A study of a peak-to-average power ratio (PAPR) reduction scheme for quasi-orthogonal spacetime
block coded multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems
based on selective mapping (SLM) is presented. The reduction technique is based upon combining the PAPRs of
the transmission blocks from four antennas and exploits the associated antenna diversity gain to mitigate errors
in the transmission of the side information (SI) necessary for SLM. Simulation studies are presented which
show the cumulative complementary distribution functions (CCDFs) with and without the combining scheme
and bit error rates of the overall system. Comparisons are made with single antenna and conventional OFDM
schemes

Faisal S. Alharbi (7203962)

Jonathon Chambers (1251609)

English

A study of a peak-to-average power ratio (PAPR) reduction scheme for quasi-orthogonal spacetime block coded multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems based on selective mapping (SLM) is presented. The reduction technique is based upon combining the PAPRs of the transmission blocks from four antennas and exploits the associated antenna diversity gain to mitigate errors in the transmission of the side information (SI) necessary for SLM. Simulation studies are presented which show the cumulative complementary distribution functions (CCDFs) with and without the combining scheme and bit error rates of the overall system. Comparisons are made with single antenna and conventional OFDM schemes. ©2008 IEEE

Alharbi, FS

Chambers, JA

Surrey Research Insight

Peak-to-average power ratio mitigation in quasi-orthogonal space time block coded mimo-ofdm systems using selective mapping

