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WSEAS TRANSACTIONS on COMMUNICATIONS

Guocai Li, Yaohuan Gong

Study on MIMO Schemes for 3G-LTE DownlinkGuocai Li and Yaohuan Gong School of Electronic Engineering University of Electronic Science and Technology of China No.4, Section 2, North Jianshe Road, 610054, Chengdu, CHINA [email protected],http://www.uestc.edu.cn/Abstract: - The combination of MIMO and OFDM becomes a key standardization work for the downlink channel in 3G Long-Term Evolution (3G-LTE). This paper studies one of the core techniques of 3G-LTE downlink: the coding and decoding schemes in a time-variable multipath environment. It discusses the MIMO schemes for 3G-LTE downlink, the STBC/SFBC, SFTC/STTC and Group layered SFC coding-decoding schemes. This paper also discusses channel estimation scheme based on pilot symbol assistance (PSA), including the pilot pattern and the channel tracking algorithms. The computation complexity, frequency efficiency, BER performance and the effects of channel estimation are analyzed under multi-path fading channel environments. Then we give computer simulation results for the coding-decoding schemes. We believe that results will provide beneficial information to design the 3G-LTE downlink channels. Key-Words: 3G long-term Evolution(3G-LTE), MIMO-OFDM- STBC/SFBC, SFTC/STTC, Group layered SFC

1 IntroductionMultipath fading channel and spectrum efficiency are the two severe challenges for 3G Long-Term Evolution (3G-LTE). 3G-LTE Data transmission in downlink is based on OFDMA. OFDM has been widely studied and it appears as the preferred multiple access schemes for 3G-LTE downlink. OFDM converts the wideband frequency-selective fading channel into multiple flat fading one. It is a popular modulation choice for many applications for its intrinsic ability to handle the most common distortions encountered in a wireless environment, without requiring complex reception algorithms. For independent fading of the users who occupied by the different subcarriers, OFDMA exploits multiuser diversity to meet users QoS requirement. Many OFDM like schemes have been proposed for 3G-LTE, such as MC-WCDMA, MC-TD-SCDMA, OFDMA, SC-FDMA, etc. Furthermore, MIMO (multiple-inputmultipleoutput) smart antenna systems have the ability to turn multipath propagation, traditionally a pitfall of wireless transmission, into a beneficial factor for wireless communications. MIMO improves spectral efficiency by exploiting the rich scattering of RF signals which is typical for indoor and urban environments. There are mainly two ways to handle the wideband MIMO: MIMO wideband equalization and combination of MIMO and OFDM. MIMO wideband equalization is quite complex to

implement. MIMO combined with OFDM substantially reduces the complexity of spatialtemporal processing. Then, MIMO-OFDM is a more effective solution for 3G-LTE. Data transmission is based on MIMO-OFDM has been widely studied. However, the situation in 3GLTE downlink is less clear considering the tradeoff among coding-decoding, channel estimation, the tracking of time varying and performance. In this paper, we discussed the 3G-LTE physical layer in the downlink direction, including the STBC/SFBC, SFTC/STTC, Group layered SFC coding-decoding schemes and channel estimation based on pilot symbol assistance (PSA). Their basic performance and computation complexity in time varying channel are simulated and compared. The rest of the paper is structured as follows. Section 2 gives a briefly description of the LTE downlink physical (PHY) layer with MIMO. The MIMO coding-decoding schemes, the PSA pilot pattern and channel tracking schemes are presented and analyzed in Section 3. In Section 4, simulation results are presented. Finally, Section 5 gathers the conclusions and future work.

2 3GPP-LTE Downlink ModelThe MIMO-OFDM system model for Space Time/Space Frequency (ST/SF) Coding in 3G-LTE downlink is shown in Fig 1 and Fig 2.

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Guocai Li, Yaohuan Gong

Pilot SymbolS1[n, k ]Frame Forming

other user data

s1[n, m]

P/S

IFFT

S/P

ST/SF Coding

sM T [n, m]S M T [ n, k ]

P/S

IFFT

S/P

Frame Forming

Pilot Symbol

Other user data

Fig 1 ST/SF Coding MIMO scheme for LTE downlink (transmitter)

y1[n, m]Remove guard symbol Pilot symbol recover

Y1[n, k ]

FFT

S/P

P/S

ST/SF Decoding

y M R [ n, m ]Remove guard symbol

Pilot symbol recover

YM R [n, k ]

