SER analysis of the MRC-OFDM receiver with pulse blanking over frequency selective fading channel
- Haitao Liu†^{1}Email author,
- Zhisheng Yin†^{2},
- Min Jia^{2} and
- Xuejun Zhang^{3}
https://doi.org/10.1186/s13638-016-0615-3
© Liu et al. 2016
Received: 14 September 2015
Accepted: 17 April 2016
Published: 18 May 2016
Abstract
Pulse blanking is a widely used method to eliminate impulsive interference in an orthogonal frequency division multiplexing (OFDM) receiver. To analyze the effect of the inter-carrier interference caused by pulse blanking on the symbol error rate (SER) performance of OFDM employing maximum ratio combining (MRC) receiver, the analytical expression of the signal-to-interference-noise ratio (SINR) of the OFDM employing MRC receiver is derived. Based on the SINR expression, furthermore, the SER performances over both Rayleigh and Ricean fading channels are also analyzed quantitatively. Simulation results validate the correctness of the derived formulas.
Keywords
1 Introduction
Orthogonal frequency division multiplexing (OFDM) is a multicarrier modulation technique which converts a frequency-selective channel into a parallel collection of frequency flat subchannels. Compared with single-carrier communication systems, OFDM has advantages, such as spectral efficiency, efficient implementation based on the fast Fourier transform (FFT), and simple channel equalization. For these reasons, the OFDM transmission scheme is widely employed in wireless and wired communications, e.g., digital subscriber lines (DSL), digital video broadcasting (DVB), digital audio broadcasting (DAB), wireless local area networks (WLAN), power line communications (PLC), long term evolution (LTE), and L-band digital aeronautical communication system (L-DACS) [1].
In practical applications, OFDM systems are often exposed to impulsive interference, e.g., ignition noise of passing vehicles, impulsive noise in power line or other systems operating in the same frequency range. Some studies have shown that the impulse interference with high power or frequent occurrence can significantly affect the performance of OFDM receivers [2, 3]. Thus, it is of great significance to eliminate the impulse interference in OFDM receivers.
To suppress the effect of impulsive noise on an OFDM receiver, an interference mitigation method based on pulse blanking is first proposed in [4–6]. However, when using this method to an actual system, two problems should be considered, the threshold of pulse blanking and the compensation of inter-carrier interference (ICI) caused by pulse blanking. To calculate the blanking threshold, an optimal threshold of pulse blanking is derived based on an expression for the signal-to-noise ratio (SNR) of the blanking nonlinearity [7]. With maximizing the signal-to-interference-and-noise ratio (SINR) criterion, an adaptive blanking threshold for the OFDM receiver is also proposed in [8]. To eliminate the ICI caused by pulse blanking, an iterative reconstructing and subtracting ICI method is proposed in [9, 10], and a frequency-domain ICI compensation scheme based on finite impulse response equalizer is proposed in [11].
Studies on the performance analysis of single-carrier systems in impulsive noise environment are presented in [12–16]. The performance of diversity combining technique over fading channels with impulsive noise is analyzed in [12]. Adopting the Middleton class A impulsive noise model, the performance of space-time coded systems over multiple-input multiple-output (MIMO) channels with impulsive noise is studied in [13, 14]. The effect of symmetric α-stable noise on space-time coded systems over MIMO fading channels is analyzed in [15]. A unified mathematical framework for the analysis of the asymptotic performance of amplify-and-forward cooperative diversity systems impaired by generic noise is provided in [16]. The influence of impulse noise on the symbol error rate (SER) performances of multicarrier and single-carrier communication systems is investigated and compared in [2]. With regard to the performance analysis of the OFDM receiver with blanking, the SNR expression of the OFDM receiver with blanking is obtained for the AWGN channel [17]. The SNR expression for the OFDM receiver with blanking is derived in frequency selective Rayleigh fading channel, as well as the SER performance on this SNR expression [18]. To the best of our knowledge, there is currently no literature regarding the SER performance of the maximum ratio combining (MRC)-OFDM receiver with pulse blanking.
