Transmit Diversity Scheme over Single SC-FDM Symbol ... - IEEE Xplore

3 downloads 207 Views 184KB Size Report
{xluo, pgaal, wanshic, xiaoxiaz, juanm}@qualcomm.com. Abstract—In 3GPP LTE-Advanced, open-loop transmit di- versity schemes for the uplink are of great ...
Transmit Diversity Scheme over Single SC-FDM Symbol for LTE-Advanced Xiliang Luo, Peter Gaal, Wanshi Chen, Xiaoxia Zhang, and Juan Montojo Qualcomm Research Center, 5665 Morehouse Drive, San Diego, CA 92121, USA {xluo, pgaal, wanshic, xiaoxiaz, juanm}@qualcomm.com

Abstract— In 3GPP LTE-Advanced, open-loop transmit diversity schemes for the uplink are of great interest. It seems that, space-frequency block code (SFBC), the diversity scheme already adopted in the downlink of LTE Release-8, would be a natural option. However, when applying SFBC directly to the uplink, the resulting waveform at one transmit antenna becomes multi-carrier like with higher peak to average power ratio (PAPR), which limits the power efficiency of the corresponding power amplifier (PA). Another option will be to apply conventional space-time block code (STBC) scheme over two consecutive single-carrier frequency-division multiplexing (SCFDM) symbols. But in some cases, one uplink slot contains an odd number of data SC-FDM symbols, then the last data symbol in the slot will become an orphan symbol over which the conventional STBC will not work. Hence, we want to find a transmission scheme that operates on a single SC-FDM symbol and is able to achieve similar diversity performance as SFBC. Meanwhile, we would like to preserve single-carrier waveform at both transmit antennas to maximize the PA efficiency. To meet this end, we propose a novel transmission scheme: “One Symbol STBC” that operates on a single SC-FDM symbol and can achieve full transmit diversity. Meanwhile, the single-carrier waveform requirement is fulfilled at both transmit antennas. In addition to theoretical justifications, link-level simulations are also carried out which proves our proposed “One Symbol STBC” indeed achieves similar diversity performance as SFBC while maintaining single-carrier waveform’s low PAPR.

Keywords: Alamouti, LTE, LTE-Advanced, SFBC, STBC, Transmit Diversity, SC-FDM, OFDM I. I NTRODUCTION To meet the ever growing demand for higher data rate in mobile communication, the 3rd Generation Partnership Project (3GPP) has developed and released the technical specifications for the Long-Term Evolution (LTE) [2], [3]. The objective of LTE is to develop a framework for the evolution of the 3GPP radio-access technology towards a high-data-rate, low-latency and packet-optimized radio-access technology [1]. Some key features of the LTE air interface are briefly listed as follows: - orthogonal frequency division multiple access (OFDMA) for the downlink (DL); single-carrier frequency division multiple access (SC-FDMA) (a.k.a. DFT-spread OFDM) for the uplink (UL); - DL supports single-user MIMO (SU-MIMO) up to 4x4 antenna configuration; UL only supports single input single output (SIMO) transmission; - with 20MHz system bandwidth, LTE provides a peak data rate up to 300Mbps (assuming 4 spatial layers) in the DL and 75Mbps in the UL (assuming 1 spatial layer).

