Wavelet packet based MC=MCD-CDMA communication system
rðtÞ ¼
k¼1 h¼1 j¼1 l¼1
h I ðt tkhjl Þwph ðt tkhjl Þ dkjh ðt tkhjl Þ
M.M. Akho-Zahieh and O.C. Ugweje A novel wavelet packet based multicarrier multicode coded division multiple access (CDMA) system is developed and analysed. The effect of wavelet family and the number of wavelet packets superstream are investigated in terms of signal-to-noise plus interference ratio. Performance of the system is compared to several CDMA based systems. Results show that the system performs significantly better than other systems.
Introduction: Multiple services with different bit rate that require high data rate transmission are currently receiving more attention. Multicarrier (MC) and multicode (MCD)-CDMA systems, for example, can provide variable and high data rate transmissions. In this Letter, a new wavelet packet (WP) based MC=MCD-CDMA system denoted as WP-MC=MCD-CDMA is developed. The wavelet packets are used as orthogonal subcarriers. Given that they have many attractive properties such as time-frequency localisation, the system is effective in suppressing interference caused by multipath, intercarrier interference (ICI) and multiple access interference (MAI). The combination of MC, MCD and WP techniques provides the system with the capability of variable and high data rate transmission without interference scaling, and enhanced robustness to multipath fading mitigation.
S/P and wavelet packets
aj (t ) ck(t )wph(t ) transmitter
coding correlator
S/P and coding
wavelet packets correlator
System model and description: The system model is shown in Fig. 1. For brevity, throughout this Letter, all subscript k denotes the user, h denotes the waveletPpacket, and j denotes the code. The data 1 i Q dk(t) ¼ dIk(t) jdQ T=( JH) (t i(T=JH)) is a random k (t) ¼ i¼1 dk complex sequence where Px is a rectangular pulse of duration x, J is the number of substreams in the multicode, T is the bit duration and H is the number of superstreams of WPs. After the serial-toparallel (S=P) conversion, the data substreams are coded by a set of orthogonal signals aj(t) to reduce interference between substreams. The coded substreams are added and the resulting signal is again S=P converted into H superstreams. The next step is the spreading by the pseudo-noise (PN) sequence ck(t) and modulation by the WP wph(t). chip duration is Tn ¼ T=Nn. The hth WP The length of ck(t) ispNn and P is given by wph(t) ¼ (N=Tn) i ph[((N t)=Tn) iTn], where ph[ ] is defined recursively by the quadrature mirror lowpass and highpass filters h0(k) and h1(k) [1], and N is the support length of ph(t). The WP with different h indices represent different H disjoint subbands. The bandwidth of each subband can be arbitrarily chosen owing to the flexibility of WP. The partition of subbands is not limited by a minimum frequency distance but determined by the channel characteristics.
dk(t )
dˆk(t )
aj (t ) ck(t )wph(t ) receiver
Fig. 1 WP-MC=MCD-CDMA system model
Assuming identical power for all users, the transmitted signal is given as
sk ðtÞ ¼
K X H X J X L pffiffiffiffiffiffi X bkhjl aj ðt tkhjl Þck 2P
H X J pffiffiffiffiffiffi X 2P Re½dk jh ðtÞaj ðtÞck ðtÞwph ðtÞe joc t
ð1Þ
h¼1 j¼1
where P is the users’ power, and dkjh(t) is the data symbol of the jth substream of the hth superstream. The received signal corrupted by additive white Gaussian noise (AWGN) n(t), can be written as
Q cosfoc ðt tkhjl Þ þ fkhjl g þ dkjh ðt tkhjl Þ i sinfoc ðt tkhjl Þ þ fkhjl g þ nðtÞ
ð2Þ
where L is the number of multipath, fkhjl is the phase delay uniformly distributed over [0, 2p], tkhjl is the time delay and bkhjl is the Nakagami distributed channel path gain. At the receiver the signal is first demodulated, despread, correlated with the WPs and then parallel-toserial (P=S) converted. The output signal is again despread by each code in the multicode part to recover the J parallel data streams. Finally, the correlated outputs from J paths is P=S converted to recover the original data bit. Considering the first user, wavelet packet, orthogonal code and path as the reference, the output of the first correlator in the WP is given by ðT x1 ¼ rðtÞc1 ðtÞwp1 ðtÞ cosðoc tÞ j sinðoc tÞ dt 0
