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MIMO-OFDM modem for WLAN Authors: Lisa Meilhac, Alain Chiodini, Clement Boudesocque, Chrislin Lele, Anil Gercekci NewLogic Technologies S.A.R.L., France OFDM signals are generated using the fast Fourier transform (FFT). Abstract: On the receiver side, the equalization of the The future 802.11n WLAN standard that will received signals, which are generally distorted by a emerge from the TGn group work should be based frequency-selective channel (due to multipath), is on a MIMO-OFDM physical layer. This paper easily performed in the frequency domain: each gives an introduction to this promising technology subcarrier is indeed equalized by a single complex and to 11n standardization process. Then, we coefficient, which makes this technique very robust highlight the changes required to extend an OFDM against multipath fading. WLAN modem to a MIMO-OFDM modem. Finally, we focus our study on the MIMO-OFDM The worldwide success of the OFDM based decoding block, giving performance and 802.11a/g WLAN standards [3-4] along with the complexity results. astonishingly high spectral efficiencies achieved by systems implementing the MIMO technology have naturally led engineers to envisioning high date 1. Introduction rate, OFDM, MIMO-based, WLAN standards to supersede existing ones. Multiple Input Multiple Output (MIMO) is an advanced physical layer technology that uses First, this paper gives an overview of this MIMO multiple antennas at both transmit and receive based WLAN standardization process. Then, in sides. It is well known that antenna diversity offers section 3, we present the general architecture of a robustness and gain over single antenna schemes. WLAN MIMO modem. Main functionalities are MIMO also improves the transmission’s spectral described. In section 4, we focus our study on the efficiency. Indeed, different signals can be specific MIMO detection block. We describe and transmitted simultaneously (i.e. time- and compare existing decoding algorithms in terms of frequency-wise) by the different transmit antennas, performance and complexity. and be correctly decoded by the multi-antenna receiver. Even more, the capacity of MIMO systems can linearly increase with the number of 2. The 11n standardization process transmit antennas under a rich multipath environment [1-2]. 802.11 has mandated Task Group “n” [5] with developing a high-throughput WLAN method On the other hand, Orthogonal Frequency Division allowing a throughput greater than 100 Mbps at the Multiplexing (OFDM) is a spectrally efficient MAC level. Now, given the inefficiency of the modulation technique invented in the 1960’s and CSMA/CA protocol, this requirement translates now widely used in such popular communication into a 130 Mbps throughput at the physical layer systems as WLAN, DVB, etc. In a nutshell, this (PHY) level. technique allows squeezing a (usually) large As of March 2005, two contending proposals have number of complex sine waves (also called emerged and are still being debated in the TGn. subcarriers) in a limited bandwidth. Since these They go under the names of TGnSync (led by Intel, subcarriers are mutually orthogonal, they don’t Agere and Qualcomm) and WWiSE, (led by TI, interferer with one another. On the transmitter side, ST). These two groups continue to progress in the definition of their own proposals whilst looking at 3. MIMO-OFDM modem ways of harmonizing in order to eventually avoid a standstill. Despite this attitude, the March 2005 architecture vote has revealed a persistent 54%-46 % split for both proposals. A schematic representation of a two-antenna To reach >130Mbps transmission rates without MIMO-OFDM receiver for WLAN is given in using complex modulation schemes, MIMO Figure 1. technique has been proposed by both groups with The first operation consists in detecting the signal 20MHz channelization and up to 64 QAM of interest and appropriately setting the analog gain. modulation as mandatory features. The main Then, the frequency offset must be estimated and differences come from the ratio data/pilot compensated for. Indeed, due to OFDM properties, subcarriers and preamble definition. Main optional the frequency synchronization is one of the most PHY modes are LDPC coding, and 40MHz critical issues. In parallel, timing synchronization channelization. Some of the features are shown in algorithms are run to correctly position the FFT Table 1. Even though major differences remain at window within the OFDM symbol. Despite the both the PHY and MAC levels, a significant presence of a guard interval, the OFDM receivers industry pressure will help both groups converge to are sensitive to timing inaccuracies. In the a standard. considered WLAN context, time and frequency synchronizations are initiated during the preamble. Features TgnSync WWiSE Then, a pilot-based tracking mechanism takes over Bandwidth (M) 20 MHz mode (M) 20 MHz mode during the rest of the packet. extension (O) 40 MHz mode (O) 40 MHz mode All of these synchronization functionalities are (M) 2 spatial (M) 2 spatial MIMO OFDM; streams streams already part of a classical WLAN OFDM receiver. SDM @ 20MHz mode @ 20MHz mode The stake in designing a MIMO-OFDM modem is (max 144 Mpbs) (max 135 Mpbs) to extend these algorithms to the multi-antenna Support for (O) 3 or 4 