Adaptive MIMO-OFDM for Future Mobile Radio Communications

Adaptive MIMO-OFDM for Future Mobile RadioCommunicationsV. Kühn, R. Böhnke, K.-D. KammeyerUniversity of Bremen, Dept. of Communications EngineeringP.O. Box 330440, D-28334 Bremen, Germany{kuehn,boehnke,kammeyer}@ant.uni-bremen.de, Fax: +49 421 218 3341Keywords: Adaptive OFDM, MIMO, Channel Coding, Bitand Power LoadingAbstractThis paper addresses the topic of bit and power loading incoded MIMO-OFDM systems. Due to the need of designingcommunication systems with high spectral efficiencies, thecombination of multiple antennas at transmitter and receiverwith OFDM represents a promising approach. Moreover,channel knowledge at the transmitter can be exploited toadapt the transmission to the channel. While loading strategiesfor the uncoded case as well as the information theoreticalsolution are already known, the optimum scheme is stillunknown for coded systems. In this paper, we compare differentloading approaches for coded systems with respect totheir error rate performance.1 IntroductionSince bandwidth is a limited and valuable resource, moderncommunication systems have to be designed to achieve veryhigh spectral efficiencies. One candidate for an appropriateair interface of future mobile radio systems is the multi-carriertechnique OFDM (Orthogonal Frequency Division Multiplexing)[1]. It has already proven its practicability by findingits way into various standards for broadcast as well as pointto-pointcommunications [5,6,7]. One of the main benefits isthe simple equalization of frequency selective channels.Additionally, OFDM allows an easy adaptation to the channelconditions due to its granularity in the frequency domain ifchannel knowledge is available at the transmitter.A second approach leading to high spectral efficiencies is touse multiple antennas at the transmitter as well as thereceiver. The high potential of multiple-input multiple-output(MIMO) systems stems from the fact that parallel datastreams can be transmitted thereby multiplying the achievabledata rate [12]. For frequency selective channels, acombination of OFDM and multiple antennas is obvious.In this paper, we consider a coded MIMO-OFDM system andassume perfect channel knowledge at transmitter and receiver.This assumption allows the exploitation of the eigenmodes ofthe MIMO channel and the transmission of independent paralleldata streams. Transmit power and signal constellationcan be individually chosen for each stream with respect to anappropriate optimization criterion.The paper is organized as follows: Section 2 describes thesystem model and Section 3 the investigated loading strategies.Simulation results comparing the different concepts arediscussed in Section 4 and concluding remarks can be foundin Section 5.2 System ModelThe structure of the MIMO-OFDM transmitter is depicted inFigure 1. The information bits are first encoded by an FECencoder that is further specified in Section 4. The encodedstream is demultiplexed into N = NCNTlayers, where NCdenotes the number of OFDM subcarriers and N T the numberof transmit antennas. Since we assume perfect channelknowledge at transmitter and receiver, each layer isindividually modulated (block ‘M’) according to anappropriate signal constellation. As OFDM ensures that eachcarrier is only affected by flat fading, the MIMO channelcorresponding to carrier ν can be represented by an NR × NTmatrix with the singular value decompositionH νHH ν = UνΣνVν. The unitary NT× N Tmatrices V ν are usedfor a linear pre-processing in order to exploit the eigenmodesof the MIMO channel, i.e. the transmitted vector becomesx = V s with containing the data symbols.νν νCs νMMMMN TN CN TV 1V NCFigure 1: MIMO-OFDM transmitterN CN COFDMN TOFDMThe N symbols are subsequently assigned to N T streams eachcomprising N C symbols forming one OFDM symbol perantenna.At the receiver depicted in Figure 2, OFDM demodulation isperformed at each of the N R antennas. Next, the permutation isreversed so that N C streams each containing the signals of N Rantennas are formed. The receive vector on theν -th subcarrier is given byy = H x + n .(1)ν ν ν ν

