Frequency-selective Nakagami-m Fading Channels Research Articles

Quasi Orthogonal Space Time Block Code Over Nakagami-m Frequency Selective Fading Channels with Simple Decoding Complexity

In this paper, a Quasi Orthogonal Space Time Coding (QOSTBC) system over Nakagami-m frequency selective fading channels is introduced. The proposed scheme is carried out for the M-QAM modulation schemes assuming imperfect channel state information at the receiver. Inter symbol interference effect introduced due to the assumption of the frequency selective fading channels is eliminated by using the Orthogonal Frequency Division Multiplexing (OFDM) technology. Through the Bit Error Rate (BER) versus Signal to Noise Ratio (SNR) simulation results under different values of both Nakagami-m parameter and channel estimation error, the validity of the proposed technique is demonstrated. The results confirm that the BER in the case of frequency selective fading is overlapped with that of flat fading. This implies that the use of OFDM technology mitigates the effect of Inter-Symbol Interference (ISI) caused by frequency selectivity in the channel. Also, the results show that as the imperfect channel estimation error increases the performance degrades.

Generalised error analysis of FRFT‐OFDM over Nakagami‐ m fading channel with arbitrary m

In this study, generalised expression of probability of error for binary phase shift keying (BPSK) and quadrature PSK (QPSK) modulated fractional Fourier transform (FRFT)-based orthogonal frequency division multiplexing (OFDM) system has been derived over frequency selective Nakagami-m fading channel for any arbitrary Nakagami parameter m in the presence of carrier frequency offset (CFO). The symbol error rate (SER) performance of FRFT-based OFDM system has been found to be better than fast FT-based OFDM system at different values of FRFT angle for BPSK and QPSK. For different values of CFO, the optimum at which the error rate is minimum has been found and used for analysis and simulation. It has been observed that over Nakagami-m frequency selective channel, SER expression of BPSK and QPSK for FRFT-OFDM system exactly follows the Monte Carlo simulation in MATLAB.

Outage and BER analysis of dual-carrier modulation over frequency-selective Nakagami-m fading channels

PurposeThis paper aims to the increasing need for high-speed low-power data transmissions over frequency-selective fading channels has drawn attention to suggest dual-carrier modulation (DCM) for multiband orthogonal frequency division multiplexing (OFDM) transceivers for ultra wideband (UWB) wireless personal area network (WPAN).Design/methodology/approachUnder frequency-selective fading channel conditions, the decoder is not sufficient enough to decode the transmission bits of severely attenuated data tones. Hence, the authors suggest DCM for a multiband OFDM transceiver because of its multiple capability of providing both frequency diversity and coding gain. It also resulted in low bit-error-rate (BER) at a given signal- to-noise ratio when compared to conventional multiband OFDM system. To achieve an optimised BER, DCM transforms four re-ordered bits into two quaternary phase shift keying symbols and further transforms to two 16-quadrature amplitude modulation-like (16-QAM) symbols with a suitable mapping technique, and at the receiver end, they are decoded with maximum likelihood decision rule. After performing the transformation, the outage probability and average BER expressions are derived to analyse the system performance.FindingsDCM is suitable for high data rate transmission and is immune to frequency-selective fading. The outage and BER performance outstands over conventional multiband OFDM transceiver because of the inclusion of DCM mapping.Practical implicationsIt is widely used in WPANs such as high definition multimedia interface and wireless universal serial bus.Originality/valueThis paper derives novel closed-form outage probability and a tight upper bound on average BER expressions for DCM-based multiband OFDM UWB transceiver over frequency-selective Nakagami-m fading channels for any arbitrary value of m. For this, moment-generating function of sum of squared, independent and identically distributed (i.i.d.) Nakagami-m random variables are used. Further, the system performance is also validated for the case of exponential decaying power delay profile, and the simulation results are provided to check the accuracy of the derived expressions.

