^{1}

^{2}

Hardware implementation of Linear Feedback Shift Register (LFSR) plays a great and very important role in communication systems, and in many security devices. In this paper, a design of LFSR with offset mask has been presented, for Direct Sequence Code Division Multiple Access (DS-CDMA) applications. Integrated electronic components have been used. An accessible model facilitating the synthesis on Printed Circuit Boards (PCB) and implementation on Field Programmable Gate Array (FPGA) is offered. In addition, a temporal and spectral analysis of the circuit is performed in order to validate the design. This latter facilitates the generation of pseudo-random codes based on LFSR and their integration into electronic systems.

LFSRs are used for DS-CDMA, errors detection and correction, and applications using pseudo-random sequences.

In this work, we first present the model that is used to design LFSR.

From this basic model we go further into the design using integrated electronic components.

Thus tests and checks have been performed on the circuit. Lastly the results have been analyzed and discussed.

For CDMA, LFSRs are mainly used for the multiple access scheme. The mask allows assignment of codes to identify users and base stations. LFSR is also helpful for generating quasi-random sequences and is used in hardware Built-In Self-Test (BIST) [

Finite fields provide the necessary theory in designing LFSR [

The model describing this polynomial is shown schematically in

The general form giving the output of each flip flop is defined by [

where Q_{i}(t) is the output of the ith register.

In this implementation, we move from modeling to realization. The following components have been used:

Two SN74273: Octal D-Type Flip-Flop (With Clear)

Six 74HC86: Quad 2-Input EXCLUSIVE-OR Gate

Four 74HC08: Quad 2-Input AND Gate

A benefit of this design is the availability of these components, and the reduction in the size of the device. The realized circuit is given in

This circuit can be divided into five main parts; the first is the LFSR. On the component U1SN74273, the outputs 3Q, 4Q, 5Q and 6Q are connected to U9SN74HC86. This is equivalent to blocks 3, 4, 5, 6 in

The selected mask corresponds to the sequence 100010010011000; this sequence also corresponds to that chosen in the work [

On this circuit to avoid the lock-up state (the state where the register is blocked at 0) there are two solutions:

・ A feedback logic that detects this state, and feeds one (up voltage) at the beginning (Q_{1}) [

・ An OR gate and a signal to initialize the LFSR

For more flexibility in the practical realization, the second solution has been adopted. The register is initialized with a defined sequence.

The signals srg_out, mask, and spread (in volt) are given respectively by blocks: LFSR, Mask and Spread.

To check the behavior of the circuit, and the conformity of the results with theory, long division of the polynomial is computed. We analyze timing diagrams at the output of the register and the mask ^{*}(X) is given by:

It helps build the LFSR in Fibonacci configuration. For this circuit we have fixed as the initial loading sequence 100000000000000 thus, the initial sequence of the LFSR output is given by the long division [

X is an element of Galois Field {2}, and P a primitive polynomial. We get the following result:

In this expression, each monomial indicates one element in the output sequence. R(X) is equivalent to:

0000000000000010011110101110101101 and therefore confirms the obtained LFSR signals (srg_out, SRG_ output) on timing diagrams

We analyze the power spectrum

This herein presented design has several advantages. The use of simple integrated components to achieve these LFSR makes them more accessible and easy to embed on larger circuit architectures. In addition with the used tool [

and its integration into information security devices.

Mouhamed Fadel Diagana,Serigne Bira Gueye, (2016) Analysis, Design, and Test of CDMA LFSR with Offset Mask Using Standard ICs. Engineering,08,226-231. doi: 10.4236/eng.2016.84019