ECE 734 Final Project Report

The structure and algorithm of IDFT DFT, the conventional method used in modulation/demodulation process in OFDM system, has matured today. Researchers have developed new transforms in an effort to replace this traditional structure, such as DHT-based structure (Discrete Hartley Transform) and DWT-based (Discrete Wavelet Transform) structure. In this project, all three structures will be implemented in MATLAB to acquire their BER (Bit Error Rate) performances, and the results will be compared and analyzed along with other two aspects, hardware performance and hardware complexity to gain a complete view of their advantages and disadvantages. Introduction In OFDM system, IDFT DFT hardware in the transceiver is conventionally designed jointly to carry out IDFT and DFT functions for transmission and receiving processes, respectively. To date, the development of IDFT DFT structure and algorithm used in the modulation/demodulation process has reached its maturity. In the last few decades, researchers have proposed several alternative transforms to replace IDFT DFT, such as DHT (Discrete Hartley Transform) IDHT (Inverse Discrete Hartley Transform) and DWT (Discrete Wavelet Transform) IDWT (Inverse Discrete Wavelet Transform). Past research has individually compared one of the many transforms to the DFT-based structure on one or two of the performance aspects, such as BER performance, hardware performance, or hardware complexity. For example, the DHT-based structure in research [1] generates similar BER performance and lower complexity. A DWT-based structure in research [2] shows better BER performance under certain conditions. A lot of effort [3] [4] [5] was put into implementing the hardware to lower the complexity or increase the operating speed. Motivation and Goal As indicated in the background research review, researchers in the field of OFDM system have compared DHT-based and DWT-based structure to DFT-based structure on either the BER performance or the hardware performance and complexity. However, I have not found research that offers an exhaustive comparison among all three structures with their respective BER performance, hardware performance, and hardware complexity. I believe by running a synthesized analysis with all three structures on all the aspects will give us more complete information and will provide a useful direction for future research to invest their research time and money. DFT-based OFDM An Orthogonal Frequency Division Multiplexing (OFDM) system is a multi-carrier system which utilizes a parallel processing technique allowing the simultaneous transmission of data on many closely spaced, orthogonal sub Inverse Discrete Fourier transform (IDFT) and Discrete Fourier transform (DFT) in a conventional OFDM system are used to multiplex the signals together and decode the signal at the receiver respectively. x = √ ∑ X The system adds cyclic prefixes (CP) before transmitting the signal. The purpose of this is to increase the delay spread of the channel so that it becomes longer than the channel impulse response. The purpose of this is to interference (ISI). However, the CP has the disadvantage of reducing the spectral containment of the channels. DHT-based OFDM For the current DFT-based OFDM compute a long-length IDFT, and the demodulator needs to compute a long DFT. For such computations, a great number of complex multiplications are required. Clearly, the complexity of a D corresponding modulator and transforms. The N-point IDFT is defined as: x = √ ∑ X H , n=0, 1 ,...,N -carriers. The N-point IDFT is defined as: W , n=0 ,1 ,...,N-1, where W = e π/ minimize inter-symbol Here is the diagram of DFT-based OFDM: -based transceivers, the modulator needs to -length FT -based OFDM would be reduced if the demodulator could be replaced by discrete Hartley -1, where H = sin 2πk/N + cos 2πk/N The DHT involves only real the DFT, there have been a number of fast algorithms and hardware architectures available for the DHT computation. It is shown that the proposed DHT achieves the same transmission performance as the DFT less computational complexity. DWT-based OFDM In DFT-based OFDM, a CP is added to eliminate ISI. But this can decrease bandwidth efficiency greatly. Discrete alternative platforms for replacing ID spectral containment of the channels is better since it do DWT-based OFDM an advantage of bandwidth efficiency. The N defined as: φ(t) = 1, 0 ≤ t Here is a diagram of DWT-based OFDM: -valued arithmetic and has an identical inverse. Like -based OFDM -based OFDM, but requires Here is the diagram of DHT-based OFDM: Wavelet transforms have been considered as FT and DFT. By using the transform, the es not use CP which gives -point IDFT is ≤ , (−1, 1/2 ≤ t ≤ 1) , x = ∑ C φ(t − nT)