Energy efficiency improvement of OFDM-based Radio-over-fiber systems enabled with PAPR decrease method

This paper proposes a high performance and low cost inverse discrete cosine transform (IDCT) processor for high definition Television (HDTV) applications by using cyclic convolution and hardwired multipliers. By properly arranging the input sequence, we formulate the one-dimensional (1-D) IDCT into cyclic convolution that is regular and suitable for VLSI implementation. The hardwired multiplier that implements multiplication with IDCT coefficients are first scaled and optimized by using the common sub-expression techniques. Based on these techniques, the data-path in the proposed two-dimensional (2-D) IDCT design costs 7504 gates plus 1024 bits of memory with 100 M pixels/sec throughput according to the cost estimation based on the cell library of COMPASS 0.6 μm SPDM CMOS technology. Also, we have verified that the precision analysis of the proposed 2-D 8 × 8 IDCT meets the demands of IEEE Std. 1180-1990. Due to the good performance in the computing speed as well as the hardware cost, the proposed design is compact and suitable for HDTV applications. This design methodology can be applied to forward DCT as well as other transforms like discrete sine transform (DST), discrete Fourier transform (DFT), and discrete Hartley transform (DHT).

Discrete Hartley transform (DHT) based orthogonal frequency division multiplexing (OFDM) outperforms the OFDM based on discrete Fourier transform (DFT) for its intrinsic frequency diversity. However, the space-frequency block coding (SFBC) cannot be applied since the symbols in Hartley domain are coupled. In this paper, by using the properties of DHT and DFT, we propose a DHT based SFBC-OFDM system design with better performance than and similar complexity to the DFT counterpart. Moreover, a low complexity algorithm is derived based on the properties of DHT to get the time domain signals of the DHT based SFBC code words with about halved complexity. Finally, analysis and simulations are provided to validate its feasibility and ability to exploit both the frequency and spatial diversity, as a promising alternative to the DFT counterpart.

In this letter, we first propose new nearly tridiagonal commuting matrices of discrete Fourier transform (DFT) matrix and generalized DFT (GDFT) matrix. Then, using the block diagonalizations technique of circular-centrosymmetric and centrosymmetric matrices, we derive novel tridiagonal commuting matrices for each discrete cosine transform (DCT) and discrete sine transform (DST) matrices of the types I, IV, V, and VIII from the commuting matrices of the DFT and GDFT based on the relationships in matrix forms among DFT, GDFT, and various types of DCT and DST. Moreover, the novel tridiagonal commuting matrices of various types of DCT and DST do not have multiple eigenvalues. Last, with these novel commuting matrices, we can easily determine an orthonormal set of Hermite-like eigenvectors for each of their corresponding DCT or DST matrix.

In this paper, we propose Speaker Identification using the frequency distribution of various transforms like DFT (Discrete Fourier Transform), DCT (Discrete Cosine Transform), DST (Discrete Sine Transform), Hartley, Walsh, Haar and Kekre transforms. The speech signal spoken by a particular speaker is converted into frequency domain by applying the different transform techniques. The distribution in the transform domain is utilized to extract the feature vectors in the training and the matching phases. The results obtained by using all the seven transform techniques have been analyzed and compared. It can be seen that DFT, DCT, DST and Hartley transform give comparatively similar results (Above 96%). The results obtained by using Haar and Kekre transform are very poor. The best results are obtained by using DFT (97.19% for a feature vector of size 40).

This paper investigates optical orthogonal frequency division multiplexing (O-OFDM) systems with index modulation (IM) based on discrete Hartley transform (DHT) for visible light communications (VLC). An interesting trade-off between spectral efficiency (SE), energy efficiency, peak-to-average power ratio (PAPR) and bit error rate (BER) performance can be made by using the IM technique. And the DHT-based O-OFDM-IM systems can achieve higher SE compared with the DFT (discrete Fourier transform)-based counterparts. Employing DHT instead of DFT enables the removal of the Hermitian symmetry requirement, which contributes to transmitting more index bits and results in SE improvement. To acquire the same SE, the proposed systems can significantly lower the constellation order leading to better BER performance by contrast with the DFT-based counterparts. We employ DC (direct current) biasing and AC (Asymmetrically clipped) techniques to investigate the O-OFDM-IM systems in this paper. Simulation results indicate that SNR gains can be obtained by the DHT-based DCO/ACO-IM in comparison to the DFT-based counterparts. We also propose a novel reduced-complexity ML (maximum likelihood) detector specifically applicable to VLC. The new detector exhibits the same BER performance as the ML detector and performs better than the LLR (log-likelihood ratio) detector with reduced computational complexity.

This paper presents a new property called the Duality Theorem for the Discrete Sine Transform (DST). Discrete Sine Transform is a finite — length discrete transform which is related to the renowned Discrete Fourier Transform (DFT) and is quite popular in signal processing arena, but has remained in the oblivion from pure mathematicians. Many of the properties of the Discrete Sine Transform are akin to those of the Discrete Fourier Transform and Discrete Cosine Transform, subject to minor differences. A formal derivation of the Duality Theorem corresponding to the Discrete Sine Transform is given which was hitherto not mentioned or derived in the literature. The usage of Duality Theorem helps in finding the discrete time — domain function from the DST frequency domain and vice versa thereby reducing considerable labour involved in the evaluation of the summation and hence, saves computation time and cost of implementation to a considerable extent. DST finds applications in Image Processing, Signal Processing applications for Communication Systems, and in the numerical solutions of differential equations as well as partial differential equations of mathematics.