In this paper, a closed-form expression for the SINR of the MRC-OFDM receiver with pulse blanking over frequency selective fading channel is derived. Furthermore, the SER performances of the MRC-OFDM receiver with pulse blanking over both Rayleigh and Ricean fading channels are also analyzed quantitatively based on this SINR expression. Finally, simulation results are presented that validate the correctness of the derived formulas.
This paper is arranged as follows. In Section 2, a system model comprising the OFDM transmitter and the MRC-OFDM receiver with pulse blanking is introduced. In Section 3, the closed-from expression for the SINR of the MRC-OFDM receiver with pulse blanking is derived, and the SER performances for both Rayleigh and Ricean fading channels are also analyzed. In Section 4, an overview of system and channel parameters is provided, and the analytically calculated and simulated symbol error performance curves are presented to validate our theoretical results. In Section 5, we draw the main conclusion.
2 System model
2.1 OFDM transmitter
with k being the subcarrier index in the frequency domain and n denoting the sample index in the time domain. As IFFT is a unitary transformation, the statistical property of s agrees with S, and \(\left \{ {{s_{n}},n = 0,1,\ldots,K - 1} \right \} \) are also i.i.d. with E{s _{ n }}=0 and \(E\left \{ {{{\left | {{s_{n}}} \right |}^{2}}} \right \} = {\sigma _{S}^{2}}\).
where \({\mathbf {0}}_{K \times {(K-K_{g})}}\) is a K _{ g }×(K−K _{ g }) zero matrix and I _{ K } is a K×K identity matrix.
The transmitted signal vector x is then converted to an analog signal x(t) by the D/A converter and x(t) is transformed into a RF signal by the RF front end. Finally, the RF signal is sent to a channel by the transmitter antenna.
2.2 MRC-OFDM receiver with pulse blanking
where x(t) denotes the transmitted signal, ∗ the convolution operation, h ^{ v }(t) the channel impulse response of the vth channel, n ^{ v }(t) the complex Gaussian white noise signal from the vth channel, i ^{ v }(t) the impulsive noise from the vth channel, and N the number of receive antenna.
where \(\mathbf {P}_{\text {out}} = \left [ {{{\mathbf {0}}_{K \times {K_{g}}}}} \quad {{\mathbf {I}_{K}}}\right ]\) denotes the cyclic prefix removal matrix.
where \({b_{n}^{v}}\) is the Bernoulli process which is the arrival of impulsive noise with probability \({{\mathrm {P}}_{\mathrm {r}}}\left ({{b_{n}^{v}} = 1} \right) = p\) and \({g_{n}^{v}}\) is the complex Gaussian RV with mean zeros and variance \({{\delta _{g}^{v}}}^{2}\).
where \({\bar {\mathbf {B}}^{v}}\) denotes the impulse blanking matrix for the vth receive branch and where \({\bar {\mathbf {B}}^{v}} = \text {diag} \left (\bar {b}_{0}^{v},\ldots,\bar {b}_{n}^{v},\ldots, \bar b_{K - 1}^{v} \right)\) with \({\bar {b}_{n}^{v}} = 1 - {{b_{n}^{v}}}\).
where \({\mathbf {H}^{v}} = \text {diag}\left ({{H_{0}^{v}},..,{H_{k}^{v}},\ldots,H_{K - 1}^{v}} \right)\) denotes the frequency domain channel transfer matrix of the vth channel and \({H_{k}^{v}}\) denotes the frequency response of the kth subchannel for the vth channel.
The signal vector \({\tilde {\mathbf {Y}}_{\text {MRC}}}\) is finally sent to the demodulator, where the output bit sequence \(\hat {\mathbf {I}}\) is sent to the sink.
3 Performance analysis
3.1 SINR for the MRC-OFDM demodulator
where \({\gamma _{k}^{v}} \buildrel \Delta \over = \frac {\rho }{{p \rho + \left ({1 - p} \right)}} {\left | {{H_{k}^{v}}} \right |^{2}}\) denotes the instantaneous SINR for the kth subchannel of the vth channel at the output of MRC. We assume the independence between different diversity reception branches, then \({{H_{k}^{v}}}\) is independent of \({{H_{k}^{j}}}\) if j≠v, and therefore \({\gamma _{k}^{v}}\) is independent of \({\gamma _{k}^{j}}\) if j≠v.