FFT

Fig 2 ST/SF Coding MIMO scheme for LTE downlink (Receiver) Suppose that the system is equipped with M T transmitting (Tx) antennas and M R receiving (Rx) antennas. The output signal from IFFT can be described as sq [ n, m] in time domain For the nth OFDM symbol, the channel response between the qth transmitter antenna and the ith receiver antenna can be described as

sq [n, m] =

1 N

Sq [n, k ]ek =0

N 1

j

2 km N

The signal with guard interval ( N g ) is

s [n, m + N ] m = N g , , 1 sq [n, m] = q m = 0 N 1 (2) sq [n, m]

S/P

P/S(1)

Channel Estimate Pilot Symbol

h i , q [n] = [hi ,q [n, 0], hi ,q [n,1],

, hi , q [n, L 1]]T

(3)

where i = 1, 2, , M R q = 1, 2, , M T and L is the channel order. The received signal after matched filtering and the guard symbol removed are

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Guocai Li, Yaohuan Gong

yi [n, m] = hi , q [n, l ]sq [n, m l ] + vi [n, m]2 k ( m l ) j 1 hi , q [n, l ]S q [n, k ]e N (4) N l =0 q =1 k =0 +vi [n, m]

L 1 M T

=

l = 0 q =1 L 1 M T N 1

Many STC-STD algorithms have been presented to apply for a wideband system, especially for the 3G-LTE.

3.1 STBC SchemeAll of the STBC schemes could be applied to MIMO-OFDM system. Assuming that the number of OFDM sub carriers is N , the interval of input signal is Ts , then the interval of data block is NTs . Suppose that two successive data vectors are S1 and

where vi [ n, m] is the AWGN noise with zero mean and variance of V .2

When the guard interval exceeds the maximum time delay of the channel ( N g > L ), the InterSymbol-Interference (ISI) can be neglected and the received signal in frequency domain can be described as

S 2 , respectively, where S1 = [ S1 (0),

, S1 ( N 1)]T ,

Yi [n, k ] = yi [n, m]em=0

N 1

j

2 km N

S 2 = [ S2 (0), , S 2 ( N 1)]T and the length of the vector is N . Based on Alamoutis design [5],during the first symbol transmission interval, two vectors of signals S1 and S 2 are transmitted from antenna 1 and 2, respectively. In the second interval * S* and S1 are transmitted. 2 The received signals at the kth subcarrier of ith antenna at the first symbol period and next period are

2 kl MT j L 1 = hi ,q [n, l ]e N S q [n, k ] + Vi [n, k ] (5) q =1 l = 0

= H i , q [n, k ]Sq [n, k ] + Vi [n, k ] (i = 1, 2,whereq =1

MT

, M R , k = 0,1,L 1 l =0 j

, N 1)2 kl N

Yi ,1[k ] =(6)

H i ,q [n, k ] = hi , q [n, l ]eSuppose input

H i ,1[k ]S1[k ] + H i ,2 [k ]S2 [k ] + i ,1[k ], Yi ,2 [k ] = H i ,1[k ]S [k ] + H i ,2 [k ]S [k ] + i ,2 [k ],* 2 * 1

S I = [ S I [0], S I [1],

information vector is , S I [Q 1]] and N > M T L ;

(11)

The output of the encoder is S = [S 0 , S1 ,Yk = Es H (ej 2 k K

, S N 1 ] ,(7)

(i {1, 2,

, M R }, )

The received signal vector of the kth carrier is)S k + n k

The receiver constructs two decision statistics based on the linear combination of the received signals

The maximum likelihood decoding algorithm is employed:

S1[k ] = Hi =1 MR

MR

* i ,1

[k ]Yi ,1[k ] + H i ,2 [k ]Y *i ,2 [k ] (12)i =1 MR

MR

S = arg min || Yk Es H (eSl =0

N 1

j 2

k N

)S k ||

2

(8)

S 2 [k ] = H *i ,2 [k ]Yi ,1[k ] H i ,1[k ]Y *i ,2 [k ] (13)i =1 i =1

3 MIMO Coding Schemes for LTEThe typical applications of MIMO are spatial multiplex and spatial diversity. The multiplex system (such as BLAST) increases the transmit rate, while the diversity system could increase the physical link reliability. In all cases of MIMO system, there are given multiplex gain and diversity gain. Increasing the number of Tx antennas provides a significant performance improvement. However, the decoding complexity becomes very high for a large number of Tx antenna.