spatial (O) 3 or 4 spatial context taking advantage of the diversity while higher rates streams streams avoiding a huge increase of the complexity. Once Higher coding (M) 1/2, 2/3, 3/4, (M) 1/2, 2/3, 3/4, rate 5/6 5/6 the synchronization is acquired, channel estimation (M) 800 ns (M) 800 ns is performed in the frequency domain using a Guard Interval (M) 400 ns dedicated preamble section. In MIMO, each sub- Transmit (O) Basic (SVD carrier’s channel frequency response is a matrix (O) Supported beamforming beamforming) and the preamble should be defined to facilitate its STBC (O) Spatial (O) Nt=1 and Nt Spreading + CS =2 STBC estimation. This matrix is then used in the MIMO (M) 52 (4 pilots) (M) 54 (2 pilots) detection block, which aims at compensating the Number of @ 20 MHz @ 20 MHz channel-induced mix between transmitted antenna subcarriers (O) 108 (6 pilots) (O) 108 (4 pilots) streams. @ 40 MHz @ 40 MHz (O) LDPC (max (O) LDPC (max The decoded sequence of bits is finally provided to Advanced coding a Viterbi decoder after de-interleaving. block: 1728 bits) block: 1944 bits) (M: Mandatory / O: Optional) Table 1 – Main characteristics of IEEE’s MIMO- OFDM standards Frequency GI Freq off FFT Domain ADC Rx Filter removal Comp. 64 / 128 MIMO Offset RF Time Time Frequency tracking decoding Deinter- Analog Domain Sync est (spatial leaving using pilots demultiplexing) GI Freq off FFT Viterbi ADC Rx Filter removal Comp. 64 / 128 Channel matrix Descrambler AGC Estimation Packet detection MAC Figure 1 – A typical MIMO-OFDM modem architecture 4. MIMO-OFDM detection block given transmitted hard bit b ij ( ± 1 ), the associated soft bit s ij is ideally a real number, which gives us 4.1. Context and notations the following information: • Through the sign of s ij we can infer whether Various detection algorithms have been developed for implementation in flat fading MIMO systems, the transmitted bit b ij was a one or a zero. assuming a constant channel matrix. They can be • The module of s ij , s ij , gives us a degree of easily extended to the MIMO-OFDM context by applying them on every subcarrier constituting an reliability concerning the correctness of our OFDM symbol. Indeed, in the case of an OFDM decision. The greater the module, the higher the system, it is customary to assume that each received confidence about the decision made. subcarrier is distorted through the application of a single channel coefficient (i.e. flat fading is The relevance of the soft-bit is very important as a assumed on the subcarrier scale). Thus, for the sake convolutional code decoder, implemented in the of both simplicity and clarity, the algorithm form of a Viterbi decoder, follows the MIMO description shall just apply to a single subcarrier. decoder. It is well known that a soft-input Viterbi algorithm performs more efficiently in terms of bit Let us denote by N and M the respective numbers errors than a hard-input one. Thus, all the decoding of transmit and receive antennas. In the 802.11n algorithms described here include a soft-bit context, mapping is done through the use of K- generation part. QAM constellations with K= 4, 16, 64. Let us denote by p = log 2 (K ) the number of bits per 4.2. Main algorithms th This section describes some reference MIMO symbol and by ai, the symbol transmitted on the i antenna. It corresponds to the set of p bits denoted decoding algorithms. by bi1, …, bip. This model is illustrated on Figure 2. 4.2.1 Soft-output ML-Bit decoder r1 b11 … b1p a1 s11 … s1p Mapping MIMO Channel Decoder This algorithm consists in directly evaluating the Matrix H Soft bit reliability of each decoded bit according to the Log- bN1 … bNp Mapping generation sN1 … sNp aN rM Likelihood Ratio criterion. Each soft-bit value is Figure 2 - Schematic representation of a MIMO given by the following formula transmission P(bij = +1 / r ) s ij = ln Let us denote by x and r the transmitted and P(bij = −1 / r ) received vectors respectively, After doing some mathematical manipulations, x = [a1 a 2 ...a N ] T using the Bayes rule and the max-log approximation, we get r = [r1 r2 ...rM ] T r−Hx r−Hx 2 2 T u designates the transpose of vector u. s i, j ≈ min - min { x / bij = −1} σ2 { x / bij =1} σ2 From the previously defined channel assumption, we get The complexity of this algorithm exponentially r = Hx+n grows with the number of transmit antennas and soon becomes prohibitive if several antennas are where n is the noise vector and H is the M × N involved. channel matrix. We assume that the noise is white and Gaussian with its covariance matrix given by σ 2 * IM where I M designates the M × M identity 4.2.2 ML-Symbol decoder matrix. The purpose of this algorithm is to reduce the complexity of the previous one by determining the MIMO detection allows recovering the transmitted sequence of bits. Soft-bits are generated for this most likely transmitted multi-antenna symbol x ˆ purpose. What we call soft bit is a metric rather than its binary elements. representing the probability of a demodulated bit x = min r − H x 2 being a one or a zero. It is obtained by weighting a ˆ given decoded bit by a reliability factor obtained { x} from the MIMO decoding. This means that for a 3 Then, a soft-bit value is obtained for each bit 4.3. Performance and complexity study composing the N-symbol through regular In this section