2003 4th IEEE Workshop on Signal Processing
`Advances In Wireless Communications
`
`A MIMO SYSTEM WITH BACKWARD COMPATIBILITY FOR OFDM BASED WLANS
`
`Jianhua Liu Jian Li
`
`Petre Sroica
`
`Dept. of Electrical and Computer Engineering
`University of Florida, P.O. Box 116130
`Gainesville, FL 3261 1, USA
`
`Department of Systems and Control
`Uppsala University, P.O. Box 337
`SE-75105 Uppsala, Sweden
`
`ABSTRACT
`Orthogonal frequency-division multiplexing (OFDM) has been
`selected as the basis for the new IEEE 802.1 l a standard for high-
`speed wireless local area networks (WLANs). We consider dou-
`bling the data rate of the IEEE 802.1 la system by using a multi-
`input multi-output (MIMO) system with two transmit and two re-
`ceive antennas. We propose a preamble design for this MIMO sys-
`tem that is backward compatible with its single-input single-output
`(SISO) counterpart as specified by the IEEE 802.11a standard.
`Based on this preamble design, we devise a sequential method for
`the estimation of the carrier frequency offset (CFO), symbol tim-
`ing, and channel response. We also provide a simple soft-detector
`to obtain the soft-information for the Viterbi decoder. Both the
`sequential parameter estimation method and the soft-detector are
`ideally suited for real-time implementations. The effectiveness of
`our methods is demonstrated via numerical examples.
`
`1. INTRODUCTION
`
`Orthogonal frequency-division multiplexing (OFDM) has been se-
`lected as the basis for the IEEE 802.11a 5 GHr hand high-speed
`wireless local area network (WLAN) standard [I]. This standard
`supports B data rate up to 54 Mbps by using a single-input single-
`output (SISO) system.
`Transmission data rates higher than 54 Mbps are of particular
`importance for future WLANs. Deploying multiple antennas at
`both the transmitter and the receiver is a promising way to achieve
`a high transmission data rate for multipath-rich wireless channels
`without increasing the total transmission power or bandwidth 121.
`The corresponding system is referred to as a multi-input multi-
`output (MIMO) wireless communication system.
`Among the various popular MIMO wireless communication
`schemes, the BLAST (Bell-labs’ LAyered Space-Time) approaches
`are particularly attractive (see, e.g., 131 and the references therein).
`BLAST attempts to achieve the potentially large channel capacity
`offered by the MIMO system (21. In BLAST systems, the data
`stream is demultiplexed into independent sub-streams that are re-
`ferred to as layers. These layers are transmitted simultaneously,
`i.e., one layer per transmit antenna. At the receiver, the multiple
`layers can be detected, for example, through successive detection
`via an interference cancellation and nulling algorithm (ICNA) [31.
`Our focus herein is on doubling the data rate of the SISO sys-
`tem as specified by the IEEE 802.1 l a standard by using two trans-
`mit and two receive antennas (referred to as the MlMO system in
`rnis work w a supported in pw by the National Science Foundation
`Grant CCR-0097114, the Intersil Corporation Contract 2001056, and the
`Swedish Foundation far Strategic Research (SSF).
`
`the sequel) based on the BLAST scheme. We propose a preamble
`design fM this M M O system that is backward compatible with its
`SISO counterpart as specified by the IEEE 802.1 la standard. That
`is, a SISO receiver can perform CFO, symbol timing, and channel
`response estimation based on the proposed preamble design and
`can detect up to the SIGNAL field. The SlSO receiver is then in-
`formed, by using, e.g., the reserved hit in the SIGNAL field, that
`a transmission is a SISO or not. Ow preamble design can be used
`with two transmit and any number of receive antennas. However,
`we mainly focus on the two receive antenna case herein.
`Based on our preamble design, we propose a sequential method,
`ideally suited for real-time implementations, to estimate the CFO,
`symbol timing, and MIMO channel response. The convolutional
`code specified in the lEEE 802.11a standard will also he used in
`our MlMO system for channel coding. As a result, soft-information
`from the MIMO detector is needed by the Viterbi Algorithm (VA)
`to improve the decoding performance. A List Spere Decoder (LSD)
`algorithm 141 was recently proposed to deliver soft-information.