These are the input of the maximum likelihood decoder. Substituting (11) into (12) and (13):

S1[k ] = H i , q [k ] S1[k ]2 i =1 q =1 * i ,1

M R MT

+Hi =1

MR

[k ] i ,1[k ] + H i ,2 [k ]i =1 2

MR

(14)* i ,2

[k ]

S 2 [k ] = H i , q [k ] S2 [k ]i =1 q =1

M R MT

+Hi =1

MR

* i ,2

[k ] i ,1[k ] H i ,1[k ]i =1

MR

(15)* i ,2

[k ]

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It can be seen that, for transmit signal pairs of

S1[k ] S 2 [k ] , the decision statistics input is the linear combinations of M R M T signals. When thefading of the channel between any Tx and Rx antenna pair is mutually independent, the scheme can achieve a full transmit diversity of M R M T . The average symbol error probability (SER) can be expressed as

Yn ,i = H n ,i ,1S n ,1 + H n,i ,2S n,2 + Z n,i

(21)

where H n ,i ,1 , H n ,i ,2 are channel response diagonal matrix. Using the odd and even part expression, Eq.(21) can be expressed as Yn ,i ,e = H n ,i ,1,eS n ,e + H n ,i ,2,eS n,o + Z n,i ,e (22)

Yn ,i ,o = H n ,i ,1,o S* ,o + H n ,i ,2,oS* ,e + Z n ,i ,o n n

(23)

Ps ( E ) = 1

MR i =1

3 4 0

MT q =1

M i ,q e

0 1 M 2sin 2 ( ) T

d

(16)

Where 0 =2 V

2 V

P

is SNR,

P

is total transmit power,

Suppose that the distance between the adjacent sub-carriers exceeds the correlated bandwidth, one can have H n ,i ,1,e H n ,i ,1,o , and H n ,i ,2,e H n ,i ,2,o . Thus the results of the following linear transformation can be used to do ML decision processing* S n ,e = (H* ,i ,1,e Yn ,i ,e + H n,i ,2,o Yn,i ,o ) n

MR

is0

noise

variance,s i ,q

i ,q = H i ,q [k ]

2

and

(24) (25)

i =1

M i ,q = p ( i , q )e

d i ,q .

* S n ,o = (H* ,i ,2,e Yn ,i ,e H n ,i ,1,o Yn ,i ,o ) n

MR

i =1

3.2 SFBC SchemeFor the STBC MIMO-OFDM the traditional STBC scheme was applied to each narrow sub-channel of a broadband system. SFBC MIMO-OFDM is also based on Alamoutis scheme. Its coding, however, is processed in frequency-space domain. S n = [ Sn (0), , Sn ( N 1)]T Let is the information symbol, for a 2 Tx system the SFBC encoder outputs S n ,1 and S n ,2 to antenna 1 and 2 during the n th symbol interval, respectively. The coding outputs are

3.3 SFTC SchemeThe SFTC MIMO-OFDM is derived from STTC (Space Time Trellis Coding). Its encoder is determined by the coefficients sets. The number of coefficients sets depends on the modulation scheme. Figure 3 [2] shows an encoder for QPSK, whose coefficients sets are:

{b

p

, q = 0,1,1 q 2 q

v2 } ,,bMT q

{a

p

, p = 0,1,

v1}

and

where

a p = [a1 , a 2 , p p].a0 a1

, a MT ] p

and

Sn,1 = * Sn [0] Sn [1] Sn,2 = * Sn[1] Sn [0]

b q = [b , b ,

* Sn [N 2] Sn [N 1] T

T

(17)

I t (1)

* Sn[ N 1] Sn [ N 2]

(18)

Let S ne and S no are the vectors constructed by taking the even and odd components of S n respectively. S n ,1,e , S n ,1,o , S n ,2,e , S n ,2,o are symbol vectors of odd and even sub-carriers of corresponding transmitter, then

av1

I t (2)

x(t )

S n ,1,e = S n ,e S n ,1,o = S* ,o n

(19)b1

b v2

S n ,2,e = S n ,o S n ,2,o = S* ,e n

(20)b0

When the guard interval exceeds the maximum time delay of channel, the received signal vector at the ith Rx antenna is