Performance analysis of OFDM based AF cooperative systems in selection combining receiver over Nakagami‐m fading channels with nonlinear power amplifier

SummaryIn this paper, performance analysis of orthogonal frequency division multiplexing (OFDM) based amplify‐and‐forward (AF) cooperative relaying network with selection combining (SC) scheme over independently but not necessarily identically distributed (i.n.i.d.) frequency selective Nakagami‐m fading channels is investigated. Theoretical analysis of closed‐form expressions for outage probability and average symbol error rate (ASER) have been proposed, while considering nonlinear distortions (NLD) introduced by nonlinear power amplifier (NLPA) at the relay node. Asymptotic behavior of outage probability is also analyzed in high signal‐to‐noise ratio (SNR) regime to evaluate the diversity order of the system under several conditions. Further, impacts of fading parameter and NLD are highlighted on the outage probability, ASER and the diversity order of the system under different situations. The derived theoretical results are compared with Monte' Carlo simulations and verify the correctness of theoretical results for different system configurations and SNR levels. The derived expressions are generalized, and hence, can be easily used for analysis over variety of fading environments. Copyright © 2016 John Wiley & Sons, Ltd.

Performance of multicarrier complementary-coded CDMA under frequency-selective Nakagami-m fading channels

Multicarrier complementary-coded code division Multiple Access (MC CC-CDMA) is becoming an attractive multiple access technique for high data rate transmission in future wireless communication systems. MC CC-CDMA systems transmitting over frequency-selective channels suffer from multiple access interference (MAI) owing to non-ideal correlation properties of complementary codes (CC). MC CC-CDMA with equalization has recently gained much attention for its ability to offer an excellent performance than traditional systems in frequency-selective fading channels. In this paper, the authors present an analytical study and investigation of MC CC-CDMA downlink system using different combining schemes. The use of parallel interference cancellation (PIC) under frequency-selective Nakagami-m fading channels is also analyzed. A comparison among different combining schemes is provided to show the impact of PIC with minimum mean square error combining (MMSEC) and maximal ratio combining (MRC) on the performance of MC CC-CDMA system. The analytical and simulation results show that the combination of general combining schemes with PIC provides an efficient solution to suppress MAI in downlink MC CC-CDMA system than conventional MC-CDMA systems using Walsh codes under frequency-selective channels.

OFDM based link adaptive one-way DF relaying

OFDM based one-way DF relaying has recently received significant attention to improve the reliability and performance of wireless communication systems. In this paper, link adaptive relaying (LAR) approach which combats performance degradation due to error propagation in digital relaying has been applied to the OFDM based one-way DF relaying. It is shown that the power of sub-carriers can be scaled to reduce the error propagation to the destination which improves the BER performance of system. The power scaling is obtained from source-relay and relay-destination channel knowledge. The proposed system has the advantage of low complexity and it can help the relay use the power more efficiently. The error performance analysis of proposed system over frequency selective Nakagami-m fading channel is investigated. The results show that the proposed system outperforms the non-link adaptive based system. BER derivation is given for Rayleigh fading channel (m=1) under high signal to noise ratio (SNR). Monte-Carlo simulation results are provided in order to confirm the obtained numerical results by considering various position of relay.

Power Allocation in Orthogonal Frequency-division Multiplexing (OFDM) Based Two-way Relaying with Relay Selection

In this paper, error performance analysis of relay selection in orthogonal frequency-division multiplexing (OFDM) based amplify-and-forward (AF) relaying two-way cooperative communication system is examined over frequency selective Nakagami-m fading channels with power allocation at source, relay and destination nodes. Furthermore, we allocated the power to the sub-channels at three terminals. Power allocation is done under the total power constraints based on scaling factor obtained by available channel knowledge of links between the nodes. It is shown that as relay selection can achieve full diversity and improves bit error rate (BER) performance, the power allocation can further improve the performance. Results show that BER performance of proposed system increases with the power allocation and it improves through higher value of fading parameter m.

A General Framework for BER Analysis of OFDMA and Zero-Forcing Interleaved SC-FDMA over Nakagami-m Fading Channels with Arbitrary m

In this letter, bit error rate (BER) analysis is presented for both orthogonal frequency-division multiple access (OFDMA) and zero-forcing (ZF) interleaved single-carrier frequency-division multiple access (SC-FDMA) systems over Nakagami-m frequency-selective fading channels with arbitrary m. Specifically, the analytical BER is derived for both cases based on a general framework, that is by exploiting the statistics of the equalized noise. In comparison with the exiting alternatives, the proposed BER analysis has only half of the computational complexity for the OFDMA system and is more general for the SC-FDMA case.