`However, LSD is too complicated to be implemented in real-time.
`We present herein a simple MIMO soft-detector, ideally suited for
`real-time implementations, based on the unstructured least-square
`(LS) fitting approach. This soft-detector is computationally much
`more efficient than LSD; yet the efficiency is achieved at a cost of
`a small performance degradation.
`
`2. SYSTEM DESIGN
`
`Our MIMO system closely resembles its SISO counterpart as spec-
`ified by the IEEE 802.1 la standard, We first give a brief overview
`of the E E E 802.1 la based SlSO system before we proceed to de-
`scribe our MIMO system.
`
`2.1. IEEE 8OZ.lla Standard
`The OFDM based WLAN system, as specified by the IEEE 802.1 l a
`standard, uses packet-based transmission. Fig. 1 shows the packet
`structure specified by the standard. The nominal bandwidth of the
`OFDM signal is 20 MHz and the I/Q sampling interval t s is 50
`ns. The OFDM packet preamble consists of 10 identical short
`OFDM training symbols ti,i = 1 , 2 , . . . ,lo, each of which con-
`tains N c = 16 samples, and 2 identical long OFDM training sym-
`bols Ti,i = 1,2, each of which contains N s = 64 samples. Be-
`tween the short and long OFDM training symbols there is a long
`guard interval ((312) consisting of 2Nc = 32 data samples. GI2 is
`the cyclic prefix (CP) for the long OFDM training symbol TI, Le.,
`it is the exact replica of the last 2Nc samples of TI.
`The infomation carrying data are encoded in the OFDM DATA
`field. The binary source data sequence is first scrambled and then
`
`0-7803-785&W03/$17.00 G22003 IEEE
`
`130
`
`HUAWEI EXHIBIT 1012
`HUAWEI VS. SPH
`
`000001
`
`

`

`c
`
`field
`
`Fig. 1. Packet structure of the IEEE 802.1 la standard.
`
`Fig. 2. Proposed MIMO preamble (and SIGNAL field) structure
`
`Convolutionally encoded (CC). The CC encoded output is then
`punctured according to the data rate requirement and is segmented
`into blocks of length NCSPS (number of coded hits per OFDM
`symbol), each of which corresponds to an data OFDM symbol.
`The binary data in each block is first interleaved among the subcar-
`riers (referred to as the frequency-domain (FD) interleaving in the
`sequel) and then mapped (in groups of log, A bits) into A-QAM
`symbols, which are used to modulate the different data canying
`subcamers. Each data OFDM symbol in the OFDM DATA field
`employs Ns = 64 subcaniers, 48 of which are used for data sym-
`bols and 4 for pilot symbols. There are also 12 null subcaniers.
`The data OFDM symbols, each of which consists of NS = 64
`samples, are obtained via taking the IFFT of the data symbols, pi-
`lot symbols, and nulls on these Ns subcaniers. To eliminate the
`inter-symbol interference (ISI), each data OFDM symbol is pre-
`ceded by a CP or guard interval (GI), which contains the last N c
`samples of the data OFDM symbol.
`The SIGNAL field contains the information including the trans-
`mission data rate and data length of the packet. The information is
`encoded in 16 binary bits. There is also a reserved bit (which can
`be used to distinguish the MIMO from SISO transmissions) and a
`parity check bit. These 18 bits, padded with 6 zeros, are then CC
`encoded and mapped via BPSK onto the data carrying subcamers.
`
`2.2. SISO Data Model
`
`To establish the data model, consider first the generation of an
`data OFDM symbol in the OFDM DATA field. Let XSISO =
`[xi I: . . . &,IT
`be a vector of A's data symbols, where (.)T
`denotes the transpose, and xks, ns = 1,2,. . . , Ns, is the sym-
`bol modulating the nsth subcamer, which is equal to 0 for null
`subcarriers, 1 or -1 for pilot subcamers, and in C for data canying
`subcaniers. Here C is a finite constellation, such as BPSK, QPSK,
`I6-QAM, or 64-QAM. Let W N ~ E CNS N S be the FFT matrix.