Loughborough University Institutional Repository

   This item was submitted to Loughborough’s Institutional Repository (https://dspace.lboro.ac.uk/) by the author and is made available under the following Creative Commons Licence conditions.      For the full text of this licence, please go to: http://creativecommons.org/licenses/by-nc-nd/2.5/  PEAK-TO-AVERAGE POWER RATIO MITIGATION IN QUASI-ORTHOGONALSPACE TIME BLOCK CODED MIMO-OFDM SYSTEMS USING SELECTIVEMAPPINGF.S. Alharbi and J.A.ChambersAdvanced Signal Processing Group Dept of Electronic and Electrical EngineeringLoughborough University, LE11 3TU, England.Email: f.alharbi@lboro.ac.uk, j.a.chambers@lboro.ac.ukAbstract - A study of a peak-to-average power ratio (PAPR) reduction scheme for quasi-orthogonal space-time block coded multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) systemsbased on selective mapping (SLM) is presented. The reduction technique is based upon combining the PAPRs ofthe transmission blocks from four antennas and exploits the associated antenna diversity gain to mitigate errorsin the transmission of the side information (SI) necessary for SLM. Simulation studies are presented whichshow the cumulative complementary distribution functions (CCDFs) with and without the combining schemeand bit error rates of the overall system. Comparisons are made with single antenna and conventional OFDMschemes.Index Terms- peak-to-average power ratio (PAPR), orthogonal frequency-division multiplexing (OFDM),selective mapping (SLM), cumulative complementary distribution functions (CCDFs), side information (SI).I. INTRODUCTIONOrthogonal frequency division multiplexing (OFDM) is an efficient digital modulation technique for highdata rate transmission especially in slowly fading and multipath channels. This technique has a relatively simpleimplementation based on the fast discrete Fourier transform, which avoids complicated equalization algorithms.OFDM divides the available spectrum into many subcarriers, instead of using only one carrier, and each oneis modulated by a low rate data stream [8]. Despite the widespread acceptance of OFDM in systems such asWiFi/WiMax [7], it has an inherent drawback of high peak-to-average power ratio (PAPR) which can increasethe complexity of the digital-to-analog converter in the transmission and increase the cost of the power amplifier.Given these facts, several researchers have extensively examined PAPR reduction in single-input single-output(SISO) systems (see, for instance, [1]- [3]). In the selected mapping approach [2] the frame to be transmittedis multiplied by a number of preselected phase signals such that the resulting PAPR is modified and then thatmapping which yields the smallest PAPR is the one which is chosen; and therefore the receiver must knowwhich out of the candidate phase waveforms is the one which was actually used. For high data rate wirelesswideband applications, multiple-input multiple-output (MIMO) transmission combined with OFDM is beingconsidered in a large number of current technology applications. If the PAPR reduction schemes in SISO aredirectly applied to MIMO, the complexity and redundancy increases proportional to the number of transmitantennas, which is not desired. In a traditional single antenna system, multi-path propagation can be a problemas it causes inter-symbol interference (ISI). As explained above the transmission of side information (SI) iscritical in the selective mapping scheme, which when corrupted leads to a high risk of interpreting all of thetransmitted symbols incorrectly. It is thus advisable to protect such information using the diversity gain affordedby MIMO transmission. By employing a MIMO system, multiple spatial channels are created and it is unlikelythat all the channels will fade simultaneously. Recent work in [4] is based upon exploiting these advantages.However, this work is limited to two transmit and one receive antenna.In this paper for MIMO-OFDM, we extend the proposed technique in [4] and study the PAPR performance ofa quasi-orthogonal space-time block code (QO-STBC) using a joint SLM technique for PAPR reduction. Insteadof applying individual SLM to each antenna, the sequence with the lowest PAPR over four transmit antennasis selected. Using the MIMO-SLM can improve the overall bit-error rate (BER) performance and increase thereliability of SI at the expense of the PAPR reduction gain. The interaction between the feedback necessary formaximum diversity gain in the full rate QO-STBC scheme we exploit and the proposed SLM scheme is alsodiscussed. In the next section, we introduce the SLM for a single antenna situation. In Section III, the notion ofblock quasi-orthogonal space-time coding is presented. Simulation results are provided in Section IV. Finally,Section V gives concluding remarks.II. SINGLE ANTENNA SLM IN MIMO-OFDM SYSTEMSThe basic principle of the SLM technique is that if there are M different ways of representing the sameunderlying signal information, Cm,m = 1, 2, ...,M , then, only one of these is likely to have the lowest PAPR2008 Loughborough Antennas & Propagation Conference 17-18 March 2008, Loughborough, UK157978-1-4244-1894-7/08/$25.00 ©2008 IEEEAuthorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on December 3, 2009 at 05:13 from IEEE Xplore.  