Doppler-assisted Channel Estimation

Technical Field

This invention concerns the reception of Orthogonal Frequency Division Multiplexed (OFDM) signals, and in particular Doppler-assisted channel estimation for highly mobile OFDM Systems. In a further aspect it concerns mobile terminals or base stations.

Background Art

To achieve very high data rates, multiple input multiple output (MIMO)-orthogonal frequency division multiplexing (OFDM) techniques have been adopted in the 3rd Generation Partnership Project Long Term Evolution (3GPP LTE) [1] and Worldwide Interoperability for Microwave Access (WiMAX) [2] standards. MIMO-OFDM symbol detection in these standards requires estimation of channel state information (CSI). The reliability of symbol detection depends on the accuracy of channel estimation at the receiver. In order to accurately estimate the wireless channel, a number of sub-carriers in an OFDM symbol are used as pilots [3]. The remaining sub-carriers are then either employed to transmit data symbols or are unused sub-carriers. Recently, high mobility transmission has been considered as one of the important key features of LTE and WiMAX standards. These standards need to provide support for high mobility users that move at speeds above 120 Km/h. When users are highly mobile, the wireless channel becomes time-variant and frequency-selective within one OFDM Symbol. The Doppler spread, caused by the high mobility, destroys the orthogonality and creates inter- carrier interference (ICI) between OFDM sub-carriers. As a consequence, the existing channel estimation methods [3]-[l l ], that assume an invariant wireless channel within one OFDM symbol, are no longer adequate.

OFDM transmission over rapidly time varying multipath fading channels has been considered in a number of recent papers [12]-[18]. In [12], estimation of time-domain channel coefficients is performed by applying a hybrid frequency/time-domain channel estimation algorithm based on a linear approximation of the time variations of each channel coefficient within one OFDM symbol. However, this linear approximation is inaccurate in the presence of very high mobility [14]. To overcome the channel estimation problem for highly mobile users, [13]-[16] propose different algorithms, that incorporate Doppler spread information in the channel estimation process. In [13] and [14], basis expansion models (BEM) [19], are employed to represent the wireless channel. The Doppler information is used to design the basis for the BEM. In [15] and [16], the Doppler spread information are used for computing the frequency-domain and time- domain channel correlations in the channel estimation process. These estimates can be used to improve the channel estimation process. In [17] and [18], iterative channel estimation schemes, where detected data symbols in previous iterations are employed to refine the channel estimation, are proposed. Disclosure of the Invention

In a first aspect the invention is a method for operating a receiver of orthogonal frequency division multiplexed (OFDM) signals, comprising the steps of:

(a) Estimating the pilot channel coefficients using received pilot symbols.

(b) Estimating each time-domain data channel coefficients as a weighted interpolation between two closest blocks of pilot channel coefficients.

(c) Using the time-domain data channel coefficients from step (b) to perform inter- carrier interference cancellation (ICI) and then estimate the data symbols.

(d) Feeding the estimated data symbols back to step (a) and repeating step (a) using the estimated data signals as additional pilot signals to improve the channel estimation.

This technique provides iterative channel estimation together with inter-carrier interference (ICI) cancellation for MIMO-OFDM systems. Iteration may continue to refine the estimation of the time-domain channel coefficients. For step (a) a set of time-domain channel coefficients may be selected for use in the channel estimation process. The selected channel coefficients are referred to as time-domain 'markers'. The time-domain markers may be estimated using received pilot symbols. Comb-type pilot tones may be placed in each OFDM symbol to estimate the channel. In any event it may be assumed that the pilot symbols are placed in each OFDM symbol in equispaced groups, that is where the groups of pilot symbols are uniformly partitioned on the symbol. The channel coefficients of the time-domain markers may be estimated using received pilot symbols and a least squares (LS) method.

For step (b) each time-domain channel coefficient may be calculated as a weighted interpolation between two time-domain markers that have the maximum correlation with the respective channel coefficient. The optimum interpolation weights may be designed based on Doppier spread information at the receiver. In this way the receiver is able to take account of the users' velocity information, in estimating the wireless channel. For step (c) the channel coefficients from step (b) may be used to perform inter-carrier interference cancellation (ICI), and then estimate the data symbols. Once estimates for channel coefficients are obtained, the estimates of ICI, caused by the Doppier spread, may be subtracted from the received signal by a parallel interference cancellation (PIC) module. The outputs of the PIC module are passed to a decision statistical combining (DSC) module [17], [20], where the decision statistics output signal is obtained by recursively combining its values in the current and the previous iterations. This has the effect of improving the signal-to- interference-noise ratio (SINR). A simplified PIC-DSC scheme may be used, where the iterative channel estimation and PIC-DSC cancellation processes are merged into one iterative process.

