10537


FACTA UNIVERSITATIS 

Series: Electronics and Energetics Vol. 35, No 4, December 2022, pp. 483-493 

https://doi.org/10.2298/FUEE2204483B 

© 2022 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND 

Original scientific paper  

NEW APPROACH TO A DS-CDMA-UWB SYSTEM  

USING A PSEUDO ORTHOGONAL CODE (POC) 

Kada Biteur1,2, Belkacem Benadda1,2, Ahmed Nour El Islam Ayad3 

1Dept of Telecommunications, University Abou Bekr Belkaid of Tlemcen, Algeria 
2Information Processing and Telecommunication Laboratory (LTIT),University Tahri 

Mohamed, Bechar, Algeria 
3Dept of Electrical engineering, university Kasdi Merbah Ourgla, Algeria 

Abstract. Ultra-Wideband Direct Sequences Code Division Multiple Access (DS-DMA) 

plays an important role in the case of multi-terminal multi-application communications of 

UWB devices. In the case of UWB systems that exploit the injection of the pulse itself directly 

to the antenna hence the very wide bandwidth, generation of suitable DS-CDMA codes poses 

a real challenge. In this paper we will describe our novel UWB transmission which uses 

pseudo-orthogonal time code (POC) as DS-CDMA sequences. The suggested codes are 

unipolar sequences with chips that may be dynamically modified to target a certain number 

of users or applications. Our approach bypasses the modulations schemes commonly used on 

UWB systems. Moreover, as perspectives to our work, it would be very interesting to realize 

our new approach based on an FPGA circuit. 

Key words: UWB systems, pseudo-orthogonal code (POC), direct sequence-CDMA 

1. INTRODUCTION 

The ultra-wideband (UWB) technology can be integrated into many applications such 

as Personal Area Networks (WPAN) [1-3] and mobile telecommunications (5G today) [4-

6]. The UWB system is a rapidly developing technology that uses short range with very 

low power consumption, to transmit information over a majority of the radio spectrum to 

occupy a bandwidth greater than or equal to 25% of the center frequency or 1.5 GHz [7]. 

The UWB transmitters use very short-in-time pulses instead of carrier signals modulation. 

The most used pulses models are Gaussian second derivatives, whose representation in the 

time domain is described by (1): 

                                       𝑈(𝑡) = (1 − 4𝜋 (
𝑡

𝜗
)

2

) 𝑒
−2𝜋(

𝑡

𝜗
)

2

                                                (1) 

Where ϑ represents a time normalization factor. 

 
Received February 23, 2022; revised April 18, 2022 and July 30, 2022; accepted August 31, 2022 

Corresponding author: Biteur Kada 
Department of Telecommunications, University Abou Bekr Belkaid of Tlemcen, Algeria 

E-mail: biteur.kada@univ-ghardaia.dz 



484 K. BITEUR, B. BENADDA, A. N. E. I. AYAD 

 

 

 

Fig. 1 Second derivative of a Gaussian pulse 

Especially for wireless communications, the United States Federal Communications 

Commission has set the power level to a very low level (lower than -41.3 dBm) [8] allowing 

UWB technology to share spectrum with other users without interference. To get the 

required spreading, various techniques can be used such as Direct Sequence (DS) and 

Time-Hopping (TH) [9]. User data is allotted to time frames in the TH-UWB systems, and 

pulse position modulation (PPM) is employed to eliminate overlap in multiple access 

networks [10-11]. On the other hand, time spreading codes are used in DS-UWB 

techniques [12] in the same way as they are in traditional direct sequence code access (DS-

CDMA) technique, so they have the same advantages than direct sequence spread spectrum 

(DSSS) [13-14]. In this paper we propose a transceiver model suitable for a new approach 

to direct sequence digital transmission, for an ultra-wideband application (DS-UWB), 

using a pseudo-orthogonal time code (POC). The proposed codes are composed of unipolar 

sequences characterized by a length L, constituted of N elements called "chips", a predefined 

number of users, and the weight of the code; chips with level "1". Moreover, to enhance the 

synchronization between transmitters and receivers, this new proposed spreading schema 

makes it possible to separately code high-level bits '1' and low-level bits '0' of the data 

stream by two different codes; the doublet code sequence is unique for each user. The 

proposed study aims to transmit DS-CDMA-UWB without using classical modulations 

associated with UWB systems. Our new model, based on pseudo orthogonal codes, build 

a DS-CDMA-UWB system for both sides receiver and emitter. Direct sequences for UWB 

systems are explained in section 2. Section 3 will introduce the classic modulation schema 

used on UWB systems. Sections 4 detail the POC mechanisms. The UWB DS-CDMA 

emitter is detailed in section 5. Sections 6 and 7 highlight the emitter signals generation; 

simulation and results for the propagation and signal acquisition at the receiver level that we 

present in section 8. Section 9 concludes this paper.   