3.2 SER of the MRC-OFDM receiver with pulse blanking over Rayleigh fading channel
For the Rayleigh fading channel, the frequency response of the kth subchannel of the vth receive branch \({H_{k}^{v}} = \sum \limits _{l = 0}^{{L_{v}} - 1} {h_{_{l}}^{v}{e^{- j2\pi \frac {{kl}}{K}}}} \) is a complex Gaussian RV of mean zeros and variance one, thus \(\left |{H_{k}^{v}}\right |^{2}\) is χ ^{2} distributed with 2 degrees of freedom and \(E\left \{ {|{H_{k}^{v}}{|^{2}}} \right \} = 1\).
In the SER expressions given in Eqs. (32), (33), (35), and (36), the SER of the kth subchannel is independent of the subchannel index, which indicates that pulse blanking has the same effect on the error performance of each subchannel of the MRC-OFDM receiver.
where \(\mu = \sqrt {{{\bar {\gamma }} \left / {\left ({1 + \bar {\gamma }} \right)}\right.}} \).
The exact expression in Eq. (38) provides insight into a few special cases. (i) When there is no interference, i.e., p=0, \(\bar {\gamma }= \rho \), Eq. (38) reduces to the symbol error probability of a conventional Nth-order space diversity receiver employing MRC. (ii) When there is interference, i.e., p≠0, and in the limiting case the input SNR is large, i.e., \(\rho \to \infty \), \(\mathop {\lim }\limits _{\rho \to \infty }\bar \gamma ={1\left / p\right.}\), thus, there will be an error floor for the SER performance curve. Considering a small p value (less than 0.1) fulfilling the condition \(\bar {\gamma }\gg 1\), the approximate theoretical expression of the error floor behaves as \({\left ({\frac {p}{4}}\right)^{N}}\left ({ \begin {array}{{c}} {2N-1}\\ N \end {array}} \right)\). Therefore, the error floor decreases proportionally with the Nth power of the probability of impulsive noise occurrence p at an Nth-order space diversity. For a given p value, the error floor can be efficiently reduced as the number of receive antenna increases. The same conclusion can be reached based on the approximate expressions in Eqs. (33) and (36).
3.3 SER of the MRC-OFDM receiver with pulse blanking over Ricean fading channel
For the Ricean fading channel, \({h_{0}^{v}}\) is assumed to be a non-zero mean complex Gaussian RV, i.e., \({h_{0}^{v}} \sim \mathrm {\mathcal {CN}}\left ({u_{v}},\delta _{0}^{{v}^{2}} \right)\), \(\left \{ {{h_{l}^{v}},l = 1,\ldots,{L_{v}} - 1} \right \}\) are assumed to be complex Gaussian RVs, i.e., \({h_{l}^{v}}\sim {\mathrm {\mathcal {CN}}}\left (0,\delta _{l}^{{v}^{2}} \right)\). The channel power is normalized to 1, i.e., \({\left | {{u_{v}}} \right |^{2}} + {\sum \nolimits }_{l = 0}^{L - 1} {{{\left | {{\delta _{l}^{v}}} \right |}^{2}}} = 1\), and the Ricean factor of the vth channel is defined as \({K_{v}} \buildrel \Delta \over = {{{{\left | {{u^{v}}} \right |}^{2}}} \left / {{\sum \nolimits }_{l = 0}^{L - 1} {{{\left | {{\delta _{l}^{v}}} \right |}^{2}}} }\right.}\). Hence, the frequency response of the kth subchannel \({H_{k}^{v}}\) is distributed according to complex Gaussian with mean u ^{ v } and variance \({\sum \nolimits }_{l = 0}^{L - 1} {{{\left | {{\delta _{l}^{v}}} \right |}^{2}}} - {\left | {{u^{v}}} \right |^{2}}\). Furthermore, \({\left | {{H_{k}^{v}}} \right |^{2}}\) is noncentral χ ^{2} distributed with 2 degrees of freedom and \(E\left \{ {|{H_{k}^{v}}{|^{2}}} \right \} = 1\).