`Then the data OFDM symbol s corresponding to xslso is obtained
`by IakingthelFFTofxsrso. that is,^ = WE,xslso/Ns, where
`( . ) H denotes the conjugate transpose.
`Let h(') = [ h t ) hj') .,. hf;_,lT be the FIR response
`of the channel. Here LF = rlOt,/tsl + 1 with t , being the
`root mean square (rms) delay spreading time and [XI denoting the
`1, h e - N ( 0 , (1 - e-is/tr)e-'F'S't-).
`smallest integer not less than x. We assume, for 1~ = 0, . . . , LF-
`This channel model is
`
`referred to as the exponential model.
`
`By discarding the first N c samples at the receiver (assuming a
`correct symbol timing), the noise-free and CFO free received sig-
`due to sampling the received signal, is
`nal vector z&o E C N S
`the circular convolution of h(t) and s. Hence the W output of the
`received data vector zs~so = z&o + eslso. where eslso is the
`additive zero-mean white circularly symmetric complex Gaussian
`noise, can be writren as [ 5 ]
`YSISO = diag{h)xs~so + WN,eslso E flSx1.
`
`(I)
`
`2.3. MIMO Preamble Design
`
`For the IEEE 802.1 la based SlSO system, the short training sym-
`bols can be used to detect the anival of the packet, set up AGC,
`compute a coarse CFO estimate, and obtain a coarse symbol tim-
`ing, whereas the long training symbols can be used to calculate a
`fine CFO estimate, refine the coarse symbol timing, and estimate
`the SlSO channel.
`The MIMO system considered herein has two transmit and
`two receive antennas. Two packets are transmitted simultaneously
`from the two transmit antennas. We design two preambles, one
`for each transmit antenna. We assume that the receiver antenna
`outputs suffer from the same CFO and has the same symbol timing.
`To be backward compatible with the SlSO system, we use the same
`short training symbols as in the SlSO preamble for both of the
`MIMO transmit antennas, as shown in Fig. 2.
`Channel estimation for MIMO systems has attracted much re-
`search interest lately. Orthogonal mining sequences tend to give
`the best performance (see, e&, 161 and the references therein). We
`also adopt this idea of orthogonal training sequences in our pream-
`ble design. In the interest of backward compatibility, we use the
`same TI and T2 as for the SlSO system for both of the two trans-
`mit antenna before the SIGNAL field, as shown in Fig. 2. After
`the SIGNAL field, we use T1 and TZ for one transmit antenna
`and -TI and -Tz for the other. This way, when the simultane-
`ously transmitted packets are received by a single SISO receiver,
`the SlSO recei!'er can successfully detect up to the SIGNAL field,
`which is designed to be the same for both transmit antennas. The
`reserved bit in the SIGNAL field can tell the SlSO receiver to stop
`its operation whenever a MIMO transmission follows or otherwise
`to continue its operation. The long training symbols before and af-
`ter the SIGNAL field are used in the MIMO receivers for channel
`estimation.
`
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`

`2.4. MIMO Data Model
`To stay as close to the IEEE 802.11a standard as possible, we use
`in our MlMO system the same scrambler, convolutional encoder,
`puncturer, FD interleaver, symbol mapper, pilot sequence, and CP
`as specified in the standard. To improve diversity, we add a simple
`spatial interleaver to scatter every two consecutive bits across the
`two transmit antennas.
`Consider the nsth subcarrier (for notational convenience, we
`drop the notational dependence on ns below). Consider the case of
`N receive antennas. Let H = [h,,,] E C N x 2 denote the MlMO
`channel matrix for the nsth subcanier, where hn,m is the channel
`gain from the mth transmit antenna to the nth receive antenna for
`the nsth subcarrier. Let y denote a received data vector for the
`nsth subcanier. Then it can he written as
`y = H x + e E @ N x 1 9
`(2)
`where x = 1x1 z 2 l T is the 2 x 1 QAM symbol vector sent on
`the nsth subcarrier and e
`circularly symmetric complex Gaussian noise with variance 0'.