-5 -4 -3 -2 -1 0 1 2 3 4
-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

nanoseconds

A
m

pl
it

ud
e



 New Approach to a DS-CDMA-UWBSystem Using a Pseudo Orthogonal Code 485 

 

2. DIRECT SEQUENCE UWB (DS-UWB) 

Direct sequence spread spectrum systems appear easier to implement since all the 

pulses are spaced at the same period, which imposes fewer constraints on the components 

of the transmission chain. Indeed, our built DS-UWB transmitter scheme uses orthogonal 

pseudo-random codes (PN) [15] as spreading sequences to encode each bit of information, and 

the bandwidth of the transmitted pulse is much greater than that used by the transmitted binary 

stream.  Figure 2illustrates a block diagram of the DS-UWB signal generator. 

 

Fig. 2 Block diagram of a DS-UWB signal generator 

3. MODULATIONS ASSOCIATED WITH UWB SYSTEMS 

There are mainly modulation methods for UWB communications, such as PPM (Pulse 

Position Modulation), OOK (On-Off Keying) and PAM (Pulse Position amplitude modulation) 

[16-17]. 

▪ PPM modulation: The information is encoded according to the position of the time-
spaced pulse; bit '0' is defined by a time-shifted pulse from a reference pulse that 

matches bit ’1’. 

▪ OOK modulation: Corresponds to the presence of a pulse representing the "1" bit 
and the "0" results in the absence of a pulse. 

▪ PAM modulation: is an access method based on the property of orthogonality 
of pulses. 

 
Fig. 3 Modulations associated with UWB systems 



486 K. BITEUR, B. BENADDA, A. N. E. I. AYAD 

 

4. PSEUDO-ORTHOGONAL CODES (POC) 

J. A. Salhi developed the POC codes in 1989 [18], these codes are composed of unipolar 

sequences c = {c j} defined by the following parameters:  

▪ L represents the code length POC 
▪ W stands for the code's weight, which denotes the number of chips at "1." 
▪ The auto and inter-correlation constraints are represented by λ a and λ c respectively. 

4.1. Numbers of user  

In the event that λ a = λ c =1, various works [18-19] have shown that the number of 

possible users of a POC code sequence is limited by the relation (2): 

                                      𝑁(𝐿, 𝑊, 1,1) ≤ ⌊
𝐿−1

𝑤(𝑤−1)
⌋                                                                     (2) 

▪ N: Number of User. 
▪ L, W:  represents the code length POC and the code's weight respectively. 

4.2. Construction of codes 

The BIBD (Balanced Incomplete Block Design) method [20] allows us to generate OC (L, 

W) code sequences when the desired spread length is a prime number. It is mathematical method 

based on properties related to primitive roots from a Galois field; it is a simpler and faster method. 

We consider the primitive root α of L, we can get the positions of the chips at 1 of the ith  

sequence Ci = [Pi,0 ; Pi,1;…; Pi,W-1] for each code according to the parity of W [21] : 

− 𝑖𝑓 𝑊 𝑖𝑠 𝑒𝑣𝑒𝑛(𝑊 = 2𝑚): {
𝑃𝑖,0 = 0

  𝑃𝑖,𝑗 =∝
(𝑚×𝑖)+(𝑗×𝑘)                                                                 (3) 

      𝑤𝑖𝑡ℎ: 𝑖 ∈ [0, 𝑁 − 1]; 𝑗 ∈ [0, 𝑊 − 2] 𝑒𝑡 𝑘 = 2 × 𝑚 × 𝑁 

− 𝑖𝑓  𝑊 𝑖𝑠 𝑜𝑑𝑑(𝑊 = (2 × 𝑚) + 1): {𝑃𝑖,𝑗 = 𝛼
(𝑚×𝑖)+(𝑗×𝑘)                                                  (4) 

       𝑤𝑖𝑡ℎ: 𝑖 ∈ [0, 𝑁 − 1]; 𝑗 ∈ [0, 𝑊 − 1] 𝑒𝑡 𝑘 = 2 × 𝑚 × 𝑁 
▪ α is the primitive root of L. 
▪ is the Pci is the position of chips at 1 for i

th Code sequence 

𝐶𝑖 = [𝑃𝑖,0; 𝑃𝑖,1; … ; 𝑃𝑖,𝑊−1] 

Table 1 shows the code positions used in our study according to the BIBD method. 

In the following figure 4, we present the positions of the chips at "1" of the POC 

code (73, 4) according to number of users N=6andthe length of the code L=73. 