¼ x1DS þ x1MPI þ x1MCDI þ x1WPI þ x1MUI þ n^ 1 x1DS
ð3Þ
x1MPI
is the desired signal, is the multipath interference where component, x1MCDI is the multicode interference component, x1WPI is the WP interference component, x1MUI is the multiuser interference component and nˆ 1 is the correlated noise component. The output of the first P=S converter for the first user’s signal in the wavelet packet is given as b^ ¼ x1DS þ
H X
0
0
0
0
0
xhMPI þ xhMCDI þ xhMWPI þ xhMUI þ n^ h
ð4Þ
h0 ¼1
The output for the first correlator in the multicode part is obtained by correlating (4) with the desired code a1(t). Signal-to-noise plus interference ratio: The desired in-phase signal power is S ¼ P=2(b1111TNn)2 and the total noise and interferences variance can be shown as ð Tn H P H P PðTNn Þ2 OQJK 2 2 ðr dr r 0 h ðtÞÞ þ ð^ 0 h ðtÞÞ h h 2 xm TNn ðJHÞ2 h¼1 h0 ¼1 0 H ð Tn X O H ðrh0 1 ðtÞÞ2 þ ð^rh0 1 ðtÞÞ2 dr þ 2 2Nn ðEs =No Þ xm TNn ðJHÞ h0 ¼1 0
s2T ¼
ð5Þ P where Es ¼ PT, O ¼ var[bkhj1] and OQ ¼ var[ Ll¼1 bkhjl]. The partial cross-correlation functions between wavelet packets are given as Ð Ð rxy(t) ¼ r0 wx(t)wy(t þ r)dt and rˆ xy(t) ¼ Trn wx(t)wy(t r)dt, 0 r Tn [2, 3]. Therefore the signal-to-noise plus interference ratio (SNIR), g ¼ (P=2(b1111TNn)2)=sT2. Results: The performance of the system in terms of SNIR using BPSK modulation is shown in Figs. 2–4. The system parameters were set to xm ¼ 12, H ¼ 8, Tn ¼ 3 108 s, r ¼ Tn=10, Nn ¼ 32, K ¼ 100, Q ¼ L ¼ 5 and O ¼ b1111 ¼ 10 dB. The effect of wavelet family is shown in Fig. 2, with N ¼ 12 for Daubechies (db6), Symmlets (sym6) and Coiflets (coif2) wavelets [1], which shows that sym6 wavelet has better performance than the other wavelets. This is because sym6 wavelet has better cross-correlation properties. Fig. 3 shows the effect of superstreams H for Es=No ¼ 15 dB and 35 dB. For Es=No ¼ 15 dB, performance is degraded for increasing H and for Es=No ¼ 35 dB the performance fluctuated. This is because the performance does not depend on H only, but also on the cross-correlation function and Es=No. Fig. 4 shows the performance comparison of WP-MC=MCDCDMA with several CDMA systems such as the conventional CDMA system and MC=MCD, WP-MC, MC, MCD CDMA systems. Observe that our proposed system outperformed all other systems. The combination of wavelets, multicarrier and multicode is a robust system effective in suppressing ICI and MAI, thus improving system performance.
ELECTRONICS LETTERS 25th May 2006 Vol. 42 No. 11
40
40
30
WP−MC/MCD−CDMA system MC/MCD−CDMA system WP−MC−CDMA system MCD−CDMA system MC−CDMA system spread CDMA system
20 SNIR, dB
SNIR, dB
35
10
0
30 db6 sym6 coif2
25 15
−10
−20 −30
20
25
30 Es / No, dB
35
−20
−10
40
0 10 Es / No, dB
20
30
40
Fig. 4 SNIR performance for different CDMA systems
Fig. 2 Effect of wavelet family on SNIR performance
Conclusions: The performance of a WP-MC=MCD-CDMA system has been presented. Sample results are given which demonstrate the validity and potential of such a system and additional analysis shows the BER and outage probability performance are continuing. Comparing our system with other CDMA based systems, it is clearly shown that the performance of the new system is better than other systems.
45
SNIR, dB
40
35 db3 Es / No = 15 dB db6 Es / No = 15 dB
30
db9 Es / No = 15 dB db3 Es / No = 35 dB
25
db6 Es / No = 35 dB db9 Es / No = 35 dB
20
15 0
# The Institution of Engineering and Technology 2006 21 March 2006 Electronics Letters online no: 20060861 doi: 10.1049/el:20060861 M.M. Akho-Zahieh and O.C. Ugweje (Department of Electrical and Computer Engineering, University of Akron, Akron, OH 44325-3904, USA) E-mail:
[email protected]
5
10 15 20 number of wavelet packets
25
30
References 1
Fig. 3 SNIR performance against number of wavelet packets superstreams
2 3
Mallat, S.: ‘A wavelet tour of signal processing’ (Academic Press, USA, 1998) Vandendorpe, L.: ‘Multitone spread spectrum multiple access communications system in a multipath Ricean fading channel’, IEEE Trans. Veh. Technol., 1995, 44, (2), pp. 327–337 Pursley, M.: ‘Performance evaluation for phase-coded spread spectrum multiple-access communication—Part I: system analysis’, IEEE Trans. Commun., 1977, 25, pp. 795–799
ELECTRONICS LETTERS 25th May 2006 Vol. 42 No. 11
