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Performance Analysis of Hybrid DSSFH MSK System in Rayleigh

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Performance Analysis of Hybrid DSSFH MSK System in Rayleigh Powered By Docstoc
					 Effects of Partial-Band Noise Interference on the Hybrid DS/SFH
             MSK System in Rayleigh Fading Channel

                                         Heung-Gyoon Ryu, Member, IEEE, Yun-Young Kim
Abstract – In Rayleigh fading channel, effects of the partial-band           Electronic Engineering, Chungbuk National University, Cheong-ju,
noise interference on the performance of a hybrid DS/SFH MSK                 361-763, Rep. of Korea.
system are analyzed, and the interference environments that cause
the worst BER are investigated. Results show that, in Rayleigh
fading channel, the full-band interference always causes the worst
performance, independent of the average SNR or average SIR. On
the other hand, in AWGN channel, the full-band interference in low
SIR and the partial-band interference in high SIR result in the
worst case BER, respectively, for all SNR.
Index Terms- hybrid, Rayleigh, AWGN, DS, SFH, BER, SNR, SIR.

                          I. INTRODUCTION


T    O DATE, the studies on spread-spectrum multiple access
     systems have been performed according to the various
modulation techniques. In the literature, there was a paper on
                                                                                                     < Transmitter Structure>

the performance analysis of the hybrid DS/SFH MSK system in
AWGN channel with multi-tone jamming [1]. However, it did
not consider the fading channel environment. Also, there has
been no paper on the hybrid DS/SFH MSK system in Rayleigh
fading channel with the partial-band noise interference (PBNI).
In this Letter, a novel analysis on the above system is presented.
After the numerical analysis, the interference environments that
cause the worst case BER performance are investigated.

                           II. SYSTEM MODEL                                                 < Partial-band Noise Interference >
   For the MSK modulation, the transmitted signal takes the
form
                
                                                         t   
sMSK (t )  2 P c1 (t )d1 (t ) cos 2 ( f c  f h (t ))    
                
                                   
                                                          Tc   
                                                         t   
              c2 (t )d 2 (t ) sin 2 ( f c  f h (t ))      (1)
                                   
                                                         Tc   
where f c is carrier frequency, P is the power of the information
signal, d1 (t ) and d 2 (t ) of the duration T s are data                                              < Receiver Structure >
sequences of I and Q channels, and c1 (t ) and c 2 (t ) of
duration T c are DS spreading sequences of I and Q                                        NI                  WI            W
                                                                                          ,            fI         f  fI  I
channels. It is assumed that there are N chips in T s ,                         S( f )   2                    2             2                    (2)
i.e., N  Ts / Tc . The f h (t ) of the duration T h is hopping                          0,
                                                                                                              el sew here
frequency derived from a set of N FH frequencies equally                     where f I and WI are the center frequency and the
spaced, and the number                                                       bandwidth of the PBNI, respectively. Denoting PI as the
of transmitted data per hop is a positive integer.  is the                  received total interference power, then the psd of PBNI is
random phase in the transmitter and uniformly distributed in                  N I / 2 P I / 2Wss , where  is the interference fractional ratio,
[0,2]. Assuming that the considered I/Q decision statistics are             and Wss is the total spread-spectrum bandwidth. Because WI
independent, it is true that the analysis on the I-channel can be            is very small compared with f I , the PBNI is the narrow-band
sufficient for giving the system BER. Thus, only I channel is                bandpass process[3]. Thus,
considered for simplicity of analysis.
   The PBNI is band-limited white Gaussian noise and its
power spectral density(PSD) is defind as [2]
                                                                                                                                               
                                                                                   nI (t )  2 ni (t ) c o s2( f I t ) nq (t ) s i n2( f I t )
                                                                                                                                                 (3)