For step (d) the output of the PIC-DSC module may be sent to a detector and the detected data symbols may be directly fed back to step (a) as additional pilot symbols to refine the estimation of the channel. This is unlike [17], where for every iteration of the channel estimation, the PIC-DSC and data detection are performed iteratively for a number of times.

This PIC-DSC technique, has a lower computational complexity and better symbol error rate (SER) performance than the one described in reference [17]. Also note that the proposed scheme has a better performance-complexity trade-off than both the standard zero forcing (ZF) and minimum mean square error (MMSE) methods.

The outputs of the PIC module may then be passed to a decision statistical combining (DSC) module [17], [20], where the decision statistics output signal is obtained by recursively combining its values in the current and the previous iterations. This also has the effect of improving the signal-to-interference-noise ratio (SINR).

In each iteration, data symbols may be detected by a detector, and the estimates of these data symbols may be utilized to refine the channel estimation, iteratively.

Simulation results show that the performance of the proposed iterative Doppler-assisted channel estimation and ICI cancellation scheme in a high mobility environment is significantly better than the techniques in [16], [17] and [18], and is close to the performance of the system where full CSI is known and users are static.

Overall there is iterative channel estimation and inter-carrier interference (ICI) cancellation by estimating the wireless channel using pilot symbols, estimates of the data symbols and Doppler spread information at the receiver.

The method may be incorporated into any wireless cellular system. For instance, it may be incorporated into a mobile terminal such as a smart phone, mobile broadband modem or any other customer premise devices operating using LTE or WiMAX systems.

The method may also be incorporated into a mobile base station or femtocell [26] base station. For example, to support users in a high speed train [27], a base station can be placed on top of the train. Unlike other existing schemes, the proposed method can guarantee users to still receive high speed transmissions.

By utilizing these techniques, the channel time variations, due to highly mobile users, can be traced more accurately than the techniques presented in [12]-[18]. Brief Description of the Drawings

To establish a system model an OFDM transmitter and receiver are described with reference to the following drawings, in which:

Fig. 1(a) is a block diagram of an OFDM system transmitter.

Fig. 1(b): is a block diagram of an OFDM system receiver.

Fig. 2 is a graph of a pilot sub-carriers placement structure for a 2x2 MIMO-OFDM.

Examples of the invention are described with reference to the following drawings, in which:

Fig. 3 is a block diagram of a receiver structure for the proposed PIC-DSC interference cancellation scheme.

Fig. 4 is a graph of a convergence characteristic of the proposed iterative channel estimation and ICI cancellation scheme under various normalized Doppler spreads. Fig. 5 is a graph showing a comparison of the SER performances of the proposed iterative Doppler-assisted under PIC-DSC, ZF, and MMSW interference cancellation schemes for the normalized Doppler spread 0.1.

Fig. 6 is a graph showing SER performance for the normalized Doppler spread of

0.025.

Fig. 7 is a graph showing SER performance for the normalized Doppler spread of 0.1.

Fig. 8 is a graph showing SER performance of the proposed iterative Doppler- assisted channel estimation and the P-IC-DSC interference cancelation scheme with imperfect Doppler spread estimation.

Fig. 9 is a graph showing SER versus normalized Doppler spread at SNR=30 dB.

Best Modes of the Invention SYSTEM MODEL

We consider a MIMO-OFDM system with M ^T transmit and M ^R receive antennas. The block diagram of a MIMO-OFDM system transmitter is shown in Fig. 1(a). At the transmitter side, a serial bit stream 10 is mapped to a symbol stream 12 by a modulator 14. Then, this serial symbol stream is converted into parallel sub-streams 16. Next, pilot symbols for the channel estimation are inserted into these parallel sub-streams 18, in the frequency-domain, prior to the OFDM modulation. The OFDM modulation is then implemented 20 by performing the inverse discrete Fourier transform (IDFT). Each transmit antenna 22 sends independent OFDM symbols. Let X _p (k) denotes the information symbol sent by the transmit antenna p at sub-carrier k. The OFDM symbols transmitted by M ^T transmit antennas can then be presented as

X = PCi? · · · > Χρ· · · · . XA/T-F ί ΐ ) where X _p = [^(0), · ·, X _P (N - l )] ^r is the OFDM symbol transmitted from pth transmit antenna, and N is the number of sub-carriers for one OFDM symbol. After performing IDFT on each transmit antenna, the time-domain modulated signal on the pth transmit antenna can be expressed as \ _p = F ^H X _P = [x _P (0), x _p (l ), · , x _p (N - \ )] ^T , where F is the N * N discrete Fourier transform (DFT) matrix with its element at row n and column k, defined as ^u' >^ ^{: = e} ' ^for " · ^{k = ()l ' * "} · ^Λ ' ^{~ 1} In order to avoid the inter- symbol interference (ISI) due to a multipath delay spread, a cyclic prefix of length equal or greater than the expected maximum time delay of the channel is inserted 24 in each OFDM symbol prior to transmission. This prefix serves as guard interval (GI) between OFDM symbols. Finally, the symbol streams are converted from a parallel to a serial form and allocated to corresponding transmitters for transmission.

