Most numerical integration techniques consist of approximating the integrand by a polynomial in a region or regions and then integrating the polynomial exactly. Often a complicated integrand can be factored into a non-negative ''weight'' function and another function better approximated by a polynomial, thus $\int_{a}^{b} g(t)dt = \int_{a}^{b} \omega (t)f(t)dt \approx \sum_{i=1}^{N} w_i f(t_i)$. Hopefully, the quadrature rule ${\{w_j, t_j\}}_{j=1}^{N}$ corresponding to the weight function $\omega$(t) is available in tabulated form, but more likely it is not. We present here two algorithms for generating the Gaussian quadrature rule defined by the weight function when: a) the three term recurrence relation is known for the orthogonal polynomials generated by $\omega$(t), and b) the moments of the weight function are known or can be calculated.

Calculation of Gauss quadrature rules.

Orthogonal frequency division multiplexing (OFDM) is an efficient multi-carrier modulation technique for wireless communication. However, one of the main drawbacks encountered in implementing it is its resultant high peak-to-average power ratio (PAPR). Many techniques have been proposed in the literature to substantially decrease the peaks in the OFDM signal. The problem with these, however, is that their effects on other parameters are not always positive. These effects include a decrease in the bit error rate (BER), an increase in complexity, or a reduction in the bit rate. The objective of this paper is to describe the PAPR problem in a bid to reduce the peaks in the OFDM signal. The paper proposes a classification, performance evaluation and optimization of PAPR reduction techniques for commercial, public safety, and tactical applications. In the taxonomy proposed herein, we also include a new category, namely, hybrid techniques. Furthermore, we compare the principal characteristics through a complementary cumulative distribution function and BER evaluation, and conclude on the importance of hybrid techniques, when the goal is to both improve the BER and reduce the PAPR.

Hybrid Peak-to-Average Power Ratio Reduction Techniques: Review and Performance Comparison

Orthogonal Frequency Division Multiplexing (OFDM) suffers from a high Peak-to-Average Power Ratio (PAPR). Designing a High Power Amplifier (HPA) with high PAPR is not a wise technique as it roots the amplifier to operate in a non-linear region which is intricate. Linearity and power efficiency are important constraints of HPA which cannot be achieved at the same time. Therefore, perfect linearity is observed when efficiency is low or vice versa and efficiency can be improved by decreasing the PAPR. In this paper, the PAPR is mitigated by using Partial Transmit Sequence (PTS), Selected Mapping (SLM), Hybrid and proposed methods. Analysis of OFDM with high PAPR passing through different HPA models is evaluated in terms of Power Spectral Density (PSD), gain and efficiency for all PAPR reduction methods considered in this work. The results are encouraging by using hybrid PAPR reduction method, HPAs can be operated in a linear region to provide higher efficiency compared to non-hybrid PAPR reduction methods. Hence, hybrid PAPR reduction methods can be used even in future wireless communications systems including 5G and beyond.

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Analysis of Hybrid PAPR Reduction Methods of OFDM Signal for HPA Models in Wireless Communications

One of the main disadvantages of multicarrier transmission is the high peak-to-average power ratio (PAPR) of the transmitted signal. If the highest transmitted power is confined by the application restrictions or regulatory, the result is to decrease the average power permitted under multicarrier transmission. Selected mapping (SLM) is a standard PAPR reduction scheme that is appropriate for orthogonal frequency division multiplexing (OFDM) scheme as it realizes the performance of PAPR reduction without signal distortion. This paper proposes a method in order to handle the difficulties of high PAPR in OFDM scheme. The offered system is an arrangement of two distinguished methods, such as clipping and SLM. Compared to other hybrid methods, where the individual methods are implemented sequentially, this paper integrates the clipping method in the SLM procedure. This produces a supplementary PAPR reduction associated to the serial arrangement. Simulation results specify that the offered scheme acquires the performance of appropriate PAPR reduction with low computational complexity. The PAPR reduction at different number of subcarriers is analyzed and compared with the existing research work. The performance of relative energy efficiency has also been focused on this paper.

Adaptive PAPR Reduction Scheme for OFDM Using SLM with the Fusion of Proposed Clipping and Filtering Technique in Order to Diminish PAPR and Signal Distortion

Partial transmit sequence (PTS) scheme has been well applied to reduce the high peak-to-average power ratio (PAPR) of the orthogonal frequency division multiplexing (OFDM) signal. However, due to the signal structure differences between the filter bank multicarrier and offset quadrature amplitude modulation (FBMC/OQAM) signal and the OFDM signal, the conventional PTS scheme is not applicable to the FBMC/OQAM signal. Considering the PAPR reduction issue for the FBMC/OQAM signal, this paper proposes a genetic algorithm (GA) based bilayer partial transmit sequence (GA-BPTS) scheme. In order to reduce the computational complexity, the proposed scheme continues to partition each subblock, transforming the single layer structure of the conventional PTS into a bilayer phase factor search structure, and introduces a penalty threshold. Then the suboptimal phase factor vector is obtained by using the GA. Meanwhile, before PAPR reduction processing, aided by the proposed prototype filter which has the better performance of out-of-band attenuation than the PHYDAYS filter, the GA-BPTS scheme can effectively reduce the PAPR of the FBMC/OQAM signal. The simulations have confirmed that the proposed scheme not only provides an excellent PAPR performance but also decreases the computational complexity compared with the conventional PTS scheme.