Also, the SER derived above is only for the kth subcarrier. It has to be averaged over all the subcarriers. Comparing Eq. (44) with Eq. (33), Eq. (45), and Eq. (36), we find that for the specific Ricean factors, the same conclusion presented in Section 3.2 can be reached based on the approximate expressions in Eqs. (45) and (46).
4 Numerical results
4.1 System and channel parameters
System and channel parameters
Parameters | Value |
---|---|
System parameters | |
Modulator | BPSK, 8PSK, 16QAM |
Subcarrier number | 512 |
Data subcarrier number | 512 |
Cyclic prefix | 16 |
Channel parameters | |
Channel models | Rayleigh (10 paths) |
Ricean (10 paths, \(\left \{ {{K_{v}}} \right \} = 10\) dB) | |
Impulsive noise model | Bernoulli-Gaussian |
Probability of interference | |
occurrence | p (see figures) |
Receiver parameters | |
Number of receive antenna | N = 2, 4 |
Channel estimation | Ideal channel estimation |
Channel equalization | ZF equalization |
4.2 Symbol error performance curves
Figures 3 and 4 show the SER performances of the MRC-OFDM receiver with pulse blanking for BPSK modulation over Rayleigh fading channel for N=2 and N=4 receive antennas. Each figure contains four pairs of curves, which shows the theoretical and simulated SER of the OFDM receiver with pulse blanking at different p values. In both figures, it can be seen that theoretical results correspond well with the simulation results.
Impact of probability of impulsive noise occurrence on the error floor
p | Error floor (theory) | Error floor (simulation) |
---|---|---|
0.02 | 7.50e −005 | 7.0e −005 |
0.03 | 1.69e −004 | 1.5e −004 |
0.05 | 4.69e −004 | 4.5e −004 |
Similarly, for the same receiver and channel, Figs. 5 and 6 show the SER performances for 16QAM modulation with N=2 and N=4 receive antennas, respectively. From the four pairs of curves in each figure, the theoretical results correspond well with the simulation results and derive the same analysis as that in Figs. 3 and 4.
Figures 7 and 8 show the SER performances of the MRC-OFDM receiver with pulse blanking for 8PSK modulation over Ricean fading channel with Ricean factors \(\left \{ {{K_{v}}} \right \} = 10\) dB for N=2 and N=4 receive antennas, respectively. Similar to the previous paragraph, from the four pairs of curves in each figure, the theoretical results agree well with the simulation results. We arrive then with the same analysis as for Figs. 3 and 4.
Similarly, for the same receiver and channel, Figs. 9 and 10 show the SER performances for 16QAM modulation with N=2 and N=4 receive antennas, respectively. Again, from the four pairs of curves of in each figure, the theoretical results correspond well with the simulation results and yield the same analysis as for Figs. 3 and 4.
5 Conclusions
In this paper, we studied the symbol error performance of the MRC-OFDM receiver with pulse blanking over frequency selective fading channel. The closed-form expression of the SINR for the MRC-OFDM receiver with pulse blanking is derived. The SER of the MRC-OFDM receiver with pulse blanking over both Rayleigh and Ricean fading channels are also given. The simulation results validate the correctness of our derived formulas. The following conclusions are obtained: (i) the pulse blanking has same effect on the error performance of each subchannel of the MRC-OFDM receiver; (ii) the error floor for the SER performance is observed for the MRC-OFDM receiver with pulse blanking and the error floor depends on the probability of impulsive noise occurrence and the number of receive antenna; and (ii) the developed analysis method in this paper can be extended to the case of the Middleton class A noise environment and the error floor for the SER performance is determined by the probability of the Middleton class A impulsive noise occurrence.
6 \thelikesection Appendix
Declarations
Acknowledgements
This work was supported in part by National Natural Science Foundation of China under Grants No. U1233117 and No. 61271404.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
- N Neji, R de Lacerda, A Azoulay, T Letertre, O Outtier, Survey on the future aeronautical communication system and its development for continental communications. Veh. Technol. IEEE Trans.62(1), 182–191 (2013).View ArticleGoogle Scholar
- M Ghosh, Analysis of the effect of impulse noise on multicarrier and single carrier QAM systems. Commun. IEEE Trans. 44(2), 145–147 (1996).View ArticleGoogle Scholar
- YH Ma, PL So, E Gunawan, Performance analysis of OFDM systems for broadband power line communications under impulsive noise and multipath effects. Power Delivery IEEE Trans. 20(2), 674–682 (2005).View ArticleGoogle Scholar
- P Lewis, A Tutorial on Impulsive Noise in COFDM Systems (2001). http://www.dtg.org.uk. Accessed May 2001.