The block diagram of a MIMO-OFDM system receiver is shown in Fig. 1(b). At the receiver side, once the GI is removed 30, the received signal at qth receive antenna and time n can be represented as where w _q (n) is additive white Gaussian noise (AWGN) and ^p ''' ' is the fth resolvable path between the pth transmit antenna and ^th receive antenna at time n. Furthermore, the time-domain channel matrix between the pth transmit antenna and ^th receive antenna, including the effects of the cyclic prefix (or GI), can be represented as

After performing the DFT 32 on the received signal, the symbol for ^th receive antenna and kl sub-carrier can be expressed as τ Λ·- Ι -1

^R i( = Hf ^q (k - m) wi,„X _P {w) + W„{k). (4>

W (k) H^'ik)

where " is the DFT of noise and ' ^; denotes the DFT of time-varying frequency- selective channel

Λ -1

-J2rnk

(5)

«=o

We can further express R _q (k) as a summation of the desired signal and the ICI component as

Mr -l desired signal

Μτ Λ ^' - Ι I. -i

ICI component

+W',(Jt). (6)

Note that if the channel is time-invariant during one OFDM symbol period, the value of

(5) would be non-zero only if * = 0 (since = °· ^for * = ^{L " '} - ^{v " l} ). Under this condition, the ICI component in (6) disappears. However, if there is a non-zero Doppler spread, this assumption is no longer true.

The received signal for all MR receive antennas can be represented as

R = ΉΧ + W, (7) . R = [R, , . . . . _Afjl P . R, = [/?,(0) . . . . , R (N - l)] ^T

where ^{1 R J} , and * * is the received signal for ^th eceiver antenna, w = fw Wu i ^r

r ^{1 l} , ' · · · ' ^Mnl , and u ⁿ is the effective channel matrix in frequency-domain, defined as

Hj,2 H ₂ , ₂ . . · H,v, _T . _{2 (8)}

Hi.

(m n) ^th H

Here, the ' ' element of matrix ^p ' ^q is denoted as " ^{, n} and defined as

<C -™)*i.n„0≤ , m < N - 1. (9)

We let the total number of pilots in one OFDM symbol be N _p , and assume that the pilot symbols for the pth transmit antenna, denoted by are inserted at sub-carriers Pi. ? = 0, · · · , Λρ - l _{Let us denote by} V _p := { ⁾ _(ι · · · · - v _p - i} . _{the set of the sub} . carriers used for pilot symbols for the pth transmit antenna.

Fig. 2 shows the pilot placement structure of a 2 x 2 OFDM system. Here, the pilots are assumed to be grouped together in N _g groups, where each of these groups are of size d. It is assumed that the pilot symbols are placed in each OFDM symbol, in equispaced groups (i.e., the groups of pilot symbols are uniformly partitioned on the OFDM symbol). This type of pilot placement structure is shown to be optimal for high mobility systems [ 16]. We also assume that the pilot sub-carriers for different transmit antennas are orthogonal in frequency-domain, as depicted in Fig. 2.

PROPOSED ITERATIVE DOPPLER-ASSISTED CHANNEL ESTIMATION

In this section, we propose a new iterative Doppler-assisted channel estimation scheme based on a weighted time-domain channel interpolation. The proposed method exploits the Doppler spread, time-domain channel correlations, and estimates of data symbols. The method can be implemented in a receiver having the structure shown in Fig. 3 which is similar to the receiver of Fig. 1(b) with the following changes:

The interference cancellation module 34 is replaced by PIC 40, and

A DSC stage 42 in each channel. f

Doppler spread, -' ^, is calculated by using the user's velocity, ^l ' ( ^{in m} / ^s \ at the receiver as

. — 3 _χ ( _m i _s

where ^Jc is the carrier frequency and ' is the speed of light. To estimate the Doppler spread at the receiver, the approaches in [21 ] and [22] can be used. These methods are based on the autocorrelation function (ACF) for estimating frequency shift that induces ICI between adjacent OFDM sub-carriers. Note that the r'l— A A f

normalized Doppler spread is defined as , where ·' is the sub-carrier spacing.

In the proposed method, each time-domain channel coefficient is expressed as a weighted interpolation of other channel coefficients. The interpolation weights are designed in a way that the channel estimation error is minimized. It utilizes Doppler spread knowledge to calculate the time-domain channel correlations at the receiver. In each iteration, the detected data symbols at the receiver are sent back to the channel estimator. These data symbols together with the pilot symbols are employed to estimate the channel coefficient by an LS method. Thus, the estimation of the channel coefficients are refined by exploiting pilot and data symbols, iteratively.