                                                                             where ni (t ) and nq (t ) are inphase and quadrature com-
Heung-Gyoon Ryu and Yun-Young Kim are with the department of
                                                                             ponents of nI (t ) , respectively, and these psds are equal to that
                                                                         1
of nI (t ) .                                                                                                                 Zd  Z I  Z M  Zn .                                                             (10)
   In this paper, the frequency-nonselective Rayleigh fading
channel with L paths is considered and its impulse response                                          In eq. (10), a desired signal term
takes the form [4]                                                                                                                 ( n 1) Ts
                                                                                                                Z d  nT                  s
                                                                                                                                                            P / 2  1 c1 (t )c1 (t  t 1 )d 1 (t  t 1 )
                                        L
                           h(t )    k (t  tk )                                       (4)                                                                   cos(t / Tc ) cos(t / Tc  1 (t )) dt
                                       k 1

                                                                                                                         P / 8  1Ts d 1, n                                                                   (11a)
where t k and  k are the time delay and the path gain,
respectively, and the path gain  k has Rayleigh distribution                                        where d1,n is the n th data symbol of I channel. A term due to
given by [3]                                                                                         the multi-path is given by
                                              2 k  
                           p(  k )                                 / k
                                                                 2

                                                  e         k
                                                                                           (5)                            L        ( n 1)Ts
                                              k                                                            Z M   nT                                     P / 2  k c1 (t )c1 (t  tk )d1 (t  tk )
                                                                                                                        k 2
                                                                                                                                           s




where  k is the second moment of  k .                                                                                                 cos(t / Tc ) cos(t / Tc   k (t )dt
                                                                                                                        L
                                                                                                                                                                                                               (11b)
   Assume that the receiver is to be in synchronous with only                                                      P / 8  k cos(  k )
the first path, but discards the others. Then,  k can be assumed                                                    k 2
                                                                                                                                                   ( n 1)Ts
to be related to the second moment of the reference path                                                                                nT          s
                                                                                                                                                                c1 (t )c1 (t  tk )d1 (t  tk )dt .
gain 1 , and its relation is given by [5]                                                              A term due to the PBNI is Z I . In eq. (9b), the psd of
                                k  1 e            ( k 1)
                                                                                          (6)         xI (t ) is uniformly distributed in the bandwidth of W DS , and,
                                                                                                     after the despreading procedure, the bandwidth of xI (t ) is the
where  is the decay rate of  k . In this paper, we assume                                          same as that of the demodulation signal. Therefore, Z I is
that the path delay t k is uniformly distributed in [0, T s ].                                                                ( n 1)Ts
                                                                                                               Z I  nT           s
                                                                                                                                                      xI (t )c1 (t ) cos(t / Tc )dt
       III. ANALYSIS OF DECISION STATISTICS                                                                                                        N 1
                                                                                                                     
                                                                                                                                  1
                                                                                                                                                    c1,i iT
                                                                                                                                                                ( i 1)Tc
                                                                                                                                                                                 ni (t ) cos( 2ft ) 
                                                                                                                                   2               i 0
                                                                                                                                                                    c
                                                                                                                                                                                                           .   (11c)
                                                                                                                                                                                                
  Passing through the first BPF with the bandwidth of Wss ,
the received signal is given by                                                                                                                             nq (t ) sin(2ft ) cos(t / Tc )dt
                                                                                                                                   1                 N 1
                                                                                                                                                                        ( i 1)Tc
                       r (t )  rs (t )  nI (t )  n(t )                                (7)                                    nI (t )dt.           c1,i iT
                                                                                                                   2 2                               i 0
                                                                                                                                                                         c

                       L
where rs (t )    k s MSK (t  t k ) and n(t ) is the band-limted                                    The last term is due to AWGN and given by
                      k 1
                                                                                                                                  ( n 1) Ts
version of AWGN with a double-sided PSD of N 0 / 2 . Also,                                                     Z n  nT               s
                                                                                                                                                          x n (t )c1 (t ) cos(t / Tc )dt.                     (11d)
because the PBNI typically interfers the total spread-spectrum
bandwidth with the probability of  , which denotes the                                                 From eq. (11a) to (11d), the variances are as follows.

