Coding Scheme for Ka -Band Fixed Satellite

Communication System

WANG Ai -hua , LUO Wei -xiong

(Department of Electronics Engineering ,Beijing Institute of T echnology ,Beijing 100081,China )Abstract :The performance analysis and simulation of coding schemes based on the modeling K a -band fixed satel -lite channel have been presented .The results indicate tha t concatenated codes w ith large inner interleaving depth have good perfo rmance and high spectrum efficiency .T he studies also show that simple block interleaving is very effectiv e in combating the slo w frequency -nonselective fading of Ka -band .Key words :K a -band ;channel model ;performance simulation ;coding scheme

C LC number :TN 927 Document code :A Article I

D :1004-0579(2002)02-0169-05

Received 2001-09-19

Sponsored by M inisterial Level Advanced Research Fundation Biographies WANG Ai -hua (1965-),doctoral student ;LUO Wei -xiong (1940-),professor ,doctoral adviser .

With the increasing requirements of satellite

communications and the development of new technol -ogy ,it is anticipated that future satellite communica -tions systems with on board sig nal processing will be developed as Ka -band (20/30GHz )for multimedia services .It is indicated by a g reat deal of measure -ment data and theoretical analy sis that Ka -band satel -lite channel is a slow frequency -nonselective fading channel .Its statistic characteristics can be decided by the joint distribution of signal envelope and phase [1]

.The paper introduces coding fitted fo r Ka -band fixed satellite sy stem .

1 System and Channel Modeling

Compared with C -band and Ku -band satellite

communication ,for Ka -band (20/30GHz )com mu -nication ,the atmosphere layer will cause signals ex tra attenuation ,w hich is not only the function of fre -quency ,but also the function of location ,elevation ,season and system availability .While including the attenuation of rain (and snow ),w ater vapour ,clouds ,oxygen and scintillations ,the free space prop -agatio n formula is modified as

P R =P T A T A R c 2d


f 2L t =P T A T A R

c 2

d 2m (f ,P o ),(1)w her

e P R ,P T are respectively the received and trans -mitted carrier average powers (W ),

f (Hz )is the carrier frequency ,d (m )is the satellite -earth termi -nal distance ,c (m /s )is the light speed in vacuum ,A R and A T are effective areas of the receivin

g and transmitting antennas respectively (m 2),and L t is the sum of attenuatio n for space link ,P o is sy stem unavailability .

The calculation shows that the factor m (f ,P o )=f 2/L t does not change significantly within a wide frequency range w hen the system availability is lower

(e .g .<99.7%)[2].Since the availability require -

ment for Ka -band satellite system is usually less than

99.7%,Ka -band satellite channel fading is frequency non -selective .Or we can say that the overall channel is affected only by an in -band `flat 'attenuation and by AWGN .Besides ,the `flat 'attenuation changes very slow ly w ith time ,and it depends o nly on the weather .

Suppose a digital modulated signal

s (t )=Re [s l (t )exp (j2πf c t )]

is transmitted over the channel ,where s l (t )is the equivalent lowpass transmitted signal and S l (f )is its frequency content ,

then the equivalent low pass

Journal of Beijing I nstitute of Technolo gy ,2002,V ol .11,N o .2

DOI :10.15918/j .jbi t1004-0579.2002.02.014

received signal may be expressed in terms of the fre-quency domain as

r l(t)=∫∞-∞C(f,t)S l(f)exp(j2πft)d f,(2) where C(f,t)is the channel time-variant transfer function.As Ka-band satellite communication channel is a slow frequency non-selective fading channel w ith-in the band,w e can regard the transfer function C(f,t)as a complex-valued constant during at least one sy mbol interval.Let C(f,t)=A exp(j),then w e have

r1(t)=∫∞-∞A exp(j)S l(f)exp(j2πf t)d f=

A ex p(j)∫∞-∞S l(f)ex p(j2πft)d f=

A ex p(j)s l(t), 0≤t≤T s.(3)

It show s that the received sig nal is sim ply the transmitted sig nal multiplied by a complex-valued constant C(f,t).C(f,t)=A exp(j)is called a multiplicative fading process.`A'and`'represent the envelope and the phase of the equivalent low pass channel respectively.Both of them are random pro-cesses.The latest research[1]show s:Ka-band satel-lite comm unication channel characteristics are mainly affected by weather conditions.The sig nal envelope and signal phase caused by w eather conditions can be modelled as Gaussian random processes.The proba-bility density function of its envelope is given by







w hereσ2and m are the variance and the mean of the signal envelope respectively.Tab.1shows the values forσ2and m under various w eather conditions.