Fig 3 structure of SFTC

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For QPSK, the data stream was split into 2 substreams (3 sub-streams for 8PSK), and then send to SFTC coder. The constrained length of codec is

v + i 1 v = v1 + v2 , where vi = . At the time t , 2 the symbol transmitted from k transmitter is

x = ( Ik t p =0

v1

1 t p

a + I t2qbqk ) mod 4k p q =0

v2

(26)

l where I t p is the bits in the lth sub-data stream, at

time1 t

t p2 t

,

the

coder mapped to

output the

maximizing diversity gain. They usually provide diversity gain without coding gain. STTC and SFTC can obtain diversity gain and coding gain at the same time. SFTC (STTC) scheme is based on TCM, which is a joint design of error control coding, modulation, transmit and receive diversity. It can simultaneously offer a substantial coding gain, spectral efficiency, and diversity improvement. However, the complexity of the SFTC (STTC) decoding (denoted by the number of trills states) is increased exponentially with transmit diversity gain d and transmit rate b , and may not be feasible for many applications.

xt = [ x , x ,

,x

MT t

].

is

constellation symbols and the coding matrix isT T G T = aT , bT , a1 , b1 , 0 0

[6] and [7] propose a Space-Frequency-Time (SFT) scheme, which can achieve the maximum diversity gain. However, It spectral efficiency is lowered because of the coding redundancy.3.6 Channel EstimationThe PSA channel estimation is shown in Fig.5. Two significant issues for PSA approach are: (a) the design of the pilot symbol pattern at transmitter; (b) the estimation of channel state information at all subcarriers and symbols based on the receiving pilot at the receiver. For the receiver it first obtain channel estimation at pilot symbols, then to obtain the channel state information at all the symbols by using transformation (IFFT-FFT)[10], interpolation [11], filtering [12] and so on.

SFTC uses vector Viterbi decoding algorithm. If SFTC is applied on all sub-carriers, for large number of carriers the decoding procedure is very complex. One way to overcome this difficulty is to group the sub- carriers, and apply the SFTC on different groups. This scheme, however, will suffer performance lost.

3.4 Group Layered SFC SchemeA group layered SF coding (SFC) system was proposed [3], shown in Fig 4. It has multiple identical SFC at the Transmitter. The decoding processing chain related to an individual sub-stream is referred to as a layer.OD FM

SFCOD FMLayered STC

OD FM OD FM

Grouped Interfe rence cancell ation ML decodin g

OD FM

SFCOD FM

OD FM

3.6.1 Pilot Pattern Two-dimension rectangular pilot pattern for a resource block (12 sub-carriers 7 OFDM symbols )[16] of LTE downlink is shown in Fig.6 (taking M T = 2 for instance), where Dt is the time interval between two adjacent pilot symbols (for LTE resource block Dt = 3n or Dt = 4n ) , and

Fig 4 structure of Group Layered SFC

D f is the distance between two adjacent Pilotsubcarriers. For the qth Tx (transmitter) antenna, the following k q , p th subcarriers are selected to transmit the Pilots

3.5 MIMO Scheme ComparisonThe two schemes derived from narrow-band STBC STBC and SFBC are attractive. All of the STBC like schemes could be applied to MIMO 3G- LTE. For STBC scheme the traditional STBC scheme was applied for each sub-carrier of OFDM, whereas SFBC scheme makes the coding and decoding processing in frequency and space domain. Both STBC and SFBC scheme concentrates on

kq, p = pDf +q1 for p = 0,1, , P1; P = N Df where P is the number of training pilots for a transmit antenna and N is the number of subcarrier of an OFDM symbol.

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Fig.5 Traditional PSA channel estimation approachesFrequencyn=0

k =0

Df

k=11Dt

Fig.6 pilot pattern for 3G-LTE downlink with MIMO

In order to recover channel state for all the subcarrier and symbols the pilot patterns should satisfy the multi-dimension Nyquist sampling theorem [12]: f D maxT 's Dt 1/ 2 D max F D f 1/ 2 (27) where f D max is the maximal Doppler frequency spread and D max is the maximal multipath delay spread, F is the subcarrier interval and T 's is the OFDM symbol period. Usually a double oversampling will be used in a practical system. The spectral efficiency loss for the rectangular pilot pattern is

3.6.2 Channel Estimation at Pilot Symbols Suppose that the MIMO-OFDM system is equipped with M T Tx(transmitting) antennas and M R Rx (receiving) antennas. The channel response between the qth Tx antenna and the ith Rx antenna is (29) where n is the OFDM symbol index, i = 1, 2, , M R , q = 1, 2, , M T and L is the FIR channel order. When the guard interval ( N g ) exceeds the maximum time delay spread of the channel, the Inter-Symbol-Interference (ISI) can be neglected and the signal model in frequency domain can be expressed asYi [n, k ] = H i , q [n, k ]S q [n, k ] + Vi [n, k ] i = 1, 2,q =1 MT

hi , q [n] = [hi , q [n, 0], hi , q [n,1],

, hi , q [n, L 1]]T

0 =

MT Dt D f

(28)