A. Selection of the time-domain markers

First, we define " ^{1 M} ' ^{M ~} where ' represents the non-zero elements of the nth row in the time-domain channel matrix r C h ^{p,<? p q} ' shown in (3). Each row of ^p,q has L non-zero elements as defined in " Thus, to estimate the wireless channel in a time-varying environment, we need to estimate N L parameters. This impacts the computational complexity of the receiver.

To reduce the number of parameters needed for the channel estimation, interpolation between time-domain channel coefficients is used. We propose

C

parameterize the time-domain matrix by utilizing a small number of its rows, defined as M. Physically, this puts M markers in time-domain, where the channels are estimated. Then, the channel coefficients at other times are interpolated by using these markers. This assumption will reduce the number of parameters to be estimated from N L to M L, where ^ ^ . Thus, we first select M rows of ^{p q} , denoted by h ^M . . . h ^M

m( i r · m (M ) ' ^ jrf markers for the time-domain channel. The subscript indicates the index of the rows selected as time-domain markers in

^C - We then define ^{Mp q '} ' ^{" '} ' ^m ( ^M ) _{as the set of these row indices of} the time-domain markers. Each channel " ' where ^M ' can then be expressed

. . . . . ΐ^·*

as a linear combination of these M markers, as h _M (l, n) = (l) ). . . . . m(M)) ^T , ( 1 1 ) for 0 < I < L— l. _f where

&η.ρ. _< , = .p, _g (m(l)). · · ^■ , <V _/ ,,,(m(A/))] ^r , ( 12) is an ^x 1 vector of time-domain interpolation weights, employed to express the channel coefficients between the pt\\ transmit antenna and ^th receive antenna at time n. Note that in ( 1 1), we utilize the same weight vector ' ^ί,ρ ' ⁹ for all of the L taps of channel " Using the same weight vector is a direct consequence of the assumption . h _M {0, n), · . · , h _p . _q {L - 1, n ) .

that are l.t. d processes for every n [ 16]. We also observe that there is a correlation between and for ^m ^ " ^' in a time-varying channel. We exploit this correlation property to further simplify the interpolation process in (11). Each channel coefficient ^ ^>F'q ^ ^' ' ^ at time n, is now expressed as an interpolation between two time-domain markers at times and where ^m W 6 M _M . _{These two markers>} ^iW*)) _and hp, _q {l.m{k )). _{are se} i _ec ted from ^ ^M in a way that they have the maximum correlation with h> ^K< >^- by using the following criteria, max {E[/. _M (/ _t m(*))¾,(/,n)]}. (13)

Thus, here we reduce the number of markers required in the interpolation process from M to 2. The interpolatio onn wweeiigghhttss vveeccttoorr ^a "" ^, ' ^pp, ' ^iq iinn ((1122)),, ccaann now be simplified to have only 2 non-zero elements, °'··Ρ. ^< Λ"Η and ⁿ ' ^p,< * ^v " ^' . The rest of its elements are set to be zero.

As an example, let us consider the scenario where = 3. L = 2. _an d p = q = 1- Here, we set the first and third rows of the time-domain channel matrix

C ₄ . , . Mil = [m(l),m(2)l = [0.21. _c - ..

¹¹ as time-domain markers, ^{1,1 1 J} From (13), for time

^{77 =} ^ the selected markers are "'^ ^{= 0} and ^m ^ ~ Let us assume for a moment, the interpolation weight vector is predefined and given as a. l l = [«i u(O),0i ] i (2)1 = [0.3.0.71.

1 ^{,1 1 1 1'1,1V} ' ^{l,l,u n 1 J} By employing (11), the channel coefficients for the channel taps ^■ f = 0, 1 and time ⁿ ~~ ^ ^ ^,e " 1) _a nd

L ,(i D) . 0.3/i (0.0) + 0.7/z _u (0.2) . o.3/> _u (i.O) +ο.7Λ _Μ (ΐ,2).

"Ι,Η-Ι. ^Α ;/ _are expressed as and

l

respectively. Therefore, according to (3), ^' can be written as

c,., = 0.3/i (1.0) +0.7u.i(1.2) 0.3/u.i(0,0) +0.7ii.,(0.2) 0 (14)

0 /,,.,(!.2) Λι.ι(0,2)

B. Calculation of the interpolation weights

In the above example, the interpolation weights are assumed to be known. The goal in this section, is to find the optimum interpolation weights based on the Doppler spread information. We assume that the wireless channel follows the Jakes' model [23].