Restrictions apply. when converted by the inverse Fourier transform (IFFT). The heart of the scheme is the methods to derive thedifferent ways to represent the original source signal.The M subvectors within C are weighted elementwise by the components of the generally complex vectorsbi, i = 1, ...,M to form Ci, i = 1, ...,M . These are then applied to the IFFT and the PAPR of their outputsare calculated and the final sequence is chosen to be the one with the lowest PAPR. The elements of thebi sequences are of the form of complex phases ejφ, typically φ ∈ (±1,±j) for computational simplicity,since phase shifts by multiplies of pi/2 can be implemented without any multiplications. To recover the data,the receiver must know which sequence has been used; this can be transmitted as SI. For the case where thenumber of carriers is sufficiently large, the time domain signal sampled at Nyquist rate is approximately zero-mean complex Gaussian based on adopting the central limit theorem. Therefore, the amplitude of these sampleshas a Rayleigh distribution and the probability that the PAPR exceeds a given threshold γ can be expressed as:Pr(PAPR > γ) = 1− (1− e−γ)N (1)where N is the number of subcarriers within the OFDM frame. Then, the probability that this happens on Mindependent sequences is:Pr(PAPRlow > γ) = Pr(PAPR > γ)M (2)where PAPRlow is the frame with the lowest PAPR. The underlying idea of the combined scheme is toexploit this result and to form an overall vector for the MIMO system which is composed of the sub-blocks foreach antenna, so the overall PAPR can be calculated in (2). In the work in [4], it was restricted to two antennasand Alamouti’s space-time block coding scheme. In this work, we extend it to QO-STBC for four antennas dueto increased diversity at full rate which is possible with closed loop operation.III. QO-STBCS SLM IN MIMO-OFDM SYSTEMSIn this work we are considering four antenna systems and the block code matrix is defined by [5]:G(S) =S1 S2 S3 S4−S∗2 S∗1 −S∗4 S∗3−S∗3 −S∗4 S∗1 S∗2S4 −S3 −S2 S1 (3)where the operation (.)∗ denotes complex conjugation. The transmit matrix G(S) corresponds to four transmitantennas transmitting a symbol block of four OFDM symbol intervals. The nth column of this matrix correspondsto the blocks transmitted from the ith antenna at consecutive symbol intervals. Feedback is also assumed as in [5]to obtain full diversity and rate performance. The time-domain OFDM signal, without cyclic prefix, transmittedfrom the ith transmit antenna is represented algebraically as:si(t) =N−1∑n=0ci,nej2pitn/N , 0 ≤ t ≤ N − 1 (4)where si, i = 1, 2, 3, 4 denote the complex valued time-domain transmitted symbols and ci,n = [Si]n is thecomplex symbol of transmitter i at the nth subcarrier in the frequency domain. We assume that the above matrixblock code is transmitted in the form of quaternary phase-shift keying (QPSK) symbols through a frequencyselective channel and the signal is received with only one receive antenna. Between each transmitter and theone receive antenna, we are assuming a multipath channel and the coefficients of that channel are modelledby independent complex valued random variables with zero mean and unity variance. We also assume thateach multipath channel is quasi-static, i.e. it remains constant over the block interval of the quasi-orthogonaltransmission. The PAPR associated with a MIMO-OFDM system can be defined as [6]:PAPR =maxi,t|si(t)|2Ei,t[|si(t)|2] (5)where Ei,t[.] denotes the expectation over transmit antennas and time. It is natural to individually apply SLMin (Section 1) to each antenna in QO-STBC. The OFDM symbol is mapped to a number of M independentcandidate symbols representing the same information. Then, the candidates Ci = [c0, ...., cN−1] are generatedby multiplying carrier-wise the original OFDM frame with M phase vectors bM = [b0, ..., bN−1], [bM ]v = ejϕv ,and ϕv ∈ (±1,±j) is randomly selected, the chosen phases are assumed to be known to both transmitter andreceiver. In order to recover the data at the receiver SI bits, of length S = [log2(M)], have to be transmitted toindicate which sequence out of the bM s was used in the transmitter. The detection probability of this SI can begiven by:2008 Loughborough Antennas & Propagation Conference 17-18 March 2008, Loughborough, UK158Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on December 3, 2009 at 05:13 from IEEE Xplore.  Restrictions apply. Pd = 1− [log2M ]× ζ (6)whereζ =(1− β)2D D−1∑d=0(D − 1 + dd)(1 + β2)d and β =1√1 + 1/SNR(7)where D represents the number of diversity channels carrying the same SI [6]. In the proposed combined scheme,SI is best transmitted over evenly distributed locations in frequency. In this work we use QPSK modulationwhich means each carries log2Q SI bits and the OFDM frame is divided into four uniformly separated regionsacross the frequency range as follows:ni =(i− 1) NLt if i ≤ Lt4N − [ N2 Slog2Q ]− (Lt2 − i) if Lt4 ≤ i < Lt4 + 1N − [ N2 Slog2Q ]− (Lt2 + 1− i) if Lt4 + 1 ≤ i < LtN + [ Slog2Q ]− ( 3Lt2 − i) if i ≥ Lt(8)where Lt denotes the number of the transmit antennas. By doing this, we are positioning the SI as far apartacross frequency as possible so that we maximize the frequency diversity gain and that same SI is transmittedon all of the antennas which maximizes the spatial diversity. It should be noted that the PAPR of a continuoustime OFDM signal cannot generally be computed precisely by using the Nyquist sampling rate. In this case,signal peaks can be missed and PAPR reduction estimates are unduly optimistic. Using a longer IFFT, i.e.interpolation, typically four times oversampling is effective in ensuring that PAPR is accurately estimated. Inthe combined SLM approach, the selection among those M random sequences is made according to the averagePAPR across the antennas and the corresponding cumulative complementary distribution function (CCDF) ofthe best sequence is:Pr(PAPRlow > γ) = [1− (1− e−γ)N×Lt ]M (9)where γ is the threshold of PAPR. The mathematical relationship between (6) and (9) could be studied further.Next, we consider a numerical evaluation of the performance of this approach.IV. SIMULATION RESULTSWe initially consider the CCDF performance of our scheme and compare the analytical results with numericalresults. In particular, Fig. 1 confirms that as the possible number of subsequences M changes from 1 to 4, withan oversampling factor of 1; the curve slope is increased. Also, it can be seen that the analytical curves accordingto (9) are identical to the simulation results. In this figure, consider when the probability of PAPR > γ = 0.001in this case when M = 1 the value of γ > 10dB. However, when M = 4 the value of γ is between 8 and 9dBdemonstrating at