This letter presents the main statistical characterization
of the underlying error process obtained in the case of
the Digital European Cordless Telecommunications (DECT) radio
system. By simulation of the transmission link, error sequences
are generated for different channel parameters. Relevant statistics
are then computed for the purpose of efficient channel coding
design and evaluation

Cosmas, J

Crespo, P

Garcia-Frias, J

Pelz, R M

IEEE Transactions on Communications

English

Brunel University Research Archive

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 44, NO. 8, AUGUST 1996 Results of Channel Error Profiles for DECT Pedro M. Crespo, R. Mann Pelz, Abstruct- This letter presents the main statistical character- ization of the underlying error process obtained in the case of the Digital European Cordless Telecommunications (DECT) radio system. By simulation of the transmission link, error sequences are generated for different channel parameters. Relevant statis- tics are then computed for the purpose of efficient channel coding design and evaluation. I. INTRODUCTION HE Digital European Cordless Telecommunications T ( D E C T )  system will provide a framework for high density, cordless, short range telecommunication links, covering a broad range of applications and environments either indoors or outdoors. As a consequence of the impairments introduced by the propagation conditions of a mobile radio channel, the use of error control techniques will be required as the means to improve the degradation suffered by the transmitted signal. Toward this end, the behavior of the DECT transmission system was first determined by a point-to-point DECT radio link simulation. From the generated error profiles, the most significant error statistics were then analyzed. The results obtained in this study should be seen as a basis for the design and evaluation of efficient channel coding schemes with the goal of achieving good service quality, when low bit rate digital video (<32 kb/s) and the associated audio are transmitted through the DECT channel. In the next section, the simulation of the radio link and the associated error process are described. In Section 111, the relevant statistics are computed from the error process using a descriptive approach. 11. LINK MODEL AND THE ERROR PROCESS The DECT time-division multiple access (TDMA) frame [ l ]  has a duration of 10 ms and consists of 1152 b (bit rate of 1.152 Mbls) in which time slots of 420 + 60 b (guard- time of 60 b) are assigned to 12 full-duplex logical channels. Only 320 b out of the 420 are used for actual transmission, leaving the remaining bits for synchronization, signalization, etc. This gives an information rate per logical channel of 32 kb/s. In the simulation, however, 420 bit slots per user have been considered. Notice that the 10 ms time separation between slots assigned to a user provides an additional time diversity protection that should be taken into account in the link simulation. Paper approved by A. Duel-Hallen, the Editor for Communications of the IEEE Communications Society. Manuscript received March 20, 1993; revised March 23, 1994 and June 8, 1995. The authors are with the Telefdnica I+D, c/Emilio Vargas 6, 28043 Madrid, Spain. Publisher Item Identifier S 0090-6778(96)05517- 1. J. P. Cosmas, and J. Garcia-Frias 913 The simulated DECT modulator consists of a Gaussian min- imum shift keying (GMSK) modulator with a Gaussian BT product of 0.5 (1/T = 1.152 Mb/s). The receiver comprises a fourth order Butterworth intermediate frequency (IF) filter with a normalized 3-dB bandwidth of BIFT = 1, a one-symbol differential demodulator, and a memoryless threshold detector. An oversampling rate of eight has been used throughout the time simulation. The radio channel is simulated as a finite transversal filter (TF) [2] with time delays close enough to verify the sampling theorem and with tap weight statistics determined by the scattering function S(r ,  v) of the underlying channel. It is assumed that the scattering function equals the product of the delay power spectrum Q(r) and the doppler power density spectrum P(u) .  