Therefore, the correlation between ' '/f' and can be expressed as i MI / M> n ^{« j} _wnere jd _an d Jo denote Doppler spread and

Bessel function of the first kind, respectively. Then, the calculation of the optimum interpolation weights is straightforward. Let us first define ,, _P .S)■= [h^LrnW h^mik'))} _{ag the} ^ _q{ ^ _time . _domain

= [a _n .p.,(»7( k) ), n„.p.,(m( k'))] ¹ markers used to represent _an d as the set of the non-zero elements of the interpolation weights vector, corresponding to the elements of ^"-Ρ ^'

. NZ

Then, the set of the non-zero interpolation weights, ^'M" that minimizes the channel estimation error defined as can be obtained by using the orthogonality principle as where ¾ = ^ = ^ ^, ,Α Μ ^ _{us define}

J ₀ [n] := Jo(27r/ _rf nr). _then ^ ^ _have 13

¾lh = [ m(k) - n], Jo[ .(k') - n]], ( 1 7)

J ₍₎ [m [k) - Jo[m(A-) - m{k')}

( 1 8)

Villi

J»[m (k') - m(fc)] Jo[m(A-') - m(fc')]

Note that " ^{p <?} corresponds to the non-zero elements of " ^ρ'η in (12) at times ^m ' ' and ^m ^ Thus, ^ί¾η ·ί ^, ·' in (12) can now be written as a _nj ,. _T = [0, · · · , 0, o _n . _M (m(fc)). 0. · · · , 0, « _η . _ρ ^(τ ^η (Α·') ).0, · · · _? 0] ^r . (19)

In this paper, we assume that the Doppler spread is fixed during the transmission of one OFDM symbol, but it can vary from one OFDM symbol to another. Therefore, the interpolation weights in (16) are determined once for each OFDM symbol, and will be updated for the next OFDM Symbol. In reality, the estimation of the Doppler spread at the receiver is not always perfectly accurate. Thus, there will be small difference between the actual and the estimated Doppler spread during the transmission of the OFDM symbol. In Section VI, we will show how the SER performance of our proposed channel estimation scheme is affected by the error in the estimated Doppler spread at the receiver.

C. Estimation of the channel

In this section, our goal is to regenerate the received signal in terms of time-domain markers in ' ^{p q'} . Here, we assume that in the rth iteration, the transmitted data symbol vector iteration, is available at the receiver. By

H ^<l ( k )

substituting in (6) with (5), (6) can be further expressed as

+e (*). (20) where denotes the summation of the estimation error at sub-carrier k and AWGN noise at the ^th receive antenna, and

A Ρ·9

, r e h _p l,m(i)) . _IL · J · I #„('")· mii) . _o represents the scale factor for ^{, ¾} in the received signal ^q in (21)

N x N

is an diagonal matrix with elements

for n = 0, · · · , Λ — 1 _an( j ' - 1. · · · - · jj _e re, _{we ensure} that each channel " is

\l ^{p q} represented by an interpolation of the selected time-domain markers " ^,(A" ) and 'r jhus, by defining a ^{1 x 1} vector as

b m"';(-;i).p,<j · · · , 1. (23)

' ι> ),ρ,¾ (L - 1) 'J we will have

Λr Λ ^? -1 M

By extending the definition of (23) into a ^{1 x} ^ vector

Km. ._ ΓΚ» ^η ·» ... " ^{, s} 1

we can further simplify (24) to become 1318

15

Air A-l

(1-1) (25)

where ^{1 w<1} > ^{' ' n,(iV} '> ^{J '} By defining

h* = [Γι ^ι * ^Γ ,··· .ϊϊ ^{Λ/ Τ} ] ^Γ ,

(25) can be expressed as i _<i (A-) = G[- ¹⁾ h ¹ ' + e,(A . (26)

Finally, we can form systems of linear equations with the size of ^ * ^ ^T ^^ as,

1 ⁽ = (G ^(f - ) ^f R,. for ¾ = !.··· , Λ fl. (28)

In the proposed scheme, since in the first iteration only the pilot symbols are known at

ν ⁽⁰⁾ ·ι , k ≠ ρ,·, i = 0. · · · , Nr,— 1 the receiver, we set ' ^Yp > to be 0 for ' and p— i ...

' However, in the next iterations, the data symbols detected at the receiver in the previous iterations, are supplied back to the channel estimator to assist with the estimation of the channel.

Once the pilot channel coefficients are estimated in the fth iteration by using (28), all the elements of the rth estimate of ^ in (7), denoted by ^ ^! ", can be calculated by using (11), (5) and (9).

Finally, the signal detection and ICI cancellation at the receiver at the fth iteration is done by performing the technique described in the next section.

IV. INTERFERENCE CANCELLATION In this section, we propose an iterative interference cancellation scheme, where in every iteration of the channel estimation, the ICI caused by the Doppler spread is suppressed by a PIC-DSC module 40/42 (see Fig. 3) [17], [20]. Unlike [17], in our proposed approach, the iterative channel estimation and PIC-DSC processes are combined into one iterative process. Here, instead of performing PIC-DSC and data detection for a number of times, for every iteration of the channel estimation as in [17], we perform PIC-DSC and data detection once, and then send the detected data symbols back to the channel estimator. We will show below that our proposed scheme has a lower computational complexity and a better SER performance as compared to the scheme in [17].