Ta b.1 Ka-band fixed satellite channel envelope models

w eather conditions mσ2

clear0.4550.00056 thunder show er0.4360.01386

blowing snow0.5000.00021


Hereby,we can set up the statistic model fo r Ka-band fixed satellite channel show n in Fig.1,in w hich C(f,t)=A exp(j)represents the multiplica-tive


fading vecto r,and n(t)represents AWGN. As Ka-band fixed satellite communication chan-nel is a slow fading channel,which will cause burst error surely.Accordingly,w e can build the sy stem model for Ka-band fixed satellite channel by concate-nated code,show n as Fig.2.Inner interleaver/dein-terleaver are utilized to mitig ate the channel memo ry. It w ill be proved by the following analysis and simula-tion that inner interleaving


mitig ates the channel memory and im proves BER perfo rmance indeed.

2 System Performance Analysis

In the follow ing w e shall study the effect of each code individually and then consider the performance of the concatenated system in the Ka-band fading channel.

2.1 Performance Evaluation of RS(N,K)Outer


The decoded BER at the output of outer decoder is closely approximated by

P RS b=







P i s(1-P s)N-i,(5) w here t=0.5(N-K)is the error correctio n capa-bility of the code,and P s is the symbol error proba-bility into RS decoder.If the bit error rate at the out-put of the inner decoder is P in b,in the case of ideal in-terleaving,fo r an RS-sy mbol consising of a bits,we have P RS s≤aP in b.

2.2 Performance Evaluation of Inner Codes

2.2.1 Performance Evaluation of Convolutional

Journal of Beijing I nstitute of Technolo gy,2002,V ol.11,N o.2

Code (n ,k ,K ) Slow -fading channel ———with infinite

channel memory

Here the fading is so slow that the fading ampli -tude is constant at the value A throug hout the mes -sage sequence .Under the circumstances of ideal co -herent detection of the received signal and Viterbi maximum likelihood decoding w ithout inner inter -leaving ,the conditional erro r event probability is

P con E /A =

Q [A (2RdE b /N 0)1/2


w here R is the coding rate ,d is the distance betw een the error path and co rrect path ,and A is the sig nal envelope .When the sig nal is affected by weather con -ditions ,the instant sig nal envelope w ill fluctuate .Fo r Ka -band fixed satellite channel ,A is a random vari -able w ith Gaussian distribution .So the unconditional

bit error probability can be determined by averaging over signal envelope A w ith the follow ing result .P con b

=E {P co n

b /A }


∑∞d =d




2RdE b σ2

N 0



exp -(RdE b /N 0)m 2

1+(2RdE b σ2

/N 0)

,(7)w here βd is the total number of bit errors in all the adversaries of a given Hamming distance d ,d f is the

free distance of the code ,σ2

and m are variance and

mean of the sig nal envelope respectively show n in Tab . Time -varying fading channel ———w ith zero

channel memory

Here the fading amplitude A i ,although constant w ithin a sig naling interval ,is independent from inter -val -to -interval .As a result ,the sequence {A i }of fad -ing amplitudes constitutes an iid (independent identi -cal distribution )sequence .As remarked previously ,this can be achieved through inner interleaving with enoug h interleaving depth .

Assuming ideal coherent detection of the received signal and Viterbi maximum likelihood decoding with inner interleaving ,the conditional error event proba -bility is

P con E /A

=Q (2RE b /dN 0)



i =1

A i


For Ka -band fixed satellite channel ,{A i }is an

independent random variable sequence w ith Gaussian

distribution .The unconditional bit error probability can be determined by averaging over signal envelope {A i }with the follow ing result .

P con


=E {P c o n b /A }≤

121+2RE b σ2

N 0


× T (D ,N )

N N =1,D =D 0



D 0=exp -(R

E b /N 0)m 2

1+(2RE b σ2

/N 0)

,w here T (D ,N )is the transfer function ,σ2

and m

are variance and mean of the signal envelope respec -tively show n in Tab .1.

2.2.2 Perfo rmance Evaluation of TCM

Using com puter simulation approach ,we shall evaluate the BER perform ance for the P -TCM sy stem w ith and w ithout RS outer code on a Ka -band fixed satellite channel under various weather conditions .

3 The BER Performance Analysis and

Simulation for Each Coding System

By the system model shown in Fig .2,we can get the following analy sis and simulation result .Note that B 0is the channel fading rate and R s is the chan -nel symbol rate .Besides ,fo r the discussion in first two items ,it is supposed that infinite inner /no outer interleaving is adopted .3.1 Co -QPSK System Using RS (255,223)and

Convolution Code (2,1,7)in Ka -Band Fad -ing C hannel

The BER perfo rmances for the convolution con -catenated sy stem under various weather conditions are show n in Fig .3.It show s that the analytical bound is tig ht for high SNR in thunder show er w eather .How -ever in clear weather ,the analytical bound is below simulation results .The reason is that only the first term of the function is considered and the errors brought by other paths and items are neglected when we calculate the inner /outer code bound .We can see that under various weather conditions ,the sig nificant coding gains for the concatenated code system are achieved .In clear w eather ,at P b =10-6,the

WAN G Ai -hua et al ./Coding Scheme for K a -Band Fixed Satellite Communication System

convolution concatenated system can get 7.5dB cod -ing gain com pared w ith the uncoded QPSK system ,and 1.9dB more gain compared with the convolution sy stem .Under bad weather ,the BER performance is improved much more g reatly .This improvement

comes ,however ,at the expense of increased band -width requirement w hich means a lowered bandwidth efficiency .For convolution concatenated system ,the bandw idth efficiency is 0.87(bit ·s -1

)/Hz .