/pdf/genetic-algorithm-based-bilayer-pts-scheme-for-peak-to-3ayzgpaqoy.pdf

Genetic Algorithm Based Bilayer PTS Scheme for Peak-to-Average Power Ratio Reduction of FBMC/OQAM Signal

Various Techniques to Reduce PAPR in OFDM Systems: A Survey

In wireless communication, to attain high throughput and better transmission quality. Orthogonal Frequency Division Multiplexing (OFDM) is one of the techniques for parallel transmission. It is used for a various services such as asymmetric digital subscriber lines, very-high speed digital subscriber lines, digital video and audio broadcasting, and wide local area network standards such as IEEE 802.11a, IEEE 802.11g, and European telecommunication standard institute (ETSI). However in fading environments the bit error rate (BER) increases. The performance can be improved by using some kind of channel coding. This form of OFDM is called coded-OFDM (COFDM). In this paper our aim is to analyze and compare the performance of COFDM using Turbo codes {with Log-MAP (Maximum A Posteriori) decoding} and Reed Solomon (RS) code with 1/2 and 2/3 convolution codes (CC) as channel coding techniques in Rayleigh, Rician & Nakagami fading environments. The performance parameter is BER and the mapping schemes used are BPSK, QPSK, 16-QAM and 64-QAM. All other parameters are as per IEEE 802.11a specifications.

Performance analysis of coded-OFDM with RS-CC and Turbo codes in various fading environment

Orthogonal frequency division multiplexing (OFDM) is one of the preferred choices for high speed transmission of data in wireless domain pertaining to its immunity towards inter-symbol interference. However high value of peak to average power ratio (PAPR) is a major problem associated with OFDM. High PAPR increases circuit complexity and reduce RF amplifier efficiency. Partial Transmit Sequence (PTS) is one of the widely used techniques for PAPR reduction, however in PTS scheme the computation of optimal phase factors necessitates exhaustive searching among all allowable phase factors. This leads to exponential increase in search and computational complexity with the increase in number of subblocks. In this paper a PTS scheme using Genetic algorithm (GA) for optimized search with low computational complexity scheme is proposed. The proposed scheme provides efficient search and PAPR performance at low computational complexity for a given value of PAPR threshold.

PAPR reduction of OFDM systems using PTS with genetic algorithm at low computational complexity

In wireless communication, concept of parallel transmission of symbols is applied to achieve high throughput and better transmission quality. Orthogonal Frequency Division Multiplexing (OFDM) is one of the techniques for parallel transmission. The performance of uncoded orthogonal frequency division multiplexing (OFDM) over fading channels is generally improved by introducing some kind of channel coding. Coded OFDM (COFDM) has therefore been chosen for two recent new standards for broadcasting namely DAB and DVB-T. Different coding schemes for OFDM have been reported in the literature. In this paper our aim is to evaluate COFDM performance using block interleaver/Reed Solomon (RS) codes with convolution code and result is compared with uncoded OFDM. The performance parameter used for evaluation is BER with AWGN channel assumption. All other parameters used are as per IEEE 802.11a specification.

Performance Analysis of Coded OFDM for Various Modulation Schemes in 802.11a Based Digital Broadcast Applications

In recent time orthogonal frequency division multiplexing (OFDM) has proved its mettle as a preferred choice for high speed transmission in wireless applications due its efficient mechanism to combat the inter symbol interference. However sudden high peaks in OFDM signal envelope lead to high peak to average power ratio (PAPR). Enhanced values of PAPR result into complex RF amplifier circuit with reduced efficiency. There are various methods available for PAPR reduction, out of them partial transmit sequence (PTS) is most effective proven choice for PAPR reduction. However PTS technique requires cumbersome searching of all possible phase factors to find optimal phase factor which produces lowest PAPR, the information regarding optimal phase set used at the transmitter need to be sent to the receiver as side information (SI) for decoding purpose, however transmitting SI requires additional transmission bandwidth thus reducing overall bandwidth efficiency. To reduce the exhaustive searching genetic algorithm (GA) could be used with PTS leading to GA-PTS system. In this paper a GA-PTS system is proposed which uses novel octagonal geometry for constellation extension purpose. This scheme does not require transmission of any side information for decoding purpose at receiver and at the same time GA-PTS system reduces the required number of searches. Simulations are presented to show that proposed scheme provides similar PAPR performance as conventional PTS but without need of SI transmission at reduced number of searches.

Alok Joshi

Papers

Various Techniques to Reduce PAPR in OFDM Systems: A Survey

Performance analysis of coded-OFDM with RS-CC and Turbo codes in various fading environment

PAPR reduction of OFDM systems using PTS with genetic algorithm at low computational complexity

Performance Analysis of Coded OFDM for Various Modulation Schemes in 802.11a Based Digital Broadcast Applications

GA-PTS Using Novel Mapping Scheme for PAPR Reduction of OFDM Signals Without SI