10 0 E b / N 0 in dB10 -1no loadingwaterfilling10 0 E b / N 0 in dB10 -1no loadingbit & power loadingbit loadingP outBER10 -210 -210 -310 -3-2 0 2 4 6 8Figure 3: Outage probability with and without water-fillingIn [10], a hard decision is assumed before the decoder. Thistransfers each of the parallel AWGN channels into a binarysymmetric channel (BSC), whose error probability can beminimized using the methods described in the previoussection. However, the reliability information about the codebits is lost due to the quantization, which leads to a severeperformance degradation that may even overcompensate thegains due to the adaptive transmission.An approximation for the coded BER with soft-inputdecoding is derived in [11]. Interestingly, the resulting rateallocation formula is identical to (9) with SNR gap inverselyproportional to the minimum Hamming distance of thechannel code. This leads to the assumption that algorithmsoriginally developed for the uncoded case are also reasonablefor coded transmission. So, all in all, both informationtheoretic and uncoded results appear to be suited for realisticcodes. However, while rate adaptation is not required forideal coding schemes, it is essential in the absence of channelcoding. It is not intuitively clear, which approach turns out tobe better.4 Numerical ResultsIn order to evaluate the different loading strategies, weconsider a MIMO-OFDM system with NC= 32 carriers andNT= NR= 4 antennas at transmitter and receiver. Thechannel impulse responses consist of LH= 6 uncorrelatedcomplex Gaussian distributed taps with equal variance andthe received SNR per bit is defined asEbNRP= .(10)N R0Figure 3 shows the outage probability of the channel. Hereand in the following figures, solid, dashed, and dash-dottedlines correspond to data rates of R = 4, 8, and 12 bit/s/Hz ,respectively. It can be observed that the gain due to waterfillingdiminishes with increasing rate.10 -40 5 10 15Figure 4: Performance of different loading schemes foruncoded transmissionIn Figure 4, results for the uncoded case are depicted. Notsurprisingly, non-adaptive transmission performs poorly,because no diversity is used and weak subchannels dominatethe average error rate. Enormous improvements are possiblewith the bit and power loading algorithm described in Section3.2, where the maximum constellation size was limited to 256QAM. Most of the gain can already be achieved bycombining the resulting bit allocation with an equal powerdistribution among active subchannels, so power loadingseems to be less important.The loading algorithms were then applied to codedtransmission. Each codeword spans LF= 10 consecutiveMIMO-OFDM symbols (consisting of LFNCN T= 1280QAM symbols) during which the channel remains constant.Figure 5 depicts the BER for a half-rate non-recursiveconvolutional code with generator polynomials (7,5) 8in octalrepresentation. Looking at a spectral efficiency ofR = 4 bit/s/Hz, we observe that pure bit loading shows thebest performance and is slightly better than the combinationof bit and power loading. Obviously, a power distributionenforcing equal bit error probabilities on all subchannels doesnot represent the optimum approach for coded systems. Thegain of bit loading compared to the non-adaptive systemsamounts to 5 dB at a bit error rate of 10-4 . The different slopesof the curves indicate that this code can not utilize the fulldiversity of the channel without bit loading. On the otherhand, water-filling performs even worse than the nonadaptivesystem. The reason is that the code is highly puncturedbecause bits assigned to channels with P μ= 0 are nottransmitted. This is in contrast to the case of bit loading,where all code bits are transmitted. For growing spectralefficiency, the water filling approach becomes the best choiceat low signal to noise ratios while pure bit loading performsbest for medium and high SNR. For R = 12 bit/s/Hz, nearlyall channels – even the worst ones – have to be used so thatpuncturing has only a minor influence. The bit loading

10 -1no loadingwaterfillingbit & power loadingbit loading10 -1no loadingwaterfillingbit & power loadingbit loadingBER10 0 E b / N 0 in dB10 -2BER10 0 E b / N 0 in dB10 -210 -310 -310 -40 5 10 15Figure 5: Performance of different loading schemes for a halfrateconvolutional codescheme gains about 3 dB. A comparison with Figure 4 revealsthat for this high data uncoded adaptive transmission isanother 2.5 dB better, because due to the code rate Rc= 1/2each QAM symbol contains on average 6 code bits while themaximum is set to 8 bits, which limits the degrees of freedomfor the loading process.Figure 6 shows the corresponding results for the turbo codeconsisting of two identical constituent encoders withgenerator polynomials (1,17 /13) 8and punctured to rateRc= 1/2. For low and medium spectral efficiencies, bitloading still performs best closely followed by bit and powerloading. The gains amount to 3 dB for R = 4 bit/s/Hz and1.5 dB for R = 8 bit/s/Hz. For an efficiency of R = 12 bit/s/Hz,the relations change and water filling achieves the lowesterror rate. Astonishingly, the combination of bit and powerloading performs worst. The gains reduce to less than 1 dB.For this powerful turbo code and the high spectral efficiency,the information theoretical approach can be confirmed. Incontrast to the convolutional code, the turbo code is able toexploit the full spatial and frequency diversity contained inthe system.5 ConclusionsIt has been shown that loading strategies exploiting channelknowledge at the transmitter can improve the error rate performancesignificantly. For weak codes, pure bit loadingseems to be an appropriate choice while the water fillingapproach performs best for strong codes and extremely highspectral efficiencies. However, it is still an open question howoptimum bit and power loading has to be performed for aspecific code.10 -40 2 4 6 8 10 12Figure 6: Performance of different loading schemes for a halfrateturbo codeReferences[1] J.A.C. Bingham. “Multicarrier Modulation for DataTransmission: An idea whose time has come”, IEEECommunications Magazine, pp. 5-14, (1990).[2] G. Caire, G. Taricco, E. Biglieri. “Optimum PowerControl Over Fading Channels”, IEEE Transactions onInformation Theory, 45(5), pp. 1468-1489, (1999).[3] J. Campello. ”Practical Bit Loading for DMT”, Proc.International Conference on Communications (ICC), pp.801-805, June 1999.[4] T.M. Cover, J.A. Thomas. Elements of InformationTheory, Wiley & Sons, London, (1991).[5] Digital Audio Broadcast, http://www.worlddab.org.[6] Digital Video Broadcast, http://www.dvb.org.[7] IEEE 802.11, http://grouper.ieee.org/groups/802/11/.[8] D. Hughes-Hartogs. “Ensemble Modem Structure forImperfect Transmission Media”, U.S. Patents No.4,679,227 and 4,731,816 and 4,833,706, (1989).[9] B.S. Krongold, K. Ramchandran, D.L. Jones.”Computationally Efficient Optimal Power AllocationAlgorithm for Multicarrier Communication Systems”,Proc. International Conference on Communications(ICC), pp. 1018-1022, June 1998.[10] C. Mutti, D. Dahlhaus, T. Hunziker, and M. Foresti. “Bitand Power Loading Procedures for OFDM Systems withBit-Interleaved Coded Modulation”, InternationalConference on Telecommunications (ICT), pp.1422-1427, 2003.[11] K. Song, A. Ekbal, and J.M. Cioffi. “AdaptiveModulation and Coding (AMC) for Bit-interleavedCoded OFDM (BIC-OFDM),” Proc. InternationalConference on Communications (ICC), pp. 3197-3201,June 2004.[12] E. Telatar. “Capacity of Multi-antenna GaussianChannels”, ATT-Bell Labs Internal Technical Memo,(1995).