                                                                                                     var Z d   1PTs / 8
interference fracitonal ratio, nI (t ) is equal to the form of the                                                                             2
                                                                                                                                                                    .                                           (12)
eq. (3).
    Denoting x1 (t ) as I channel output of the second BPF, it is                                    var{ Z M }  
                                                                                                                    L

                                                                                                                   k 2
                                                                                                                         P
                                                                                                                        16
                                                                                                                                    2    ( n 1)T
                                                                                                                                                                    
                                                                                                                            E{ k } var nT c1 (t )c1 (t  tk )d1 (t  tk )dts
                                                                                                                                                                                    s
                                                                                                                                                                                                           
written as                                                                                                                                                                                                       (13)
                                                                                                                  L PT 2
                                                                                                                s 1e  ( k 1)
                                                
          x1 (t )  BPF r (t ) cos 2 ( fc  f h,1 (t ))t  h,1 (t )                                        k  2 24 N


                  xs (t )  xI (t )  xn (t ) .                                          (8)                        1 N 1N 1         ( i 1)T ( m 1)T                  
                                                                                                     var{ Z I }  E    c1,i c1, m iT          mT ni (t )ni ( )dtd 
                                                                                                                                                                                    c       c


                                                                                                                     8  i 0 m0                                           
where f h,1 (t ) and  h,1 (t ) are the dehopping frequency and
                                                                                                                                                                             c          c




                                                                                                                1 N 1 ( i 1)T ( i 1)T
                                                                                                                iT           iT Eni (t )ni ( )dtd
                                                                                                                                               c            c
the phase generated from the frequency dehopper, respectively.
                                                                                                                8 i 0        c                       c


   In eq. (8),
                                                                                                                  NT 2 PW
                                                                                                                c I DS                                                                                         (14)
                                                                                                                    8Wss
                       L
x s (t )  P / 2   k  f h,1 (t ), f h, k (t  t k )
                      k 1
                                                                                                                    NN 0Tc
                            c1 (t  tk )d (t  tk ) cost / Tc  k (t )              (9a)        var{ Z n }             .                              (15)
                                                                                                                       8
                                   
xI (t )  BPF nI (t ) cos 2 ( fc  f h,1 (t ))t  k                                               From the above variances, the signal-to-total interference
                                                                                                     power ratio is given by
      
          1
                n (t ) cos( 2ft   )  n (t ) cos( 2ft   )
                  i                                  k               q               k   (9b)                               zI                    1         1
                                                                                                                                                                  (16)                      1
            2                                                                                                                               2Eb      2Eb 
                                                                                                                       1        ( k 1)
                                                                                                                                                                L
                                                                                                                           e                          
where f  fc  f h,1 (t )  f I . And, x n (t ) is the band-limited                                                  3N k  2              NI       N0 
AWGN component.                                                                                      where Eb  1P / R, NI  PI / Wss , and R is the bit rate. In eq.
 After despreading, the I channel correlator output Z 1 is                                           (16), P / PI and Eb / N 0 denotes the average signal-to-
                      ( n 1)Ts
                                                                                                     interference power ratio (SIR) and the average signal-to-noise
           Z 1  nT       s
                                  x1 (t )c1 (t ) cos(t / Tc )dt                                     ratio (SNR), respectively. Also, in case there is no interference,

                                                                                                 2
the desired signal-to-total interference power ratio is
                                       1
                  zn                                  1
                                                            .        (17)
                          1     L
                                   ( k 1)
                                               2E 
                            e                b
                         3N k  2              N0 
   In the general fading channel, that is, the Rician fading
channel, the pdf of the instantaneous signal-to-noise ratio is
given by [6]