`In Section 4, we will provide a soft-detector based on this model.
`
`- N(O,U'IN) is the additive white
`
`3. SEQUENTIAL CHANNEL ESTIMATION
`In this section, we present our sequential CFO, symbol timing,
`and MIMO channel estimation approach based on our preamble
`design. The estimates are obtained in the order presented below.
`
`3.1. Coarse CFO and Symbol Timing Estimation
`Let zn(l) = z:(l) + e,,(I), n = 1 , . . . , N , denote the Ith time
`sample of the signal received from the nth receive antenna, stm-
`ing from the moment that the receiver AGC has become station-
`ary (the receiver AGC is assumed to become stationary at least
`before receiving the last two short OFDM training symbols and
`remain stationary while receiving the remainder of the packet). In
`the presence of CFO, e, we have 171:
`n = 1 , . . . , N .
`$ ( l + N ~ ) = z r ( ~ ) e j ~ ~ C ~ '
`(3)
`,
`
`For each receive antenna output, consider the correlation between
`two consecutive noise-free received data blocks, each of which is
`of length N c . Then the sum of the correlations for all receive
`antennas can be written as
`z ~ ( I ) ( z : ( I + NC))' = Pe
`
`N k + N C - l
`
`- j 2 N ~ ~ r
`9
`
`(4)
`
`n=l I=k
`
`A
`
`where P = E:=, C,"=-,-' lzp(l)1'. (.)* denotes the complex
`conjugate, and k is any non-negative integer such that zEe(k +
`2Nc - 1) is a sample of the nth receive antenna output due to the
`input (transmit antenna output) being a sample of the short OFDM
`training symbols. Let
`zn(l)z;(l + N ~ )
`- - j Z N ~ n c + e
` = Pe
`PI (5)
`
`N N c - 1
`
`PS =
`n=1 1-0
`where e p is due to the presence of the noise. We calculate the
`coarse CFO as 181
`
`where L x denotes taking the argument of x.
`We next correct the CFO using Zc to get the data samples
`n = 1 , 2 , , . . , N . In the
`
`ziC'(I) as ~ ~ " ( 1 ) = zn(I)e-'*'"'c,
`sequel, we only consider the CFO corrected data given above. For
`notational convenience, we drop the superscript of ~ ~ ~ ' ( 1 ) .
`Now we can use a correlation method similar to the one pro-
`posed in 171 to estimate the coarse symbol timing. Here the symbol
`timing is referred to as the starting time sample due to the input
`being the long OFDM training symbol TI (before the SIGNAL
`field). Once the starting time sample due to T I is determined, we
`can determine the starting time sample for every OFDM symbol
`thereafter. (According to the specification of the EEE 802.11a
`standard and the sampling rate of 20 MHz, the true symbol timing
`TO is 193.)
`From (4), we note that the correlation (after the CFO correc-
`tion) is approximately the real-valued scalar P (plus a complex-
`valued noise). Hence we propose to use the following real-valued
`correlation sequence for coarse symbol timing determination. We
`calculate the correlation sequence in an iterative form similar to
`the complex-valued approach in L7] as follows:
`Pn(k + 1) Pn(k) +
`[zn(k + Nc)z,(k + 2Nc) - zn(k)z;(t + N c ) ] ,(7)
`Re
`" - 1
`where Re (.) denotes the real part of a complex entity. We start the
`iteration by using PR(O) = Re(Ps).
`When some of the data samples of the sliding data blocks are
`taken from the received data due to the input being GI2 or the
`long training symbols following the short OFDM training symbol,
`P R ( ~ ) will drop since (3) no longer holds. This property is used
`to obtain the coarse symbol timing. Let T p denote the first time
`sample when PR(k) drops to less than half of its peak value. Then
`the coarse symbol timing can be written as
`Tc = TP + -Nc + hrc.
`3
`2
`Note that the second term at the right hand side of (8) is due to the
`fact that P R ( ~ ) will drop to approximately one half of its maxi-
`mum value when the data samples of the second half of the second
`of the two sliding blocks are due to GI2 in the preamble; the third
`term is due to one half of the length of G12, since our goal of
`c o m e timing determination is to place the coarse timing estimate
`between the true timing To = 193 and TO - Nc = 177 to make
`accurate fine CFO estimation possible.