Table 1 The different positions of (73, 4, 1, 1)  code according to the BIBD method 

  
 

First 
chips  

j 

0 1 2 

Code  
(73,4,1,1) 
N = 6 

 
 
i 

0 (C1) 0 1 8 64 
1 (C2) 0 25 54 67 
2 (C3) 0 36 41 69 
3 (C4) 0 3 24 46 
4 (C5) 0 2 16 55 
5 (C6) 0 35 50 61 



 New Approach to a DS-CDMA-UWBSystem Using a Pseudo Orthogonal Code 487 

 

 

Fig. 4 Positions of chips at "1" of the code POC (73,4) 

5. NEW MODEL OF DS-CDMA-UWB EMITTER 

For our proposed model, the bit flow equal to "1" is convoluted by the chips of a user's 

POC code and the bit flow equal to "0" bit by another user code, which gives an increased 

bandwidth to the signal by emitting low-energy Gaussian-shaped pulses that are coherent 

on reception as explained by Figure 5. 

 

 

 

 

 

 

 

Fig. 5 DS-CDMA-UWB emitter 

The DS-CDMA-UWB signal transmitted to a user can be expressed as follows: 

      𝑆𝑃𝑂𝐶𝑐𝑜𝑑𝑒 (𝑡) = [ ∑ 𝑏1
𝑘

∞

𝑘=−∞

∑ 𝐶𝑗
𝑈 + ∑ 𝑏0

𝑘

∞

𝑖=−∞

∑ 𝐶𝑗
𝑈∼

𝑁𝑐−1

𝑗=0

] ⊕ 

𝑁𝑐−1

𝑗=0

𝑊(𝑡 − 𝑖𝑇𝑠 − 𝑗𝑇𝑐 )              (5) 

0 50 100
0

0.2

0.4

0.6

0.8

1
User1

0 50 100
0

0.2

0.4

0.6

0.8

1
User2

0 50 100
0

0.2

0.4

0.6

0.8

1
User3

0 50 100
0

0.2

0.4

0.6

0.8

1
User4

0 50 100
0

0.2

0.4

0.6

0.8

1
User5

0 50 100
0

0.2

0.4

0.6

0.8

1
User6

Spread 

Spectrum 

 

Data 

Source 

 The bits 

‘’0’’ 

The bits 

‘’1’’ 

POC 

code of 

a user 

POC code 

of another 

user 

UWB 

Pulse 

Generator  



488 K. BITEUR, B. BENADDA, A. N. E. I. AYAD 

 

▪ 𝑏0
𝑘,𝑏1

𝑘 : is  the 0 and the 1 bit respectively of binary data sent by the kth source 

▪ 𝑊 is the pulse waveform 
▪ 𝑇𝑐 , 𝑇𝑠are chip and symbol duration respectively 
▪ 𝑁𝑐 is the number of chips  

▪    𝐶𝑗
𝑈 ,𝐶𝑗

𝑈∼ is a code of two different users which only takes chips 1 or 0 up to N the 

number of users. 

6. EMITTER SIMULATION 

We first consider a random sequence of 8 bits modeling the useful information as 

limited bit stream. Then we use two selected POC codes to spread the spectrum, which is 

completely independent of the random data sequences [20], this data transmission method 

uses more bandwidth than necessary to traditional transfer. For this paper purpose we have 

selected as an example the 4th and 6th POC sequences (73,4) for our user (all other codes 

use the same principle), i.e. the bit flow equal to "1"  is convolved by 73 chips of code #4 

and the bit flow equal to "0"  convolved by 73 chips of code #6. 

𝑆(73,4)(𝑡) = [( ∑ 𝑏1
𝑘

∞

𝑘=−∞

∑ 𝐶𝑗
4) + ( ∑ 𝑏0

𝑘

∞

𝑖=−∞

∑ 𝐶𝑗
6) 

73−1

𝑗=0

] ⊕ 

73−1

𝑗=0

𝑊(𝑡 − 𝑖𝑇𝑠 − 𝑗𝑇𝑐 )           (6) 

The spread of the spectrum as represented in Figure 6 modulates a sequence of data 

“10011011” by means of two pseudo-random POC codes chosen at a bit rate much higher 

than that of the information signal to be transmitted. That is to say the convolution is done 

once between the 73 code chips of user #4 with bits equal to and the 73 code chips of user 

#6 with bits equal to 0. 

.  

Fig. 6 Spread spectrum phase for the data sequence “10011011” 

0 2 4 6 8
0

0.5

1
\data

0 20 40 60 80
0

0.5

1
\code of user#4

0 20 40 60 80
0

0.5

1
\code of user#6

0 200 400 600
0

0.5

1
\Speared spectrum

0 50 100
0

0.5

1
\Speared spectrum zoom of the bit '1' and '0'



 New Approach to a DS-CDMA-UWBSystem Using a Pseudo Orthogonal Code 489 

 

6.1. Generation of UWB pulses 

In this paper, we used the second derivative of the Gaussian generated by equation (1) 

because of their ease of implementation in UWB systems [19-20]. As shown in the figure 

7, the UWB pulse generator receives the spread data to create a second order Gaussian 

derivative pulse train and output the signal through the antenna [22]. 