we present some performance demapping (and possibly weighting). simulation results in typical WLAN propagation environments. We have applied the channel model 4.2.3 Linear decoders studied and developed by the IEEE 802.11 TGn Channel Model Special Committee whose principle The idea consists in finding a matrix G such that is described in [6]. This model introduces several x = Gr ˆ reference channels, called A to F, corresponding to different environments. We use the channel model be an estimate of the transmitted symbol vector. G B, which corresponds to a typical residential can be the pseudo-inverse of the channel matrix H environment with a delay spread of 15ns, and the G = ( H H H ) −1 H H channel model D, which simulates a typical office This estimator is called Zero-Forcing. It produces environment with a delay spread of 50ns. an enhancement of noise. G can also be defined by minimizing the Minimum Mean Square Error The simulation has been performed following the criterion. This leads to TgnSync features. However, as the main purpose is G = ( H H H + σ 2 I N ) −1 H H to compare the decoding algorithm performance, the same conclusions would have been obtained using the WWISE scheme. 1000-byte packets have 4.2.3 Successive interference cancellation been transmitted over 2 antennas and received with (SIC) based decoders 2 antennas. Two modulation coding schemes (MCS) have been tested: MCS = 10, which The idea here is to successively estimate each involves a QPSK and a coding rate ¾, and MCS = component of the transmitted N-symbol vector 14, which features the same coding rate but a 64- while treating the other ones as mere interference. QAM. Figures 3 and 4 present the performance Each detected component is then removed from the results in channel B and D for MCS of 10. Figure 5 composite received signal, thereby decreasing the presents the results in channel D for MCS 14. overall level of interference before the estimation of the following component takes place. This One can see on the different figures that the ML-Bit process improves the estimator performance on the algorithm performs at least 3dB better than the ML- next component compared to the previous one. symbol one. This incidentally confirms a well- However, it may suffer from an error propagation known result regarding the performance of hard effect. The order in which the components are versus soft input decoding. On the other hand, processed is indeed crucial to achieving high linear and SIC decoders reach about the same performance. An optimal ordering procedure performances. But, the most critical remark is the (typically based on the SINR) is thus needed to loss of the linear approach compared to ML based enhance the performance of the algorithm. one. The algorithm steps are given below. • Determine a detection order ( i1 , i 2 … i N ) • Perform initialization o k = 1; o y =r 1 • Loop over index k, while k <=N o Define the estimator g k = hik (σ 2 I M + ∑ hil hil ) −1 H H l >k o Calculate the estimate of the k-th symbol ~ aik = g k y k o Make a decision on the estimation ~ aik = slicing (aik ) ˆ Figure 3 – MIMO-OFDM detection algorithms o Remove the estimated symbol from comparison in PER vs SNR for a 2x2 system with received signal QPSK modulation and channel of type B y k +1 = y k − aik hik ˆ o Increment the symbol index k = k+1; 4 5. Conclusion In this paper, a comparative study of several popular MIMO detection algorithms has been presented. Performance-wise, simulations results have clearly established that the ML-bit one outperforms its peers. However, its prohibitive complexity makes its near future implementation highly unlikely given the current state of the art. On the other hand, since ZF and SIC perform rather poorly, it is very likely that one will move towards a suboptimal, hybrid detection scheme. Figure 4 – MIMO-OFDM detection algorithms References comparison in PER vs SNR for a 2x2 system with [1] G. J. Foschini and M. J. Gans, “On limits of QPSK modulation and channel of type D. wireless communications in a fading environment when using multiple antennas,” Wireless Pers.Commun., vol. 6, no. 3, pp. 311–335, Mar. 1998. [2] D. Gesbert, M. Shafi, D.-S. Shiu, P. J. Smith, and A. Naguib, “From theory to practice: An overview of MIMO space-time coded wireless systems,” IEEE Jour. Select. Areas in Commun., vol. 21, no. 3, pp. 281– 302, April 2003. [3] Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: High- Speed Physical Layer in the 5 GHz Band, IEEE Standard 802.11a-1999. Figure 5 – MIMO-OFDM detection algorithms comparison in PER vs SNR for a 2x2 system with [4] Further Higher-Speed Physical Layer Extension 64QAM modulation and channel of type D. in the 2.4 GHz Band, Draft IEEE 802.11g Stand. [5] “IEEE 802.11n,” http://grouper.ieee.org/groups/802/11. Finally, Figure 7 presents a coarse comparison of the different algorithms in terms of complexity. In [6] J-P. Kermoal, L. Schumacher, K. I. Pedersen, P. particular, it illustrates the exponential complexity E. Mogensenand, F. Frederiksen, “A stochastic of ML based algorithms. MIMO radio channel model with experimental validation” IEEE Jour. Select. Areas in Commun., vol. 20, no. 6, pp. 1211– 1226, August 2002. Figure 7 – MIMO-OFDM detection algorithms comparison in terms of complexity for 2x2 systems and different constellation size. 5