Accurate BER Analysis of OFDM Systems Over Static Frequency-Selective Multipath Fading Channels

Bit error rate (BER) analysis of orthogonal frequency division multiplexing (OFDM) systems over frequency-selective Nakagami-m fading channels is considered in this work. The provided analyses are applicable for multipath channels with any number of taps and the Nakagami-m fading parameter can be finite or infinite. The results obtained demonstrate that the Gaussian approximation (GA) can be inaccurate if the number of channel taps is less than five. The analytical results confirmed by simulation demonstrated that the probability distribution functions for infinite fading parameter m are substantially different from those where m is finite. It was also found that the effect of m depends on the number of multipath components L. For even values of L, increasing m decreases the BER while the opposite happens for odd L values. Therefore, the worst case scenario for even L values occurs for m = 1, while for odd L values it occurs for m = ∞, i.e., the amplitudes of the multipath components are constants and equal.

Precise SER Analysis and Performance Results of OSTBC MIMO-OFDM Systems over Uncorrelated Nakagami-m Fading Channels

Although the topic of multiple-input multiple-output (MIMO) based orthogonal frequency division multiplexing (OFDM) over different fading channels is well investigated, its closed form symbol error rate (SER) expressions and performance results employing orthogonal space time block codes (OSTBCs) over uncorrelated frequency-selective Nakagami-m fading channels are still not available. The closed form expressions are extremely useful for evaluating system's performance without carrying out time consuming simulations. Similarly, the performance results are also quite beneficial for determining the system's performance in the sense that many practical wireless standards extensively employ MIMO-OFDM systems in conjunction with M-ary quadrature amplitude modulation (M-QAM) constellation. This paper thus, derives exact closed form expressions for the SER of M-ary Gray-coded one and two dimensional constellations when an OSTBC is employed and Nt transmit antennas are selected for transmission over frequency-selective Nakagami-m fading channels. For this purpose, first an exact closed-form of average SER expression of OSTBC based MIMO-OFDM system for M-ary phase shift keying (M-PSK) using traditional probability density function (PDF) approach is derived. We then compute exact closed form average SER expressions for M-ary pulse amplitude modulation (M-PAM) and M-QAM schemes by utilizing this generalized result. These expressions are valid over both frequency-flat and frequency-selective Nakagami-m fading MIMO channels and can easily be evaluated without using any numerical integration methods. We also show that average SER of MIMO-OFDM system using OSTBC in case of frequency-selective Rayleigh fading channels remains independent to the number of taps, L of that fading channel and the performance of the same system for two-tap un-correlated Rayleigh and Nakagami-m fading channels is better than that of the correlated one. Moreover, Monte Carlo simulation of MIMO-OFDM system using multiple transmit and receive antennas for different modulations is presented to validate our theoretical results. Finally, due to availability of closed form expressions, we further provide the performance results of MIMO-OFDM system over frequency-selective Nakagami-m fading channels employing (M-QAM) using OSTBCs under the transmission rate equal to 1, 2 and 3 bit(s)/s/Hz, respectively.

Accurate error-rate performance analysis of OFDM on frequency-selective Nakagami-m fading channels

Error rates of orthogonal frequency-division multiplexing (OFDM) signals in multipath slow fading Nakagami-m fading channels are considered. The exact probability density function of a sum of Nakagami-m random phase vectors is used to derive a closed-form expression for the error rates of OFDM signals. The precise error-rate analysis is extended to a system using multichannel reception with maximal ratio combining. An asymptotic error-rate analysis is also provided. For a two-tap channel with finite values of Nakagami-m fading parameters, our analysis and numerical results show that the asymptotic error-rate performance of an OFDM signal is similar to that of a single carrier signal transmitted over a Rayleigh fading channel. On the other hand, our analysis further shows that a frequency-selective channel that can be represented by two constant taps has similar asymptotic error-rate performance to that of a one-sided Gaussian fading channel. It is observed that, depending on the number of channel taps, the error-rate performance does not necessarily improve with increasing Nakagami-m fading parameters.