Additionally, a zero mean in the tap weight random processes has been assumed which is tantamount of not having a dominant line of sight (LOS) component (worst case situation). A classical P( v) has been modeled I 0, ' otherwise. The link simulation has been carried out for four different channel parameters: two delay spread t ,  of values 0 ns and 100 ns, and two maximum Doppler frequencies fo,,, of 2.5 Hz (speed: 1.5 km/h) and 25 Hz (speed: 15 km/h). For the case of a delay spread of 100 ns, the channel impulse response is approximated by a six-tap TF with time delays of 0.1 ,us. The values of the corresponding power delay profile Q ( T ~ )  are given (in dB) by 0, -4, -8, -11.5, -15.5, and - 19.5 (one-sided single exponential [3]). It is important to mention at this point that we have imposed the constraint that the user only has access to a 32 kbls unprotected binary channel and therefore does not have access to the soft decisions at the output of the demodulator. In other words, we consider the whole DECT link as a binary (hard decisions) discrete-time channel with memory. We understand, however, that with soft decisions decoding, significant improvements can be achieved. Therefore, the radio link will be completely described by the error process {ek, 5 E Z } .  The error sequence e represents a realization of the error process that can be related to the channel input and output as follows: e = {.. . ,e l ,  eo, e l , .  . .} - {. . . ,  u - q - l ~ & - q - l , u ~ ~ ~ & - q , u - q + l ~ & - q + l , . . . }  where a = { ~ ~ ~ , u - l , u o r a ~ , ~ ~ ~ }  nd ii = {...,&-I, 60, &I, . . .} are the transmitted and received data sequences, respectively, and 17 2 0 is an appropriate delay. @ denotes 0090-6778/96$05.00 0 1996 IEEE 914 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 44, NO. E, AUGUST 1996 1 oo tm=O. 2.5 Hz . . . . . .  - tm=O, 25 Hz - + tm=100 ns, 2.5 Hz - . tm=10Q ns, 25 Hz - * -7 . . . .  . . .  . . . . .  <.:.. a i o  - k  1 k ! L  \\ ' f  ,~ . . . . . . . . . . . . . . . .  . . . . . . . . .  \\ .... '.; . . . . . . . . . . . . . . . . .  - --. . uiii... . . . . .  . . >  _ . , . . . .  - \,, ' -  .. L I . ,  I . . . .  I I I I I I I J 5 10 15 20 25 30 35 40 SNR ( lOlog(Eb/No) ) Fig. 1. BER versus SNR. modulo 2 addition. An error is said to occur whenever e k  = 1. The bit-error rate (BER) is simply given by K gap process is further reduced and is completely characterized by f ( r ) .  Fig. 3 plots the covariance of successive gap lengths cov(gkgkSn)  for the 100 ns power delay spread channel (the same behavior has been observed for t ,  = 0 ns). Notice that in the case of a Doppler frequency of 2.5 Hz, the covariance almost vanishes for n 2 1, indicating that error process is quite close to a renewal process. In the next section, the relevant statistics are computed as a function of the gap length distributions. p =  lim ~ ~ - + a  2K + 1 Fig. 1 plots the BER as a function of the signal-to-noise ratio (SNR). A K = 2.1 x lo6 have been used throughout the analysis. Also, the simulation results that follow have been based on error profiles with a BER of approximately I O p 3  (SNR M 30 dB). Since the probability of error p is much less than 0.5, more zeros are to be expected than ones in a typical error sequence. This leads to the notion of an error gap [4] as a means of describing the error process. A gap is defined as the string of r - 1 consecutive zero's between two one's and having a length equal to r. Therefore, the binary error process can be likewise described in terms of the corresponding successive gap lengths gZ. In general, a stationary gap process can be adequately described by the multigap-length mass distribution, f "  ( r )  [5] defined as the probability of occurrence of s consecutive gaps with a length r equal to the sum of the composite gap lengths (r 2 s). Notice that with the above notation, the probability of occurrence of a single gap of length r 2 1 is denoted by f ( r ) .  We also denote by F ( r )  = C,W=,+,f(j) the error gap distribution (EGD). Fig. 2 shows the complementary EGD, Le., 1 - F ( r )  = C;,,f(j) which gives the probability of having a gap of length less than or equal to T.  