For real values of the Nakagami fading parameter rn, tht: integral in eqn. 9 can be easily computed numerically. However, for inte- ger values of rn, a closed form result may be obtained. In this case, it can be shown that the hypergeometric function in eqn. 5 can be written as (see Appendix of [9]).
ZF’ (1, m
+
5;
m+
1; 5 =Further, using integration by parts in eqn. 6, and the fact that [8]
1
{
(T)
+
(5)
cos[2(n -S)4
cos2”(2) =Ql may be evaluated in closed form [4]. After some simplification the result is
(12) where
a,
= -\i{ay,/[ay,sin2(.nlM)+rn]}cos(~l~ andpL
= d{ayol[ay,
sin2(.n/M)+rn]}sin(~/M). Fig. 1 shows the average symbol error rate for several values of rn and M.X I
\\ \
1061 0 5 10 ( ! V i -~ 15 20 25 30 35 40 SNR 163611Fig. 1 Average symbol error rate for M P S K in Nakagami fading channel
(i) M = 2 (ii) M = 4 (iii) M = 8 (iv) M = 16
EJfect of diversity: The results can be easily extended to include
the effect of diversity on system performance. When N-order MRC diversity is employed at the receiver to mitigate the effect of multipath fading, the PDF of the output SNR is given by
For real values of the Nakagami fading parameter rn, the result becomes
a
sin Bu sinZ+
m ) N 7 n + $ P e ( M ) = 1 m x zFl (1, N m+
i;
Nm+
1; ay0 sin2 Bu+
mwhile for integer values of m, wc have
Conclusion: We have derived new expressions for the symbol error
rate performance of coherent M-ary phase shift keyed signals in slow nonselective Nakagami fading and additive white Gaussian noise channel. For integer values of the Nakagami fading parame- ter m, a closed-form expression is derived for the symbol error
rate. However, for real values of nz, a simple formula which can be easily computed numerically is presented. The effect of N-order MRC diversity reception on the MPSK system is also considered. The results presented are sufficiently general to offer a convenient method to evaluate the perforniance of digital land mobile coher- ent MPSK systems.
0 IEE 1996
Electronics Letters Online No: 19961032
V. Aalo and S. Pattaramalai (Departnient of Electrical Engineering,
Florida Atlanric University, Boca Raton, Florida 33431, U S A )
I 2 June 1996
References
1 PROAKIS, J.G.: ‘Digital communications’ (McGraw-Hill, New York,
1989)
2 PAUW, c.K., and SCHILLING, D.L..: ‘Probability of error for M-ary PSK and DPSK on a Rayleigh fading channel’, ZEEE Trans., 1988, 3 EKANAGAKE, N.: ‘Performance of M-ary PSK signals in slow
Rayleigh fading channels’, E/esr,ron. Lett., 1990, 26, (10) pp. 618- 619
4 CHENNAKESHU, s., and ANDERSO”, J.B.: ‘Error rates for Rayleigh fading multi-channel reception of MPSK signals’, ZEEE Trans.,
NAKAGAMI, M.: ‘The nz-distribution ~- a general formula of intensity
distribution of rapid fading’ zn HOFFMAN, W.G. (Ed.): ‘Statistical methods of radio wave propag,ation’ (Pergamon Press, Oxford, England, 1960), pp. 3-36
6 WOJNAR, A.H.: ‘Unknown bounds on performance in Nakagami channels’, ZEEE Trans., 1986, COM-34, (I), pp. 22-24
7 MIYAGAKI. Y . , MORINAGA, N., and NAMEKAWA, T.: ‘Error probability characteristics for CPSK signa.1~ through m-distributed fading channel’, ZEEE Trans., 1978, CO’M-26, (l), pp. 88-100
GRADSHTEYN, IS. and RYZHIK, 1 . w ‘Tables of integrals, series and products’ (Academic Press, New York, 1965)
ENG, T., and M I L S T E I N , L.B.: ‘Coherent DS-CDMA performance in
Nakagami fading multipath channel’, IEEE Trans., 1995, COM- 43, no. 2 4 , pt. 2, pp. 11341 14.3 COM-36, (6), pp. 755-756 1995, COM-43, (l), pp. 338-346 5 8 9
Differential matched filter architecture for
spread spectrum comimiunication systems
W . - C . Lin, K.-C. Liu a n d
C.-K.
WawgIndexing termr. Spread spectrum communication, Matched jflters
~ ~~~~~
The authors present a new digital matched filter architecture: digitd differential matched filter (DDMF), that employs novel schemes to reduce the number of multiplications and accumulations (1M and A). Theoretical analysis shows that the DDMF saves half of the M- and A hardware in comparison with the conventional filter, and maintains identical processing gain. This makes the proposed DDMF more suitable for direct sequence spread spectrum (DSSS) communication systems and low power VLSI implementations.
Introduction: The direct sequence spread spectrum communication system has many attractive properties compared with other com- munication techniques. The most well known properties are its anti-jamming capability, multipath rejection, low probability of intercept, etc. [I]. In those systems the despreading of random code is an important issue [l] Among many despreading algo- rithms, the use of a matched filter is supposed to be a fast way to acquire the random code [2]. However, the major disadvantage of
conventional digital matched filters is that as the number of stages increases the amount of multiplication and accumulation (M and A) will be greatly increased. This constrains the chip rate and the hardware implementations. The number of stages of commercial digital matched filters i s mostly in the range X-64, and the chip rate is limited to <30 M chip/s [3].