 

Fig. 7 UWB pulses 

To comply with the regulatory agency's recommendations, the frequency band allocated for 

UWB transmissions has been grouped into two parts, a so-called "low band", comprising 

between 3 and 5 GHz, and the other called "high band", include between 6 and 10 GHz [23]. 

Our transmitted DS-UWB signal is included in low band according to figure 8 which shows 

UWB signal spectrum and power spectral. 

 

 

Fig. 8 The spectrum and the power spectral of UWB signal 

0 100 200 300 400 500 600
0

0.5

1
\UW B

0 100 200 300 400 500 600 700
-1

0

1
\UW B Signal

0 20 40 60 80 100 120 140
-1

0

1
\Zoom UWB Signal of the bit ''1'' and ''0''

0 200 400 600
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Frequency (Hz)        x 10
7

A
m

pl
itu

de
(V

)

Spectrum of UWB signal

0 200 400 600
-100

-90

-80

-70

-60

-50

-40

-30

-20

Frequency (Hz)        x 10
7

20
lo

g1
0(

db
)

Power Spectral of UW B signal



490 K. BITEUR, B. BENADDA, A. N. E. I. AYAD 

 

7. TRANSMISSION CHANNEL  

In our work, we did not examine multi-user interference (MUI) [24] and intersymbol 

interference (ISI) [25] since these phenomena are not predominant. In our work, the only 

phenomenon which imperfects our system is the noise AWGN the received signal can be 

described by r(t) = s(t) + n(t) where s(t) is the signal generated by the transmitter and n(t) 

denotes the additive Gaussian noise [26-27-28]. Figure 9 shows the noise signal based on 

the AWGN channel model. 

 

Fig. 9 AWGN Channel output, where Eb/No=2dB 

8. THE CORRELATION RECEIVER 

Gaussian white additive noise (AWGN) channel the correlation receiver as shown in 

the figure 10   is the most optimal of a DS-CDMA-UWB chain by adding a filter adapted to 

the received signal, it uses a correlation device, it breaks down into three steps main [29]: 

▪ Multiplication of the received signalr(t) by the POC code users #4 and #6 with the 
pulse generator UWB: 

  𝑅𝑐𝑜𝑟𝑟 (𝑡) = 𝑟(𝑡) ∗ [(∑ 𝑏1
𝑘∞

𝑘=−∞ ∑ 𝐶𝑗
4) + (∑ 𝑏0

𝑘∞
𝑖=−∞ ∑ 𝐶𝑗

6) 73−1𝑗=0 ] ⊕ 
73−1
𝑗=0 𝑊(𝑡 − 𝑗𝑇𝑐 )]  (7) 

▪ Integration of the correlated signal over the bit time 

                       𝑍1
(𝑖)

= ∫ 𝑟𝑐𝑜𝑟𝑟 (𝑡)𝑑𝑡     
𝑇𝑏

0
                                            (8) 

▪ Decision making by comparison to a threshold knowing that user POC code #4 and 
#6 indicates bit '1' , '0' respectively. 

 

Fig. 10 Correlation Receiver 

0 100 200 300 400 500 600 700
-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5



 New Approach to a DS-CDMA-UWBSystem Using a Pseudo Orthogonal Code 491 

 

At the reception, it suffices to compare the correlator signal with the possibly generated 

POC sequence to recover the transmitted signal. Figure 11 illustrates the correlator output signal 

with its power spectral, the spectrum of the correlator output signal and recovered data. 

 

Fig. 11 The correlator output signal with its power spectral, the spectrum and the data 

recovered 

The new DS-UWB system based on POC orthogonal unipolar codes without modulation 

was analyzed. Only the end-to-end DS-UWB transmission chain we are interested in. We 

removed the modulation part on our new approach. POC codes are preconfigured (calculated 

in advance). Our perspective is to realize our new DS-UWB approach based on components 

such as FPGA [30-31-32], SoC [33]… because nowadays it is easy to build a transceiver. 

9. CONCLUSION  

In this work, we suggested a new approach to a multi-users DS-CDMA-UWB system 

using a family of pseudo-orthogonal codes POC on an AWGN channel for a correlation 

receiver. Applying POC code offered a whole new and different approach than any other 

used before in literature with the ultra-broadband system. We have given a complete 

description of the DS-CDMA-UWB system, including the transmission and reception 

formalism. This work allowed us to present and analyze new emission reception approach 

based on DS-CDMA-UWB signal. 

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