least 1dB reduction.4 5 6 7 8 9 10 11 12 1310−610−510−410−310−210−1100γ [dB]Prob (  PAPR > γ  )Individual (Analytical)Individual (Numerical)Combined (Analytical)Combined (Numerical)M = 1M = 4Fig. 1. CCDF of PAPR, the frame with lowest averagePAPR is selected out of M statistically independentframes for both single and combined SLM methods,Lt = 4 transmit antennas, N = 128, and QPSKmodulates each carrier, oversampling factor of unity.5 6 7 8 9 10 11 12 1310−510−410−310−210−1100γ [dB]Prob [  PAPR > γ  ]Individual (Analytical)Individual (Numerical)Combined(Analytical)Combined (Numerical)M = 4M = 1Fig. 2. As Fig. 1. except for an oversampling factor of4.Fig. 2 generates a more accurate representation of the true PAPR through oversampling by a factor of 4.Importantly, in case of QO-STBCs for example, the minimum PAPR threshold that was found is different. In2008 Loughborough Antennas & Propagation Conference 17-18 March 2008, Loughborough, UK159Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on December 3, 2009 at 05:13 from IEEE Xplore.  Restrictions apply. the case of no interpolation for the combined scheme, the minimum PAPR achieved was 9dB for the combinedQO-STBCs. However, with interpolation the new minimum PAPR changed to 9.5dB for the same number ofantennas. This 0.5dB difference corresponds to properly finding the peaks in the time-domain signal through theoversampling operation. In Fig. 3 we investigate the BER performance of the complete conventional basebandOFDM system. We compare this with our proposed combined closed-loop phase scheme and open-loop schemeboth for four transmit and one receive antennas over frequency selective channels, N = 128 and M = 2. Itis noted that, at BER = 0.001 the closed-loop scheme needs Eb/No of approximately 11dB while this valueincreased to at least 17dB with the conventional scheme. Moreover, the overall BER performance matches theperfect SI detection when exploiting four antenna diversity.0 5 10 15 2010−610−510−410−310−210−1100Eb/NoBERPerfect SI detectionSingle SLMCombined SLM        Open−LoopConventional OFDM system        Closed−LoopFig. 3. BER comparison with respect to side infor-mation for both single and combined SLM methods ofQO-STBCs with and without feedback, N = 128 andM = 2.0 2 4 6 8 10 12 14 16 18 200.940.960.9811.021.04Eb/No, [dB]Prob.ofSIDetection  Combined (Numerical)Combined (Analytical)Lt = 4Lt = 2Fig. 4. Probability of side information detection usingSLM method for 2 × 1 STBC-SLM and a combined4× 1 QO-STBC, N = 128 and M = 2.For the final simulation, in Fig. 4 we provide the probability of detection of SI for both Lt = 2 MIMO-STBC and Lt = 4 QO-STBCs based on the SLM technique. We observe that when Lt = 2, the numericaland the analytical results give a probability of SI detection around 0.95 at Eb/No = 2dB and with Lt = 4,this probability is increased by approximately 4%. It is evident that this scheme is a promising solution forconsiderably increasing the probability of SI detection. The QO-STBC scheme requires to operate in closed-loopmode in order to have full diversity and full rate. To achieve this, feedback is required from the receiver to thetransmitter. When such a feedback is used at the transmitter, the transmitted symbols are rotated by a phasevalue. This operation should not be performed in isolation from the phase rotations that we are applying interms of the PAPR mitigation scheme. Therefore, future work will be looking at the combination of the feedbacktogether with the PAPR mitigation.V. CONCLUSIONIn this paper, a combined SLM approach was proposed for PAPR mitigation in MIMO-OFDM transmissionover four transmit antenna systems which exploits closed loop operation with a full rate and full diversity QO-STBC. Performance improvement was demonstrated in terms of comparison with a conventional OFDM SLMscheme in terms of average BER and probability of SI detection.REFERENCES[1] A.D.S. Jayalath and C. Tellambura, “Adaptive PTS approach for reduction of peak-to-average power ratioof OFDM signal,” Electronic Lett., vol.36, no.14, pp.1226-1228, July 2000.[2] R.W. Bauml, R.F.H. Fischer, and J.B. Huber, “Reducing the peak-to-average power ratio of multicarriermodulation by selected mapping,” Electronic Lett., vol.32, no.22, pp.2056-2057, October 1996.[3] Li. Xiaodong and L.J.Jr. Cimini, “Effect of Clipping and Filtering on the Performance of OFDM,” ElectronicTrans., vol.2, no.5, pp.131-133, May 1997.[4] Y.-L. Lee, Y.-H. You, W.-G. Joen, J.-H. Paik, and H.-K. Song, “Peak-to-average power ratio in MIMO-OFDM systems using selective mapping,” IEEE Commun. Lett., vol.7, no.12, pp.575-577, December 2003.[5] C.Toker, S.Lambotharan, and J.A. Chambers, “Closed-Loop Quasi-Orthogonal STBCs and Their Perfor-mance in Multipath Fading Enviroments and When Combined With Turbo Codes,” IEEE Trans. Commun.,vol.3, no.6, pp.1890-1896, November 2004.[6] J.G. Proakis, Digital Communications. New York: McGraw-Hill, 1989.[7] H. Yagoobi, “Scalable OFDMA Physical Layer in IEEE 802.16 WirelessMan,” Intel Technology Journal,vol.8, pp. 201-212, August 2004.[8] A. R. Bahai, and B. R. Saltzaberg, Multi-Carrier Digital Comunications:Theory and Applications of OFDM.New York: Kluwer Academic/Plenum Publishers, 1999.2008 Loughborough Antennas & Propagation Conference 17-18 March 2008, Loughborough, UK160Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on December 3, 2009 at 05:13 from IEEE Xplore.  Restrictions apply. 

Peak-to-average power ratio mitigation in quasi-orthogonal space time block coded MIMO-OFDM systems using selective mapping.

https://repository.lboro.ac.uk/articles/Peak-to-average_power_ratio_mitigation_in_quasi-orthogonal_space_time_block_coded_MIMO-OFDM_systems_using_selective_mapping_/9554465/files/17186243.pdf

Peak-to-average power ratio mitigation in quasi-orthogonal space time block coded MIMO-OFDM systems using selective mapping.

Abstract

Similar works

Full text

Available Versions

Surrey Research Insight

Loughborough University Institutional Repository