`
`(8)
`
`N
`
`3.2. Fine CFO and Symbol Timing Estimation
`The fine CFO estimate can be computed as
`
`We can use PF in the same way as Zc to correct the CFO. We as-
`sume that for the data we use below ZF has been already corrected.
`(The fine CFO estimation is accurate enough for the following fine
`symbol timing and MlMO channel response estimation. However,
`it can never he perfect due to the noise. Hence before data bits de-
`tection, we need to use the pilot symbols to track the CFO residual
`phase for each data OFDM symbol. A maximum-likelihood (ML)
`CFO residual tracking scheme is given in Appendix A,)
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`Let yn denote the Ns-point FFT of the data block from the
`nth receive antenna, starting from Tc, and let hc:,,,
`be the FIR
`channel in the time-domain between the mth transmit antenna and
`the nth receive antenna, m = 1,2, n = 1,2,. . . , N. Then, by
`neglecting the existence of the residual CFO, yn can be written as
`yn = X B W N ~ Ea=, h:),,,+WNsen, whereXB isadiagonal
`matrix with the 52 known BPSK symbols and 12 zeros, which
`form the TI in Fig. 2, on the diagonal. We get an estimate of
`h:) = E,=,
`- NS ~y.,/Ns. Let TI denote
`(t) ash, ^ ( t ) - w H X
`hn,,,,
`2
`the index of the first element of Cr='=, lhc)I that is above 1/3 of
`1h:)l. Then the fine
`the maximum value of the elements of
`symbol timing TF is obtained as
`TF = Tc + TI - 3.
`(10)
`The last term above is chosen to be 3 to ensure that TF > To with
`negligible probability.
`
`3.3. MIMO Channel Estimation
`After we obtained T F , we can now estimate the MIMO channel
`response. Let yn,l denote the Ns-point FFT of the average of the
`two consecutive blocks, each of which is of length N s , associated
`with the two long training symbols before the SIGNAL field, from
`the nth receive antenna. Let yn,2 denote the counterpart of yn,l
`after the SIGNAL field. Then, for the nsth subcanier, we have
`%,l = Z B (h,J + h",l), yn,2 = Z B (h,J - hn,2) ,
`( I 1)
`where X B denotes the nsth diagonal element of XB and yn,i de-
`notes the nsth element ofy,,;, i = l, 2. Solving (11) yields
`&%,I = ZE(Yn.1 + Ys,2)/2,
`jLn2 = XB(Y,,l - y*,2)/2.
`
`(12)
`(13)
`
`4. A SIMPLE MIMO SOFT-DETECTOR
`
`With the CFO, symbol timing, and MIMO channel determined and
`accounted for. we can proceed to detect the data bits contained in
`each BLAST layer and subcanier of the data OFDM symbols in
`the OFDM DATA field. In the sequel we present a very simple
`soft-detector for the MlMO system. Note that this soft-detector
`can be used in a general setting of the BLAST system and hence
`we present it in a general framework based on the data model of
`(21, where H is assumed to he N x M and x to be M x 1. (We
`use H to replace H in some of our simulations.)
`Consider first the ML hard detector of the BLAST system. For
`the data model of (2), the ML hard detector is given by:
`
`? = arg min
`lly-~x11~,
`X E C M X l
`
`(I4)
`
`where 11.112 denotestheEuclideannorm. Let" =
`Then we'can obtain an UnstNCtured LS estimate Sui of x as:
`
`= Hty = x + H t e f x + c .
`
`(15)
`
`Note that S,, is the soft-decision statistic that we are interested in.
`We refer to this simple scheme of obtaining a soft-decision statistic
`ac the MIMO soft-detection scheme. We remark that a necessary
`
`condition for HHH to be nonsingular is N 2 M and c is still
`Gaussian with zero-mean and covariance matrix
`
`E[ccH] = U ' H ~ ( H ~ ) ~ = u2(HHH)-'.