For those cases where successive gap lengths are uncorre- lated, i.e., the gap process is renewal, the description of the 111. RELEVANT STATISTICS AND RESULTS The most frequently used measure to indicate the reliability of a block-coded forward error correction (FEC) system is the probability of block error. The channel statistic necessary to evaluate this in the case of random error correction is P(m,  n), the probability of exactly m errors occurring in a block of n digits. In the case of burst error correction, the statistic is Q(1, n ) ,  the probability of an error burst of length 1 occurring in a block of n digits, where a frequently used definition of a burst in a block, is the length starting from the first error to the last error irrespective of the structure in between. The bit-error auto-correlation function is another relevant statistic that is useful in the design of bit interleaving. An additional insight into the error process can be gained by analyzing the burst error length distribution C(Z, d) ,  which is defined as the probability of occurrence of a burst of length 1. Here, we have adopted the burst definition given in [6]. A burst is specified by two quantities, the error density 0 < d 5 1 and the burst length 1. With the specified error density d chosen, a burst is a sequence of binary digits, that starts and ends with an IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 44, NO. 8, AUGUST 1996 915 f 0 "" ' . '  ' ' I I 1 oo 10' 1 o2 1 o3 1 o4 gap length Fig. 2. Complementary EGD versus gap length for a SNR ~ 3 0  dB. 1 0.8 5 m c a, -a, 5 0.4 * 0 > 0 0 0 -0.2 ................... ............ .................................... i I I I ................. 4 ........................ ................................ i 25 ~~i - i 2 5 Hzi : . .  ............ ..... ......................................................... i ................ I I I .............. ............... ............. ................ 0 10 20 30 4 0  50 60 70 8 0  90 100 n Fig. 3. Cov(go,g,) versus n for a delay spread t,, = 100 ns and a SNR M 30 dB error, in which the ratio of the number of errors to the total number of digits of the sequence exceeds d. If the successive inclusions of the next error keeps the density above d, the burst is continued; the burst ends if further inclusions of an 916 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 44, NO. 8, AUGUST 1996 ffZ Ql ff0  0 0.4542 n 0 -0.4664 n 5.065e-04 -1.239e-01 -2.131e-01 2.204e-04 -8.290e-02 -2.107e-01 TABLE I POLYNOMIAL COEFFICIENTS, IN DESCENDING POWERS; OF m , FOR THE LS APPROXIMATION F: log,,{CJn_m+l P ( j ,  n ) }  0 3  I Q2 I Q1 I f f0  11 12 1 fDmn= 1 tm d fD,,, tm 1 2.5Hz Ons 1 2.5Hz lOOns 0.5 2.5Hz Ons 0.5 2.5Hz lOOns error reduces the error density below d. Finally, ithe burst does not begin with an error belonging to the previous burst. The computation of the above relevant statistics can be obtained by inference from the error sequences. ]However, this will be a cumbersome operation (except for the bit correlation), since it would require almost a bit-by-bit analyslis of the error sequence. It can be shown [4] that P(m,  n) can be expressed as a function of multigap distributions in the following way: n-1 P(m,n) =P (. - "(2 - 2 f " ( j )  + f"+l(j)) j=m-l  (3 1 1 5 m 5 n, with the convention f o ( j )  = 6(j) The computer simulation shows that the log of the block error probability, in the case of having a block code capable of correcting up to m random errors in a block. of length n, can be approximated by a third degree polynomial in m (least squares (LS) fitting) where m 5 n. The values of the {a,}'s are given in Table I. The computation of Q(m,n) and C(1,d) is much more cumbersome than in the case of P(m,n) since it involves, beside multigap distributions, joint and conditional gap dis- tributions [4]. However, in cases of low Doppler frequencies (fo,,, 5 2.5 Hz), one can infer from the curves of Fig. 2 that a renewal assumption on the gap process is valid. This assumption substantially simplifies the computation of the above two quantities since then they can be expressed only in terms of f ( u ) .  It can be shown that I n--l (4) where V ( j ,  I )  can be computed by 1-.7+1 V ( j ,  I) = f ( i ) V ( j  - 1, I - i), 2 5 j 5 I z = 1  and with V(2, I )  = f ( l  - 1) for 1 2 2. Simulation results show that the log of the block error probability in the case of using a block code capable of correcting a single burst of length I ( I  < n) in a block of length n, i.e., log,,{C3n,z+l Q ( j ,  n)} can be approximated by a third order polynomial in I .  