Transmit selection diversity with maximal-ratio combining for multicarrier DS-CDMA wireless networks over Nakagami-m fading channels

We propose the scheme to integrate transmit selection diversity/maximal-ratio combining (TSD/MRC) with multicarrier (MC) direct-sequence code-division multiple access (DS-CDMA) for various wireless networks. Applying this TSD/MRC-based scheme, the transmitter jointly selects the optimal subcarrier-and-antenna pair to significantly decrease the peak-to-average power ratio (PAPR), which is one of the main problems inherently associated with MC DS-CDMA communications. Over the frequency-selective Nakagami-m fading channels, we develop the unified analytical framework to analyze the symbol-error rate (SER) of the scheme implemented in different types of wireless networks, while dealing with the perfect and imperfect channel state information (CSI) feedbacks, respectively. The imperfect feedbacks we focus on include delayed feedbacks and erroneous feedbacks. Taking the imperfectness of the feedback into account, the resultant SER is compared with that of both conventional selection diversity (SD)/MRC-based and space-time block coding (STBC)/MRC-based schemes. Our analyses show that in a wide variation of the feedback imperfectness, our proposed TSD/MRC-based scheme has significant advantages over the other two schemes for both downlink cellular networks and ad hoc wireless networks. However, our analytical findings indicate that TSD/MRC-based scheme cannot always outperform SD/MRC-based and STBC/MRC-based schemes even when the perfect CSI feedbacks are available.

Multiband-OFDM MIMO coding framework for UWB communication systems

The emerging ultrawideband (UWB) system offers a great potential for the design of high speed short-range wireless communications. In order to satisfy the growing demand for higher data rates, one possible solution is to exploit both spatial and multipath diversities via the use of multiple-input multiple-output (MIMO) and proper coding techniques. In this paper, we propose a general framework to analyze the performance of multiband UWB-MIMO systems regardless of specific coding schemes. A combination of space-time-frequency (STF) coding and hopping multiband OFDM modulation is also proposed to fully exploit all of the available spatial and frequency diversities, richly inherent in UWB environments. We quantify the performance merits of the proposed scheme in case of Nakagami-m frequency-selective fading channels. Different from the conventional STF coded MIMO-OFDM system, the performance of the STF coded hopping multiband UWB does not depend on the temporal correlation of the propagation channel. We show that the maximum achievable diversity of multiband UWB-MIMO system is the product of the number of transmit and receive antennas, the number of multipath components, and the number of jointly encoded OFDM symbols. Interestingly, the diversity gain does not severely depend on the fading parameter m, and the diversity advantage obtained under Nakagami fading with arbitrary m parameter is almost the same as that obtained in Rayleigh fading channels. Finally, simulation results are presented to support the theoretical analysis.

Bit Error Rate Analysis for MC-CDMA Systems in Nakagami-"Equation missing" Fading Channels

Multicarrier code division multiple access (MC-CDMA) is a promising technique that combines orthogonal frequency division multiplexing (OFDM) with CDMA. In this paper, based on an alternative expression for the Q-function, characteristic function and Gaussian approximation, we present a new practical technique for determining the bit error rate (BER) of multiuser MC-CDMA systems in frequency-selective Nakagami-m fading channels. The results are applicable to systems employing coherent demodulation with maximal ratio combining (MRC) or equal gain combining (EGC). The analysis assumes that different subcarriers experience independent fading channels, which are not necessarily identically distributed. The final average BER is expressed in the form of a single finite range integral and an integrand composed of tabulated functions which can be easily computed numerically. The accuracy of the proposed approach is demonstrated with computer simulations.

Nakagami-m fading modeling in the frequency domain for OFDM system analysis

Nakagami-m fading modeling in the frequency domain is investigated. For frequency-selective Nakagami-m fading channels, we show the magnitudes of the channel frequency responses to be also Nakagami-m distributed random variables with fading and mean power parameters as explicit functions of the fading and mean power parameters of the channel impulse responses. Based on this new model, the bit error rate performance of an orthogonal frequency-division multiplexing system with receive diversity over correlated Nakagami-m fading channels is analytically evaluated and some numerical results are given.