`
`(16)
`
`Due to the use of the interleaver and deinterleaver, the data
`bits contained in x are independent of each other. By ignoring
`the dependence among the elements of c, we can consider only
`the marginal probability density function (pdf) for the elements
`, M , o f S u S . L e t H t =[6 ... ~ I M ] ~ E
`d , . ( m ) , m = l , 2 , . . .
`C M X N . Then the mth element of c, m = 1 , 2 , . . . , M , can be
`written as cm = h z e . Obviously, c, is still Gaussian with zero-
`mean and variance
`
`"
`uf = E[lcmI2] = llhmll u .
`2 2
`
`(17)
`
`(The estimate of the above noise variance u' can he easily ob-
`tained via the difference of the two consecutive blocks of the nth
`receive antenna, from which we got y..~ [cf. (1 111.) uf and i!$)
`provide the soft-information for the mth, m = 1,2,, , , , M , sym-
`bol in L, needed by the VA. Note that the noises corresponding
`to different layers have different variances which means that the
`symbols corresponding to different layers have different quality.
`This unbalanced layer quality is the reason why we want to use a
`spatial interleaver.
`
`5. NUMERICAL EXAMPLES
`
`In this section, we provide numerical examples to demonstrate the
`effectiveness and performance of our sequential parameter estima-
`tion method as well as the simple MlMO soft-detector.
`We consider doubling the maximum 54 Mbps data rate by us-
`ing two transmit and two receive antennas, i.e., M = N = 2. In
`our simulations, each of the M N = 4 time-domain MlMO chan-
`nels is generated according to the exponential model; the 4 chan-
`nels are independent of each other.
`Due to the fact that 52 out of 64 subcaniers are used in the
`OFDM WLAN system, the S N R for the SlSO system used herein
`is defined as 52/(64u2) for the constellations whose average ener-
`gies are normalized to 1. Whereas for the MIMO system, the SNR
`is defined as 52/(128u2) (i.e., we use the same total transmission
`power for the MlMO system as for its SISO counterpart).
`We first provide a simulation example for symbol timing esti-
`mation. Two curves in Fig. 3 show the lo4 Monte-Carlo simula-
`tion results of the coarse symbol timing estimates for the exponen-
`tial channels with t, = 25 and 50 ns, respectively, when SNR = IO
`dB. The other two curves in Fig. 3 show the lo4 Monte-Carlo sim-
`ulation results of the fine symbol timing estimates based on their
`corresponding coarse timing estimates. Note that our simple fine
`symbol timing approach gives highly accurate timing estimates.
`We then provide a simulation example to show the effective-
`ness of the MlMO channel estimator and the PER (uacket error
`rate) performance of the MIMO soft-detector. (One'.packet con-
`sists of 1000 bvtes.! In Fie. 4. we show the lo4 Monte-Carlo sim-
` ~.~ , ~ ,
`
`ulation results of the PER performance of the MIMO soft-detector
`as a function of the SNR for the MlMO system, with t, being 50 ns
`for the exponential channels, when the data rate is 108 Mbps. We
`consider two cases: the case of perfect knowledge for CFO, sym-
`bol timing, and MIMO channel and the case of estimated channel
`parameters. (For the second case, besides the parameters obtained
`with our sequential approach, we correct the CFO residual phase
`
`~~
`
`~
`
`~
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`coarse timing. l,=25ns
`
`~
`
`IDrCOarSBflmlng
`
`0 6
`
`0 3
`
`0 2
`
`0 1
`
`symbol liming
`
`Fig. 3. Coarse and fine symbol timing estimates,
`
` :
`.. :
`
`.
`
`.
`
`
`
`: .
`
`6
`
`.
`
`.
`
`I C ’
`
`patible with its SlSO counterpart as specified by the IEEE 802.1 l a
`standard. Based on this preamble design, we have devised a se-
`quential method for the estimation of CFO, symbol timing, and
`MIMO channel response. We have also provided a simple MIMO
`soft-detector. Both the sequential parameter estimation method
`and the soft-detector are ideally suited for real-time implementa-
`tions.