Now, we explain the iterative receiver with the proposed PIC-DSC module, shown in Fig. 3. The decision statistics in the rth iteration for symbols transmitted from the pth antenna are given as

Y(t ) _ ία ' ^{) †} \ /R v d-i ⁾ _ γ (' ^-ι > \ (29)

where ⁹ and ^ndiaB are defined as

L Diag(H _lK ) Diag{ and ) NDiaglK,

NDiag (H¾ ) NDiag( )

n ndi g ( 1 )

NDiag{ H^ (0 _TMll ) J In (30), ^{p v} for ^ ^ ^ refers to the operation to force the non-diagonal elements of H ^p< ' ^q) equal to zero. Furthermore,

NDiag(U _p ⁽ ). for p = 1. · · · , M _T , q = 1, · · · , _{in (31)( refers t0 the} it) X ^(i-1)

operation to force the diagonal elements of equal to zero. ( ^ίΐΤΟ ·ρ· j _s the estimate for the transmitted, symbol in ~ ^~ l)" ¹ iteration, except for the elements corresponding to the pth transmit antenna, which are set to zero. ^ *"·" ' ^p the pth row of pseudo- inverse of matrix ¾ ^D(<IA) 9 in (30).

In (29), the ICI component on every sub-carrier are .calculated by the term _v \n χα- ι ) , ¾<,':· X"- ¹ '

M ^aa '' ^rro > and then subtracted from the received signal R.

In a high interference scenario, the detector output becomes unreliable. Under these conditions, [20] propose to use a combining method, called decision statistics combining (DSC), which gives an improved SINR. The decision statistics are generated by DSC module as a weighted sum of the current PIC output, and the DSC output in the

Y« -l )

previous iteration, DSCp' Therefore, the output of DSC can be given by v(f) _ ( ^a DSC.p) ² y(t) , ( ^{σ 2} _ν (ί- 1) _\

1 DSC.p ~ Z P ~ ^l I DSC.p' ^u - '

J ^L ) ²

where ^{* ~} "P ^J ^ ^' DSCp / · ^ DSC.p t a _a n _n d _d * P> are the variances of DSC estimate is passed to the detector. Then the detected data symbols are sent back to the channel estimator. This process is then repeated. In later iterations, as the correlation between detector inputs increases, this combining does not produce further improvements. However, in later iterations, the interference estimates become more reliable and a reduced interference level is likely to drive the detection convergence [20]. In addition, for the comparison, we also perform interference cancellation using MMSE and ZF methods. Considering the OFDM signal model in (7), the MMSE estimator [24] that minimizes the mean squared error is given by

(33) where ^[ W ⁷ ] _] - _S ^ autocorrelation matrix of AWGN noise vector, W.

The ZF estimator that forces the interference to zero is given by x<" = u ^<t)H m ^{t) H ^t)H r ^l R. (34)

The MMSE solution minimizes the squared error in the presence of channel noise, and becomes the zero-forcing solution when no noise is present. Note that the performance of ZF is very similar to the performance of MMSE when the symbol-to-noise-ratio (SNR) is high. However, at low SNR, MMSE improves the performance further. This has also been verified in the simulation results in Section VI. In the next two sections, we will show that the proposed simplified PIC-DSC scheme offers the best performance- complexity trade-off compared to the MMSE and ZF methods.

COMPARISON WITH OTHER SCHEMES

In this section, to see the merit of using the proposed channel estimation and interference cancellation scheme described above, we opt to compare it with the schemes in [16], [17] and [18], since the techniques used in this paper are closely related to [16], [17] and [18]. The comparison of these schemes is done in terms of the algorithms and the complexity orders as follows.

A. Algorithms Comparison

In the Doppler-assisted channel estimation in [16], all channel coefficients are expressed as a weighted interpolation of the first, middle and the last rows of the time-domain channel matrix in (3). The weights are designed according to the Doppler spread. When users are highly mobile, the Doppler spread is high and the channel variations are fast. As a consequence, the correlation between the rows in the time-domain channel matrix in (3) reduces. This results in less accurate calculation of the channel coefficients by interpolating the first, middle and the last rows.

5

In [17], the authors model the time-domain channel tap coefficients as a line with a median and slope, which are to be approximated. The approximation of the fth channel tap coefficient at time n in [17] is expressed as _{l ft} 0 y- ") = ' (') + ¾(') x (« - ¥)- _f 0

for * = , . „

1 . . . L - 1.

where ¾,(0 h ^{p q} ( 1\

is the median and sloped J denotes the slope of the line for the fth channel tap. Furthermore, the estimation of each channel coefficient is iteratively refined by using the detected data symbols. However, when the Doppler spread is high and the channel variations are fast, this technique that assumes linear variations for channel impulse 15 response within the duration of one OFDM symbol, cannot track the channel well.