The Fast Hartley Transform (FHT) is similar to the Cooley-Tukey Fast Fourier Transform (FFT) but performs much faster because it requires only real arithmetic computations compared to the complex arithmetic computations required by the FFT. Through use of the FHT, Discrete Cosine Transforms (DOT) and Discrete Fourier Transforms (DFT) can be obtained. The recursive nature of the FHT algorithm derived in this paper enables us to generate the next higher-order FHT from two identical lower-order FHTs. In practice, this recursive relationship offers flexibility in programming different sizes of transforms, while the orderly structure of its signal flow graphs indicates an ease of implementation in VSLI.

Conventional orthogonal frequency division multiplexing (OFDM) systems use discrete Fourier transform (DFT) as the basis function. Recently, it was shown that it is possible to use other sinusoidal transforms, e.g. discrete cosine transform (DCT), as OFDM basis functions. However, relative little is known regarding the performance of these alternative basis functions and how they compare with traditional DFT. This paper investigates the performance of OFDM modems employing alternative basis functions under different fading channel models in both double sideband and single sideband operation modes. A semi-analytical approach is also developed to predict and compare the error performance between different basis functions. The predicted results are close to the simulations thus verifying the simulation model. It was found that in general DFT has a better error performance, but interspersed basis is capable of offering a higher net throughout under certain channel conditions.

A precise method for calculating the bit error probability of a discrete cosine transform (DCT)-based orthogonal frequency-division multiplexing (OFDM) system on AWGN channels in the presence of frequency offset is derived. These accurate results are used to examine and compare the bit error probability performances of a DCT-OFDM system and the conventional discrete Fourier transform (DFT)-based OFDM system. Several signaling formats, such as binary phase shift keying (BPSK), quaternary phase shift keying (QPSK), and 16-ary quadrature amplitude modulation (16-QAM) are considered. Analysis and simulation results show that the DCT-OFDM system outperforms the DFT-OFDM system in the presence of carrier frequency offset.

The use of discrete Hartley transform (DHT) pre-coding was recently shown to achieve peak to average power (PAPR) reduction for OFDM. In this paper, we show that DHT precoding also achieves full diversity. We consider the sparse matrix formed by the combination of DHT and the discrete Fourier transform (DFT) and propose a receiver configuration that minimizes complexity. Furthermore, we present a detailed account of the system complexity to show that it is slightly more than uncoded conventional OFDM. Also, since this system saves the complexity required for achieving diversity gain and reducing the peak to average power (PAPR), it reduces the system complexity when the PAPR reduction and diversity techniques are taken into account for conventional OFDM. We analytically show that this system achieves full diversity and then verify it using simulation results. Simulations results also show that the system has a substantial improvement in bit error performance over conventional OFDM.

Block frames called <i>directional analytic discrete cosine frames</i> (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational complexity, 2) memory usage, and 3) global memory access. These characteristics are strongly required for current high-resolution image processing. Specifically, we propose two DADCFs based on discrete cosine transform (DCT) and discrete sine transform (DST). The first DADCF is constructed from parallel separable transforms of DCT and DST, where the DST is permuted by row. The second DADCF is also designed based on DCT and DST, while the DST is customized to have no DC leakage property which is a desirable property for image processing. Both DADCFs have rich directional selectivity with slightly different characteristics each other and they can be implemented as non-overlapping block-based transforms, especially they form Parseval block frames with low transform redundancy. We perform experiments to evaluate our DADCFs and compare them with conventional directional block transforms in image recovery.

Chapter 7 - Applications

According to Wang, there are four different types of DCT (discrete cosine transform) and DST (discrete sine transform) and the computation of these sinusoidal transforms can be reduced to the computation of the type-IV DCT. As the algorithms involve different sizes of transforms at different stages they are not so regular in structure. Lee has developed a fast cosine transform (FCT) algorithm for DCT-III similar to the decimation-in-time (DIT) Cooley–Tukey fast Fourier transform (FFT) with a regular structure. A disadvantage of this algorithm is that it involves the division of the trigonometric coefficients and may be numerically unstable. Recently, Hou has developed an algorithm for DCT-II which is similar to a decimation-in-frequency (DIF) algorithm and is numerically stable. However, an index mapping is needed to transform the DCT to a phase-modulated discrete Fourier transform (DFT), which may not be performed in-place. In the paper, a variant of Hou&apos;s algorithm is presented which is both in-place and numerically stable. The method is then generalised to compute the entire class of discrete sinusoidal transforms. By making use of the DIT and DIF concepts and the orthogonal properties of the DCTs, it is shown that simple algebraic formulations of these algorithms can readily be obtained. The resulting algorithms are regular in structure and are more stable than and have fewer arithmetic operations than similar algorithms proposed by Yip and Rao. By means of the Kronecker matrix product representation, the 1-D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions. These algorithms, which can be viewed as the vector-radix generalisation of the present algorithms, share the in-place and regular structure of their 1-D counterparts.

Chapter 1 - Discrete Cosine and Sine Transforms

Fractional Fourier domain equalization for DCT based OFDM system with CFO