摘要：Vedic mathematics is the system of mathematics followed in ancient Indian and it is applied in various mathematical branches. The word “Vedic” represents the storehouse of all knowledge. Because using Vedic Mathematics, the arithmetical problems are solved easily. The mathematical algorithms are formed from 16 sutras and 13 up-sutras. But there are some limitations in each sutra. Here, two sutras Nikhilam sutra and Karatsuba algorithm are considered. In this research paper, a novel algorithm for binary multiplication based on Vedic mathematics is designed using bit reduction technique. Though Nikhilam sutra is used for multiplication, it is not used in all applications. Because it is special in multiplication. The remainder is derived from this sutra by reducing the remainder bit size to N-2 bit. Here, the number of bits of the remainder is constantly maintained as N-2 bits. By using Karatsuba algorithm, the overall structure of the multiplier is designed. Unlike the conventional Karatsuba algorithm, the proposed algorithm requires only one multiplier with N-2 bits only. The speed of the proposed algorithm is improved with balancing the area and the power. Even though there is a deviation in lower order bits, this method shows larger difference in higher bit lengths.

摘要：The advanced communication system uses wireless broadband access technologies which provide high speed data connectivity to the subscribers. One of the most popular wireless access technology is Worldwide Interoperability for Microwave Access (WiMAX) and it is based on IEEE 802.16 standard. WiMAX used Orthogonal Frequency Division Multiplexing (OFDM) is an effective modulation technique to improve the timing synchronization. The performance of channel is affected due to the synchronization mismatching between the transmitter and receiver ends. To achieve the timing synchronization in IEEE 802.16 systems, the cross correlator is used to synchronize the received signal with the known signal. In this paper, two high speed correlators are proposed based on Q1.15 format, which is used to validate the timing synchronization problem. The proposed work has been mapped on XC6VCX75T FPGA and simulations are carried out on the Xilinx-ISIM platform. The implementation result shows that the power delay product reduction is 40.81%, and delay reduction is 39.59% over the conventional multiplier less correlators.