Table I1 shows its coefficients for the different cases considered. Notice that only a 2.5 Hz Doppler frequency has been considered to comply with the renewal property of the underlying gap process. In addition, since it was observed from the results of computing P(m, n)  using a nonrenewal (3) and a renewal formulation [see [4] for the renewal expression of P(m,  n)], that both results were quite close as long as n was sufficiently small (n 5 15), only results for block lengths n less than or equal to 15 are shown in Table 11. Similarly, C(1,d) can be evaluated [6] as where U(1, m) is the probability of a sequence of 1 symbols with m errors, which can be computed recursively according to I ,  U(Z,m)  = E' U ( j ,  m - j=m-1 l)U(Z - and U ( j , 2 )  = f ( J  - 1) for j = 2,3,...(Z - max(LZdJ,2) + 2),m = max( 1ZdJ. a ) ,  . . . , I - I ,  1 and 1 2 3. The notations 1x1 and ([XI) denote the largest (smallest) integer less (greater) than x. For the case of d = 1, i.e., for error bursts consisting of sequences of consecutive one's, the logl,{C,"_,+, C ( j ,  d ) }  which gives the occurrence probability of a burst of length greater than I ,  can be approximated by 0111, whereas for the other error density considered in the simulation d = 0.5, this quantity is better approximated by a second order polynomial. Table I11 gives the different coefficients for the different channel parameters. In the above LS approximations, the order of the polynomials has been chosen such that the normalized LS approximation error is always less than -30 dB. Also, the approximations are valid for probabilities of error up to lop6. Finally, the bit correlation functions are given in Fig. 4. Two conclusions can be drawn from these curves. First, for large Doppler frequencies the memory of the channel is limited by the slot length of the DECT frame (420 b) and it is IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 44, NO. 8, AUGUST 1996 917 1 0.8 0.6 C 0 a .- c -0.4 s c i3 0.2 0 -0.2 1 I I I tm=O, 2.5 Hz - tm=O, 25 Hz ... tm=100 ns, 2.5 Hz - .  tm=lOO ns, 25 Hz - - . . . .. , . ;. , .. . ,  , ..:. . . . . .  . . . :  . . . . , . . . . I I 10’ 1 o2 n (correlation lag=n-1) 1 o3 Fig. 4. Bit correlation function versus correlation lag for a SNR z 30 dB. TABLE 111 POLYNOMIAL COEFFICIENTS, IN DESCENDING POWERS OF I ,  FOR THE LS APPROXIMATION OF: log,,{C,”o,l+l C ( j ,  d ) }  independent of its delay spread. On the contrary, for low Doppler frequencies its memory depends on the slow fading characteristics of the channel as well as on its delay dispersion. IV. CONCLUSION The computation of relevant statistics for the purpose of code performance evaluation has been obtained. The results should be seen as a guideline for the design and evaluation of efficient channel coding schemes with the aim of achieving transmission quality in implementing video and audio services, using a DECT radio system. REFERENCES [ 11 ETSI, “Digital European cordless telecommunications common interface part 2: physical layer,” prETS 300, 1992. [2] P. A. Bello, “Characterization of randomly time-variant linear channels,” IEEE Truns. Commun. Syst., Dec. 1963. [3] T. A. Wilkinson, “Channel modeling and link simulation for DECT testbed program,” in Con$ Rec. Mobile Radio Personal Communicu- tions, Univ. of Warwick, U.K., Dec. 9-12, 1991, pp. 293-299. [4] L. K. Kanal and A. R. K. Sastry, “Models for channels with memory and their applications to error control,” Proc. IEEE, vol. 66, pp. 724-744, July 1978. [5] J. P. Adoul, “Error intervals and cluster density in channel with memory,” IEEE Truns. Inform. Theory, vol. IT-20, pp. 103-111, Jan. 1974. [6] S. Tsai and P. S .  Schmied, “Interleaving and error burst distribution,” ZEEE Trans. Commun., vol. COM-20, pp. 291-296, June 1972. 

Channel modeling and link simulation for DECT testbed program,”

Characterization of randomly time-variant linear channels,”

Error intervals and cluster density in channel with memory,”

ETSI, “Digital European cordless telecommunications common interface part 2: physical layer,” prETS 300,

Interleaving and error burst distribution,”

Models for channels with memory and their applications to error control,”

Results for Channel Error Profiles for DECT

Results for Channel Error Profiles for DECT

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