A similar iterative concept as above is developed in [18]. The authors propose an iterative frequency-domain channel estimation. The main difference here is that the

H 1 < p < Mr authors focus on the diagonal elements of w in (8), for and

1 < q < MR.

20 and treat ICI term as additional embedded Gaussian noise. However, in the presence of very high mobility, the proposed channel estimation and interference cancellation scheme in this paper, that closely regenerate the ICI term in the channel estimation process, results in a more accurate estimation. Furthermore, the Doppler spread knowledge has not been used in the channel estimation process.

25

Unlike [16], [17] and [18], in the proposed channel estimation and interference cancellation scheme, each channel coefficient is expressed as a weighted interpolation of two time-domain markers that have the maximum correlations with that channel coefficient. These interpolation weights are designed based on the Doppler spread 30 information. By using this technique, the desired channel coefficient can be estimated more accurately than [16], [17] and [18]. In addition, in the proposed iterative Doppler- assisted channel estimation and interference cancellation scheme, the data symbol P T/AU2011/001318

20

estimates are used iteratively as additional pilots to improve the estimation of the channel.

B. Complexity Comparison

The complexity order, which is defined as the number of floating point operations, for the proposed iterative Doppler-assisted channel estimation and ICI cancellation as well as for the schemes in [16], [17] and [18] are listed in Table I. Furthermore, the complexity orders of the proposed iterative Doppler-assisted channel estimation scheme with the ZF and MMSE interference cancellation techniques as well as PIC- DSC are shown. ^{I E} and ^1,1 ' in Table I denote the number of iterations for the channel estimation and interference cancellation processes, respectively. It is concluded that the investigated schemes can be ordered in terms of the complexity in an ascending manner as, Doppler-assisted channel estimation in [16], channel estimation scheme in [18], the proposed iterative Doppler-assisted channel estimation and PIC- DSC interference cancellation scheme, pilot-assisted channel estimation in [17], and finally, the proposed iterative Doppler-assisted channel estimation with ZF and MMSE interference cancellation schemes. However, the simulation results in Section VI confirm that the proposed iterative Doppler-assisted channel estimation and PIC-DSC interference cancellation scheme outperforms the schemes in [16], [17] and [18], especially for high Doppler spreads. It is also shown that the SER performance of the proposed iterative Doppler-assisted channel estimation and PIC-DSC interference cancellation scheme only slightly degrades the performance of ZF or MMSE interference cancellation techniques. However, the complexity order of PIC-DSC scheme is much lower that the complexity order of ZF and MMSE schemes.

NUMERICAL RESULTS

Monte Carlo simulations have been carried out to assess the performance of the proposed iterative Doppler-assisted channel estimation and ICI cancellation scheme, and compare it with the schemes in [16], [17] and [18]. For a lower bound comparison, we simulate the system where users are static and full CSI is available at the receiver. The system parameters correspond to the parameters in the 3GPP LTE standard [1]. These parameters are shown in Table II. In all simulations, we define the SNR to be ^jV ° ^" 1318

21

where ^s is the symbol energy and ^{* 0} is the noise power. A simplified tapped delay- line channel model [1], [25] is used to represent a mobile environment, where in each tap, the channel impulse response is generated by using Jakes' model [23]. We assume that there is no ISI by adjusting GI to be larger than the maximum channel delay.

We let M, which is the number of time-domain markers, to be equal to 16, and assume that '"(*) ^■ ' — I ^{; " *} · Μ ^> _are uniformly distributed in time. Here, we set the number of transmit and receive antennas, M ^* r and - fl. ^' to be equal to 2. The total number of pilots in one OFDM symbol, is set to be 48. It is also assumed that the pilots are grouped in 16 groups of 3 pilots each (i.e., ^{* 9} = 16 and d = 3).

Fig. 4 illustrates the SER performances of the proposed iterative Doppler-assisted channel estimation and ICI cancellation scheme for various numbers of iterations u _nder various normalized Doppler spreads. It can be seen that the proposed scheme converges after 5 iterations. Fig. 5 presents the comparison of the SER performances of the proposed iterative Doppler-assisted channel estimation and interference cancellation scheme under three different ICI cancellation schemes, MMSE,

ZF and the proposed PIC-DSC, for the normalized Doppler spread of 0.1. This is equivalent to a user moving at the speed of 324 KnVh with the LTE system parameters in

Table II. It can be seen that at high SNR, the SER performance of the PIC-DSC scheme degrades the SER performances of ZF and MMSE schemes for 0.85 dB and 1.20 dB, respectively. However, the computational complexity orders of MMSE and ZF schemes A'

are ^2A ' ^r times higher than the one's for the proposed PIC-DSC scheme. Therefore, it can be concluded that the proposed PIC-DSC scheme is the preferred choice, where complexity needs to be low.

