as reference, the reference signals xi(t) for uniform line array with element spacing D this will be matrix 1,where xi(t) = a(x)s(t) and M is the no of array elements and a(x) is the steering vector which controls the direction of the antenna beam according to beam according to Sangeeta Kamboj, and Dr. Ratna Dahiya

• For adaptive beam forming, each element output x (t) i is multiplied with weight wi that modif phase and amplitude relation between the branches and summed to give output as matrix 2.

• The overall antenna pattern is continuously modified by adjusting weight vector. For digital communication system, the input signals are in discrete time sampled data form. Hence y(k) = wkxT (k) where is the sampling instant.

LMS Algorithm

• The LMS algorithm operates with a priori knowledge of the direction of arrival and the spectrum of the signal but with no knowledge of the noise and interference in the channel.

• This algorithm is useful when the interference contains some spectral correlation with the SOI.

• Uses a gradient based method of steepest decent to lead to the minimum mean square error.• The basic description of the LMS algorithm is given as:

• Where;1. e(k) : Error signal between the reference signal and the desired output.2. w(k) : Weight vector before adaptation.3. w(k +1) : Weight vector after adaptation.4. μ : Gain constant controlling rate of convergence and stability.

Beam-steering Examples

• The magnitude of the initial pattern is determined by the initial (arbitrary) choice of weights, w whereas the magnitude of the final pattern is determined by the strength of the desired signal, the direction and strength of the interfering signal and the noise in the system.

• M is the no of the array elements; x is the angle of beam-steering

Beam Steering with x = 60°; M =15Beam Steering with x = 30°; M =5 Beam Steering with x = 45°; M =8

Conclusion: Radiating Systems

• We can see that the LMS algorithm does not require squaring, averaging or differentiating and hence can be implemented in most practical systems.

• Its popularity is accredited to the fact that it is simple, easy to compute and efficient.• The parameter μ is the gain constant that regulates the speed and stability of adaptation. It

determines the convergence rate. This gain factor is bounded by the limits 0 < μ < 1/λmax

• λmax : Largest Eigen value of the input correlation matrix.• LMS algorithm is relatively simple; it does not require correlation function calculation and

matrix inversions.• LMS is used to demonstrate the self-steering capability of an adaptive antenna array. It can

be easily done by changing number of elements in antenna array and angle of beam steering.• In satellite communication system, beam of adaptive antenna array by using LMS algorithm

can be steered in direction of desired signal by changing number of elements in antenna array and angle of beam steering.

• Maximum radiation may be received at an appropriate angle.

References

1. Sangeeta Kamboj, and Dr. Ratna Dahiya," Adaptive Antenna Array for Satellite Communication Systems"

2. Stevan M. Davidovich, "Concept for Continuous Inter-Planetary Communications"3. Mary Ann Ingram and Robert Romanofsky," Optimizing Satellite Communications With

Adaptive and Phased Array Antennas."4. R.C Hansen, "Phased Array Antennas“5. Revati Joshi , Ashwinikumar Dhande, “Adaptive Beamforming Using Lms Algorithm”6. Robert G Gallagar ,MIT 1963, “Low Density Parity Check Codes”7. Amin Shokrollahi, “LDPC Codes: An Introduction “