We propose a digital differential matched filter (DDMF), which employs novel schemes to reduce the amount of M and A. For those matched filters with long stages, this new architecture saves half the number of M and A in comparison with the conventional filter, while maintaining an identical processing gain (PG). By cut- ting down the number of M and A, not only the hardware imple- mentation but also the power consumption is reduced. This makes digital matched filters more suitable for low power personal com- munication system (PCS) implementation.
summation
-
~-
output - $ 6 2 ”Fig. 1 Conventioiial marchedfilter striictiiw
Architecture: A block diagram of the conventional digital matched
filter (CDMF) with N stages is shown in Fig. 1 [I]; where a block with Tc is a tap with one chip time delay. The output of the matched filter at time n-l and n can thus be expressed as follows:
(1)
f ~ : , , ~ - l ai\rxO
+
O ~ \ - - ~ Z I+
...+
C L ~ X . \ - - ~+
C I ~ X . \ - - ~f C , n = n.wx1
+
a!V-lJ.’Z+
...+
aarcl\--l+
CL1J.’.\-where N is the length of the PN sequence, a,, = 1-N are the PN sequence coefficients, and x,, = 0-N is the received digital signal.
By subtracting two consecutive outputs of this matched filter. a new sequencej;, Z J ; . ~ -j’ca+l, i = I , 2, .__ can be generated, where
f D . n - - b . v + i ~ o
+
b v ~ i+
~ A - ~ X Z+
...+
bnX.V-1+
b i ~ . . v - ~ -aAVxO+
(a&-ai?r--1)21+
... f ( a 2 - a l ) X . \ - - l+
CLJZn (2) Apparently, by accumulating the ,f;>,<, i = 1, 2, .._, n; ,f( ,, can be obtained. Therefore, a D D M F structure, as shown in Fig. 2, can be constructed. Since a,, i = 1, 2, ..., N are either 1 or -1, the h,, i = 1, 2, ..., N in D D M F are 2, -2, or 0 except h, and hl,-l, For a coefficient of zero, there is no need for multiplication. Thus the iirunber of multiplication is reduced. Table 1 is a comparison of the number of multiplications in C D M F and in D D M F . In t h s comparison, a well known maximum length random code (m- sequence) [l] is used.Table 1: Comparison of M&A number between conventional and
proposed matched filter
Ratio of M&A number between CDMF and
DDMF
1
CDMF1
DDMF1
r : order of generator polynomial of m-sequence [I]
It is obvious from the comparison that the number of M and A is reduced by one half. For a system with M sampleichip, the
D D M F furthermore reduces the number of M and A to 1i2M
times. Thus the power and the hardware are reduced accordingly in a real implementation, while the original property of CDMF, such as processing gain, is still retained.
Fig. 2 Proposed d$fereiztinl nzatched,filter .structure with lzalf the coef’
ficients eqiuil to rci’o
Coizchion: A differential digital matched filter for DSSS is pro-
posed. This filter reduces the number of M and A by half for one sainp1e;chip system, and to 1/2M for M sampleichip system, while maintaining all the properties of the conventional matched filter. These advantages will be more apparent for matched filters with long stages, thus leading to a more suitable implementation of low power VLSI in long operation time handset application.
0 IEE 1996
Electioizics Letters Online No: 19961072
W.-C. Lin (Depaitnwnt of Comnzunication Engineering, National
Cliiuo Tirug C’izii,ersrtj., Hsriichu, Taiwan, Republic of Chinu)
K.-C. Liu and C.-K. Wang (Dei,artment of Conimunicntion Engineering, Ceiirrcil Tung University, CIiuizg-Li, Taiwan, Republic of
30 May 1996
Ch incl)
References
SIMON. M . K , OMURA. J . K , SCHOLTZ. R A . , and LEVJTT, H.K.: ‘Spread spectrum communications’ (Computer Science Press, Rockville, Maryland. 1985)
su. Y T.: ‘Rapid code acquisition algorithms employing matched
filters’, IEEE Trurzs., 1988, COM-36, (6)
POVEY. G J R and GRANT. P M.: ‘Simplified matched filter receiver
design for spread spectrum communication applications’, Electron.
~ ~ / 7 i l 1 7 1 0 1 . Eilg. J . , 1993, pp. 59-64
Improving the performance of cell-loss
recovery in
ATM
networks
Hyo T a e k Liin, DaeHun Nyang and J o o S e o k Song
Indexing terms: Foiivard error correction, Asynchronous transfer
iiiotle
A new method for improving the performance of cell-loss recovery using FEC (fonvard error correction) in ATM networks is proposed. This method provides more correcting coverage than existing methods.
Introduction: The major source of errors in high-speed networks
such as B-ISDN is buffer overflow during congested conditions which results in cell loss. Conventional cell loss recovery methods using FEC in ATM networks recover up to 16 consecutive cell losses because lost cells arc recognised from a 4 bit sequence number (SN). A cell loss recovery method which can recover up to 18 consecutive cell losses in ATM networks is presented in [l]. This means that the method cannot extend the row length of the coding matrix to more than 18. We review the method briefly and then employ a new algorithm for recovering more cell losses. The performance estimation is based on the two-state Markov model