Fig. 6 compares the average SER performances of the proposed iterative Doppler- assisted channel estimation and PIC-DSC interference cancellation scheme and the schemes in [16]— [18] for the normalized Doppler spread of 0.025. This is equivalent to a user moving at the speed of 81 Km/h with the LTE system parameters in Table II. We observe that the proposed iterative Doppler-assisted scheme and the schemes in [16] and [17] have a similar SER performance. It is also shown that their performance is close to the performance of [18]. This is not a surprising result, since for the normalized Doppler spread of 0.025, the channel variations are slow, and as a result, even a simple channel estimation technique performs adequately.

On the other hand, due to its ability to closely track the time-varying channel, the proposed iterative Doppler-assisted channel estimation and PIC-DSC interference cancellation scheme outperforms the schemes in [16]-[18] for high normalized Doppler spreads. Fig. 7 depicts the achieved SER performances of the proposed iterative Doppler-assisted channel estimation and PIC-DSC interference cancellation scheme and the schemes in [16]-[18] for the normalized Doppler spread of 0.1. The simulation results show that the proposed iterative Doppler-assisted channel estimation and PIC-DSC interference cancellation scheme outperforms the schemes in [16]-[18]. It is also shown that the degradation of the iterative Doppler-based scheme with 5 iterations for a system with the normalized Doppler spread of 0.1, compared to the performance of the system with a zero Doppler spread is only 1.1 dB.

In reality, the estimation of the Doppler spread at the receiver is not accurate. Thus, there will be small difference between the actual and the estimated Doppler spread during the transmission of the OFDM symbol. Fig. 8 shows the SER performance of our proposed Doppler-assisted channel estimation and PIC-DSC interference cancellation scheme, where there is 10% estimation error in the Doppler spread at the receiver. As it can be seen, the proposed scheme is relatively insensitive to this error. The performance degradation of the proposed scheme, due to 10% error in the estimation of the Doppler spread, for the normalized Doppler spreads of 0.025 and 0.1 are 0.4 dB and 1.15 dB, respectively.

Furthermore, Fig. 9 compares the SER performances of the proposed iterative Doppler- assisted channel estimation and ICI cancellation scheme, and the schemes in [16]-[18] for various normalized Doppler spread values at SNR equal to 30 dB. The simulation results show that the performance of the proposed scheme is relatively insensitive when the normalized Doppler spread is less than 0.1.

Note that in this paper, we do not incorporate the encoder and decoder modules in the transmitter and receiver structures. However, extending the system structure to incorporate the encoder and decoder is straightforward, and will provide further improvements to the performance of the schemes in [16]-[18] as well as the proposed scheme in this paper.

CONCLUSIONS

In this paper, we proposed a new iterative Doppler-assisted channel estimation and PIC-DSC interference cancellation scheme in high mobility MIMO-OFDM systems. In the proposed method, the wireless channel is estimated by using the knowledge of users' velocity, pilot symbols and estimates of the data symbols at the receiver. Each time-domain channel coefficient is expressed as a weighted interpolation between two selected time-domain channel coefficients referred to as markers. These two markers are selected in a way that they have the maximum correlation with the channel coefficient. The interpolation weights are designed based on the users' velocity information at the receiver. In addition, at the receiver, data estimates are utilized iteratively as additional pilots to improve the channel estimation. The simulation results show that the proposed scheme outperforms the best known schemes from [16], [17] and [18], especially for high Doppler spreads. The SER performance of the proposed scheme with the normalized Doppler spread of 0.1, is only 1.6 dB weaker compared to the one with a zero Doppler spread. Note that the normalized Doppler spread of 0.1 is equivalent to a LTE user moving at the speed of 324 Km h operating in the 5GHz band with a sampling frequency of 7.68 MHz.

It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the invention as shown in the specific embodiments without departing from the scope of the invention as broadly described. For instance, the invention may be used with multiple antenna applications, and multi-input, multi-output (MIMO) applications. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive. TABLE I

COMPLEXITY ORDER OF ITERATIVE DOPPLER-BASED CHANNEL ESTIMATION AND ICI CANCELLATION AS WELL AS FOR THE SCHEMES IN [16], [17] AND [18]

TABLE II

PARAMETERS OF THE SIMULATED SYSTEM

Parameter Value

Modulation QPSK

Operating frequency 5 GHz

Bit transmission rate 7.2 bps

Sampling time 0. I 6// S

Sampling frequency 7.68 MHz

FFT size 5 12

Number of data sub-carriers 240

Number of pilot sub-carriers 48 ( 16 groups of 3 sub-carriers each) REFERENCES

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