(a )clear

(b )thunder

Fig .3 BER performance of concatenated code with (2,1,7)convolutional code and RS (255,223)outer code in

Ka -band under different w eather conditions

1,5-uncoded simul ation result ;2,6-convolutional code simulation result ;

3,7-convolutional concatenated code analytical bound ;4,8-convolutional concatenated code simulation result

3.2 64-State ,2/3,8PSK P -TC M Concatenated

System with RS (255,223)Outer Code in Ka -Band Fading Channel

Fig .4gives out the BER simulation result of P -TCM concatenated system under various weather con -ditions .We can also see that under various w eather

conditions ,the sig nificant coding gains fo r TCM con -catenated code system are achieved .In clear weather ,

at P b =10-6,this sy stem can get 4.5dB coding gain compared w ith uncoded QPSK system ,and 1.8dB more g ain compared w ith P -TCM system .Under bad

weather ,the BER perfo rmance is improved m uch more g reatly .Com pared with convolution concatenat -ed system ,TCM concatenated system has a sm aller coding gain (about 3.0dB difference )and a higher bandw idth efficiency ,w hich is 1.72(bit ·s -1)/Hz



(a )clear (b )thunder

Fig .4 BER performance of concatenated code w ith P -TCM inner code and RS (255,223)outer code in Ka -bank under different w eather conditions

1,4-uncoded s imulation res ult ;2,5-TCM code simulation result ;3,6-TCM concatenated code simulation result

3.3 C ombating the Channel Memory Effectively

with Simple Block Interleaving

Fig .5shows the different sensitivityies of convo -lution concatenated system and TCM concatenated sy stem to inner interleaving (no outer interleaving )in

thunder shower w eather .Clearly ,the inner inter -leaving is very effective to combat the slow frequency -nonselective fading of Ka -band for the co ncatenated coding system .To achieve ideal interleaving ,the in -terleaving depth should be higher than the ratio of the

Journal of Beijing I nstitute of Technolo gy ,2002,V ol .11,N o .2

sy mbol rate to the fade rate and the interleaving w idth should be 3-4times as large as the decoding

depths for the Viterbi decoder



 (a )convolutional cascade

(b )TCM cascade

Fig .5 BER performance of concatenated code in Ka -band w ith no outer interleaving and different inner interleave depths under thunder s how er condition (R s /B 0=1000)

1-convolutional concatenated system w ith no inner interleaving ;2-16bit ×16bit ;3-128bit ×16bit ;4-1024bit ×256bit ;5-ideal inner interleaving s imulation result ;6-TCM concatenated system w ith no inner interleaving ;7-18bit ×18bit ;

8-126bit ×66bit ;9-1026bit ×258bit ;10-ideal inner interleaving s imulation res ult

4 Conclusion

By analyzing and simulating the system BER perfo rmance and system bandwidth efficiency for Ka -band fixed satellite channel w ith different interleav -ing s and codings ,it is proved that both system BER

perfo rmance and bandw idth efficiency w ill be better for a concatenated system w ith inner interleaving (with enoug h interleaving depth ).It is also proved that ,in bad w eather ,the inner block interleaver is very efficient

to combat

the slow

frequency -

nonselective fading of Ka -band .

References :

[1] Loo C .Impairment of digital transmission throug h a K a -band satellite channel due to weather co nditions [J ].I n -ternational J Satellite Communication ,1998,16:137-145.

[2] M atricciani E .Evaluation of the feasibility of satellite

systems desig n in the 10-100G Hz frequency range [J ].Internation J Satellite Communicatio n ,1998,16:237-247.

Ka 频段固定卫星通信系统编码方式

王爱华, 罗伟雄

(北京理工大学电子工程系,北京 100081)

摘 要:在建立了K a 频段固定卫星通信信道模型的基础上,对几种编码方式的性能进行了分析与仿真.分析及仿真结果表明:采用足够内交织深度的级联码系统的BER 性能及带宽效率均较好.特别是内码为P -TCM 的级联码系统,在基本不扩展占用频带的情况下,还可以获得可观的编码增益,因此特别适用于Ka 频段的宽带数据传输.研究结果还表明:采用内分组交织可以有效地抵抗Ka 频段卫星通信信道的非频率选择性慢衰落.关键词:K a 频段;信道模型;性能仿真;编码方式

WAN G Ai -hua et al ./Coding Scheme for K a -Band Fixed Satellite Communication System