- NP Cowley, A Payne, M Dawkins, COFDM tuner with impulse noise reduction. EP1180851 (2003). http://www.freepatentsonline.com/EP1180851B1.html.
- CR Nokes, OP Haffenden, JD Mitchell, AP Robinson, JH Stott, A Wiewiorka, Detection and removal of clipping in multicarrier receivers. EP1043874: (2000). http://www.freepatentsonline.com/EP1043874A2.html.
- SV Zhidkov, Performance analysis and optimization of OFDM receiver with blanking nonlinearity in impulsive noise environment. Veh. Technol. IEEE Trans. 55(1), 234–242 (2006).View ArticleGoogle Scholar
- U Epple, M Schnell, in Global Communications Conference (GLOBECOM), 2012. Adaptive threshold optimization for a blanking nonlinearity in OFDM receivers (IEEEAnaheim CA, USA, 2012), pp. 3661–3666.View ArticleGoogle Scholar
- S Brandes, U Epple, M Schnell, in Global Telecommunications Conference, 2009. GLOBECOM 2009. Compensation of the impact of interference mitigation by pulse blanking in OFDM systems (IEEEHonolulu HI, USA, 2009), pp. 1–6.View ArticleGoogle Scholar
- C-H Yih, Iterative interference cancellation for OFDM signals with blanking nonlinearity in impulsive noise channels. Signal Process. Lett. IEEE. 19(3), 147–150 (2012).View ArticleGoogle Scholar
- D Darsena, G Gelli, F Melito, F Verde, ICI-free equalization in OFDM systems with blanking preprocessing at the receiver for impulsive noise mitigation. Signal Process. Lett. IEEE. 22(9), 1321–1325 (2015).View ArticleGoogle Scholar
- C Tepedelenlioglu, P Gao, in Global Telecommunications Conference, 2004. GLOBECOM ’04. On diversity reception over fading channels with impulsive noise (IEEEWashington, DC, USA, 2004), pp. 3676–3680.View ArticleGoogle Scholar
- P Gao, C Tepedelenlioglu, Space-time coding over fading channels with impulsive noise. Wireless Commun. IEEE Trans. 6(1), 220–229 (2007).View ArticleGoogle Scholar
- R Savoia, F Verde, Performance analysis of distributed space-time block coding schemes in middleton class-a noise. Veh. Technol. IEEE Trans. 62(6), 2579–2595 (2013).View ArticleGoogle Scholar
- J Lee, C Tepedelenlioglu, Space-time coding over fading channels with stable noise. Veh. Technol. IEEE Trans. 60(7), 3169–3177 (2011).View ArticleGoogle Scholar
- A Nasri, R Schober, IF Blake, Performance and optimization of amplify-and-forward cooperative diversity systems in generic noise and interference. Wireless Commun. IEEE Trans. 10(4), 1132–1143 (2011).View ArticleGoogle Scholar
- U Epple, K Shibli, M Schnell, in Communications (ICC), 2011 IEEE International Conference On. Investigation of blanking nonlinearity in OFDM systems (IEEEKyoto, Japan, 2011), pp. 1–5.View ArticleGoogle Scholar
- HT Liu, ZS Yin, XJ Zhang, Performance analysis of OFDM receiver with pulse blanking in frequency selective Rayleigh fading channel. J. Beijing University Posts Telecommun. 38(4), 29–32 (2015).Google Scholar
- Y Li, G Stuber, Orthogonal Frequency Division Multiplexing for Wireless Communications (Springer, New York, 2006).View ArticleGoogle Scholar
- JG Proakis, Digital Communications Fourth Edition, 4nd edn (Publishing House of Electronics Industry, Beijing, 2011).Google Scholar
- M-S Simon, MK Alouini, Digital Communications over Fading Channels 2nd Edition, 2nd edn (Wiley, New York, 2005).Google Scholar