`
`Appendix A. Phase Correction using Pilot Symbols
`
`As we mentioned earlier, each data OFDM symbol contains four
`known pilot symbols. We denote these pilot symbols by a 4 x
`1 vector p. The pilot symbols can be used to correct the CFO
`residual phase foreach data OFDM symbol after CFO correction
`Let yp’ be the vector containing the corresponding four
`using i ~ .
`elements of the FFT output of an data OFDM symbol in the OFDM
`DATA field received from the nth antenna, n = 1 , 2 , . . . , N . Let
`hkk be the 4 x 1 estimated channel vector from transmit antenna
`. -
`m to receive antenna n for the four corresponding subcarriers. Let
`P = diag{p}. We have yip) = e1$P El=, h$k + &),n =
`1 , 2 , . . . , N , where Q is the CFO residual phase and {eiP’}Ll
`are zero-mean white circularly symmetric complex Gaussian noise
`vectors. Then the ML criterion leads to
`N I1
`
`112
`
`20
`
`21
`
`22
`
`23
`
`24
`
`25
`SNR (dBl
`
`26
`
`I
`27
`
`,
`28
`
`
`,
`29 30
`
`Fig. 4. PER versus SNR at the 108 Mhps data rate for the expo-
`nential channels with t , = 50 ns.
`
`as well.) As a reference, we also give the PER curves of the soft-
`detector for the SISO system (with the data rate being 54 Mhps).
`We see, from the PER curves, that both the preamble design and
`the sequential channel parameter estimation algorithm are effec-
`tive in that the gap between the PER curves corresponding to the
`perfect channel knowledge case and the estimated channel param-
`eter case for the MIMO system is no more than that of the SlSO
`system. We also see that the MIMO soft-detector is effective in
`that the MIMO system needs only 2 to 3 dB extra total transmis-
`sion power to keep the same PER (we are mostly interested in
`PERs being 0.1, according to the IEEE 802.11a standard) as its
`SlSO counterpart, but with the data rate doubled.
`Note that the MIMO soft-detector is outperformed by LSD
`in terms of PER. However, the MIMO soft-detector is orders of
`magnitude more efficient than LSD, and is ideally suited for real-
`time implementations.
`
`6. CONCLUDING REMARKS
`
`We have proposed a preamble design for the MIMO system with
`two transmit and two receive antennas, which is backward com-
`
`7. REFERENCES
`
`[I] IEEE Standard 802.1 la-1999, “Wireless LAN medium access
`control (MAC) and physical layer (PHY) specifications: High
`speed physical layer (PHY) in the 5 GHz band,” 1999.
`[2] G. 1. Foschini and M. J. Cans, “On limits of wireless commu-
`nications in a fading environment when using multiple anten-
`nas:’ Wireless Personal Comniunications. vol. 6, pp. 31 1-335,
`March 1998.
`131 G. Golden, C. Foschini, R. Valenzuela, and P. Wolniansky,
`“Detection algorithm and initial laboratory results using V-
`BLAST space-time communication architecture,” Electronic
`Letters, vol. 35, pp. Ik15, January 1999.
`141 B. M. Hochwald and S. ten Brink, “Achieving near-capacity
`on a multiple-antenna channel,” IEEE Transactions on Com-
`munications, submitted in 2001.
`(51 Z. Wang and G. Giannakis, “Wireless multicarrier communi-
`cations,” IEEE Signal Processing Magazine, vol. 17, pp. 29-
`48, May 2000.
`[61 E. G. Larsson and J. Li, “Preamble design for multiple-
`antenna OFDM-based WLANs with null subcaniers,” IEEE
`Signal Processing Letters, vol. 8, pp. 285-288, Nov. 2001.
`[7] T. M. Schmidl and D. C. Cox, “Robust frequency and timing
`synchronization for OFDM,” IEEE Transactions on Commu-
`nications, vol. 45, pp. 1613-1621, December 1997.
`[81 J. Li, G. Liu, and G. B. Giannakis, “Carrier frequency offset
`estimation for OFDM based WLANs,” IEEE Signal Process-
`ing Letters, vol. 8, pp. 80-82, March 2001.
`
`134
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`HUAWEI EXHIBIT 1012
`HUAWEI VS. SPH
`
`000005
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