           1 K        z                            z        
p( z )       exp  K  (1  K ) I 0  2 ( K 2  K )          ,   z0
            z          z                           z        
                                                                
                                                              (18)
where K is the Rician factor, which denotes the power ratio of
the direct wave and the indirect wave, and z and z denote the                       Fig. 2. The effect of the interference fractional ratio on the
instantaneous SNR and the average SNR, respectively. Using
                                                                                system performance when SIR  20dB , L  2 and   3 .
the eq. (18), the average bit error probability is obtained by
                         
                               
              Pe  0 Q z p ( z )dz .                                (19)
                                                                                   The effect of the fractional ratio,  , on the system
                                                                                performance is shown in Fig. 1, when the average SNR is fixed

                                     
In eq. (19), we used Q z since we just consider z as the
                                                                                as 20dB. In Rayleigh fading channel, the worst case is when
                                                                                  =1 (full-band interference), independent of the average SIR.
total signal-to-interference ratio, not the pure SNR. In Rayleigh               On the other hand, in AWGN channel, the performance of
fading channel, since no direct component is present, K=0.
                                                                                system is different according to the average SIR. More
Therefore,
                                                                                specifically, the full-band interference in low SIR and the
                                                                              partial-band interference in high SIR cause the worst case,
                       1             z  .
              Pe            1                                    (20)       respectively.
                       2           2 z 
                                                                                 Fig. 2 shows the effect of the fractional ratio on the system
                                                                                performance, in case the SIR is fixed as 20 dB. The worst case
Replacing z with eq. (16) and (17), the average bit error                       BER, in Rayleigh channel, is occurred by the partial-band
probabilities in case of being interfered and not, Pe, I and Pe, N ,            interference, independent of the average SNR. On the contrary,
can be obtained, respectively. Consequently, the total bit error                in AWGN channel, the full-band interference causes the worst
probability in fading channel is given by                                       BER, irrespective of the average SNR.

                  Pb  Pe, I  (1   ) Pe, N .                     (21)                              V. CONCLUSION
                                                                                   In this paper, the performance of a hybrid DS/FH MSK
                                                                                system is analyzed in Rayleigh fading channel with the partial-
  IV. NUMERICAL ANALYSIS AND DISCUSSIONS                                        band noise interference, and the interference environments that
  In this section, when the total processing gain is fixed as                   cause the worst BER performance of the above system are
1000(30dB), we evaluate the BER performance of a hybrid                         investigated. Results show that, in Rayleigh fading channel, the
DS/SFH-MSK system                                                               full-band interference always causes the worst performance,
                                                                                independent of the average SNR or SIR. On the other hand, in
                                                                                AWGN channel, the partial-band interference the worst case for
                                                                                high SIR (about 20dB) and the full-band interference for low
                                                                                SIR (about 0dB) result in the worst BER, respectively,
                                                                                independent of SNR.


                                                                                                         REFERENCES
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                                                                                    DS-SFH/MSK Spread-Spectrum System under Multione
                                                                                    Jamming,” IEEE MILCOM’99, pp. 567-570, 1999.
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                                                                                    vol. 44, no. 2, pp. 238-246., February 1996.
                                                                                [3] J. G. Proakis, Digital Communications, 3rd ed., McGraw-
  .                                                                                 Hill, 1995.
    Fig. 1. The effect of the interference fractional ratio on the              [4] Z Tan and I. F. Blake, "Performance analysis of
system preformance when SNR  20dB , L  2 and   3 .                              noncoherent DS-SFH spread spectrum multiple access for
                                                                                    indoor wireless communications," IEEE MILCOM '92,
                                                                                    vol.3, pp.851-855, 1992.
                                                                                [5] T. Eng and L. B. Milstein, "Coherent DS-CDMA

                                                                            3
    Performance in Nakagami Multipath Fading," IEEE Trans.
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    February/March/April 1995.
[6] S. Sampei, Applications of Digital Wireless Technologies
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