, M R , k = 0,1,

, N 1

(30)

where Yi [n, k ] is the received signal at the ith antenna, S q [n, k ] is the symbol transmitted by the qth Tx

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antenna, H i , q [n, k ] = hi , q [n, l ]el =0

L 1

j

2 kl N

is the channel

frequency response at the kth subcarrier of nth OFDM symbol between the qth Tx antenna and the ith Rx antenna and Vi [n, k ] is AWGN noise with 2 mean zero and variance V . Using the known Training Pilots and the corresponding received symbols, the frequency response for the kq , p th pilot estimated by LS method is

between the M T Tx antennas and the ith Rx antenna can be rewritten as h i [n] = [hT,1[n], hT,2 [n], , hT, MT [n]]T (35) i i i According to the MMSE criterion, the cost function of the estimation is J (hi [n]) = E{| Yi [n, k p ] Yi [n, k p ] |2 } (36) where Yi [n, k p ] = S q [n, k p ]H i , q [n, k p ] = hT [n]w p [n] iq =1 MT

(37)

for p = 0,1,

, P 1 and, w T T , p [ n ] M T

H i , q [ n, k q , p ] =

Yi [n, kq , p ] S q [ n, k q , p ]

(31)

T w p [n] = w1, p [n], w T p [n], 2,

(38)T

T Let H i , q = [ H i , q [n, kq ,0 ], H i , q [n, kq ,1 ], , H i , q [n, kq , P 1 ]] ,

the time domain channel response between the qth Tx and the ith Rx antenna is

j 2 j 2 k p li ,q ,1 k p li ,q ,2 Sq [n, k p ]e N , Sq [n, k p ]e N , wq, p [n] = j 2 , S [n, k ]e N k pli ,q,L q p

(39)

1 hi , q [n] = WqH H i ,q ; P i = 1, 2, , M R ; q = 1, 2,

(32)

, MT

where Wq is a P N matrix whose (k , m)th element is

Substitute (37) into (36), the cost function becomes J (hi [n]) = E{| Yi [n, k p ] hT [n]w p [n] |2 } (40) i A LMS-Like algorithm is employed to find the optimal estimation of the channel coefficients. Let hi [n, p] be the estimation of optimal

[ Wq ]k , m = e

j 2 ( q 1+ kM T )( m 1) N

(33)

hi , q [n] = [hi , q [n, 0], hi , q [n,1],

, hi , q [n, N 1]]T is an

h i [n] after p times iteration, the instantaneous estimate of the gradient vector of J (hi [n, p]) (41) 2 = Yi [n, k p ] hT [n, p]w p iisJ (h i [n, p ]) = 2w *p [n]Yi [n, k p ] + 2w p [n]w H [n]hi [n, p ] p

N 1 complex vector consisting of N estimated fading coefficients. In real wireless environments, the number of fading paths is limited and thus most of the estimated coefficients in hi , q [n] might be the estimation error. The Significant Taps Catch (STC) technique [14] is employed in the scheme to pickout L paths with larger power gains hi , q [n, l ] . After STC the channel coefficients can be expressed by the vector pairs2

(42)

Here [i] donates the vector conjugate. Lete[n, p] = Yi [n, k p ] w T [n]hi [n, p ] p

(43)

The estimation is updated as

hi [n, p +1] = hi [n, p] + [J (hi [n, p])]

li,q,1 , li,q,2 , , li,q, L hi,q [n] = [hi,q [n, li,q,1 ], hi,q [n, li,q,2 ], , hi,q [n, li,q, L ]]T (34) q = 1,2, , MT ; i = 1,2, , MRThe STC technique reduces the estimation error and the complexity of the adaptive tracking process significantly. 3.6.3 Adaptive tracking for time-varying Time domain adaptive tracking algorithm is resorted to tracking the time varying channels. Based on the STC results, the estimation of the MISO channel

T

hi [n, p +1] = hi [n, p] + 2w*p [n]e[n, p] where is the step size. To guarantee the convergence property of the algorithm, is1 . MT L Since usually channel varies continuously between successive OFDM symbols, it is reasonable to initialize the estimation in the current OFDM symbol by the estimation results in the previous OFDM symbol, i.e. (45) hi [n,0] = hi [n 1]

(44)

selected to satisfy 0