A nice introduction to SC-FDMA can be found in [10]. Compared to orthogonal frequency division multiplexing (OFDM) waveform, single-carrier frequency division multiplexing (SCFDM) waveform enjoys lower peak-to-average power ratio (PAPR) [11]. As a result, the power amplifier (PA) at the user equipment (UE) can operate at higher efficiency with SC-FDM waveform. Thus, the usage of SC-FDM waveform can help to close the link for those power-limited UEs(e.g. cell edge UEs). Besides, SC-FDM can lead to longer battery life than OFDM. Hence, SC-FDMA was selected as the uplink multiple access scheme in LTE. In the mid of 2008, LTE-Advanced (LTE-Adv) study item was created within 3GPP to study possible technologies for further advancements of the LTE technologies. As mentioned in [4], it is required that LTE-Adv should target 15bps/Hz as the UL peak spectrum efficiency. To achieve this requirement, LTE-Adv UL has to support multi-antenna transmission up to 4x4. With multiple transmit antennas being available at the UE, open-loop transmit diversity (OLTD) schemes for uplink are of great interest and importance. Unfortunately, spacefrequency block code (SFBC) [9], the usually adopted diversity scheme in MIMO OFDM systems including the LTE downlink [2], will render the transmitted waveform at one transmit antenna not single-carrier anymore, which will potentially decrease the PA capability. To achieve the similar diversity performance as SFBC without violating the requirement of keeping SC-FDM waveform at both transmit antennas, spacetime block code (STBC) [6] with careful tone mapping was proposed in [7]. However, this STBC scheme needs two paired SC-FDM symbols to construct the STBC code block. In some cases, there are only an odd number of SC-FDM symbols available for sending data within one slot of length 0.5ms, e.g. in the case of extended cyclic prefix (CP) configuration [2]. So an “orphan symbol” will be created when applying the conventional STBC scheme. Hence, we would like to find a transmission scheme which is able to achieve similar diversity performance as SFBC and does not require pairs of SC-FDM symbols to be operable. Meanwhile, we would like to preserve single-carrier waveform at both transmit antennas to maximize the PA power efficiency. In this paper, we present a novel transmission scheme that 1) operates over a single SC-FDM symbol; 2) can achieve full transmit diversity; and 3) fulfills the single-carrier waveform requirement at both transmit antennas. The remaining part of the paper is organized as follows: in Section II, we introduce

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

SC-FDM Symbol Generation

h1 (n)

Antenna 1:

s1

M-Point DFT

S1

Tone Mapping

X1

N-Point IFFT

M-Point DFT

S2

Tone Mapping

X2

N-Point IFFT

x1

CP Insertion P/S

Equiv. Channel Tx Ant 1, Rx Ant 1

CP Insertion P/S

Equiv. Channel Tx Ant 2, Rx Ant 1

+

Antenna2:

s2

x2

and the equivalent channel between the Transmit Antenna 2 at the UE and the Receiver Antenna at the eNB is modeled as {h2 (n)}. Assuming the time domain equivalent channels have L taps, we can define two length N vectors as follows: h1 h2

Antenna 1:

Antenna2:

h2 (n) Receiver Processing

Fig. 1.

R

Tone DeMapping

Y

N-Point FFT

y

CP Removal S/P

Multiple-antenna transmission in LTE-A uplink.

the system model for LTE-Adv uplink with multiple transmit antennas; Section III details the proposed diversity scheme for LTE-Adv uplink which we call “One Symbol STBC”; Simulated performance is shown in Section IV; and Section V concludes the paper. II. S YSTEM M ODEL In the following discussion, we will assume that UE has 2 transmit antennas and the base station (a.k.a. eNB in 3GPP terminology) has 1 receive antenna 1 . The key signal processing blocks in LTE-Adv uplink are illustrated in Fig. 1 and the functions of each block are explained as follows: M-Point DFT: this block is to perform a DFT precoding to the time domain vectors s1 = [s1 (0), ..., s1 (M − 1)]T and s2 = [s2 (0), ..., s2 (M − 1)]T , which are of length M and composed of complex modulation symbols from constellations such as QPSK, 16QAM, 64QAM and so on, i.e., S1 = FM ·s1 , S2 = FM · s2 , where FM is the M × M unitary DFT matrix; Tone Mapping: the function of the ”Tone Mapping” block is to map the precoded symbols in S1 := [S1 (0), ..., S1 (M −1)]T and S2 := [S2 (0), ..., S2 (M − 1)]T onto the assigned subcarriers for transmission. Since the multiplexing scheme used in LTE uplink is SC-FDMA, the sub-carriers that are mapped to should be a set of contiguous tones. Without loss of generality, we can assume the set of tones assigned for the uplink transmission are tones: 0, 1, 2, ..., M − 1. After the tone mapping, the output vectors are of the following form: XT1 = [ST1 , 0, ..., 0], XT2 = [ST2 , 0, ..., 0]; N-Point IFFT: this block simply performs N -point IFFT to the frequency domain vectors X1 and X2 and the outputs are: † † X1 and x2 = FN X2 , where FN is the N × N x1 = FN unitary DFT matrix; CP Insertion: this is a standard block in any OFDM system and is to insert cyclic prefix to the beginning of time domain vectors x1 and x2 ; Equiv. Channel: the equivalent discrete time channel abstracts the combination effects of the analog front end at the transmitter, the wireless channel between the transmitter and the receiver, and the analog front end at the receiver. The equivalent channel between the Transmit Antenna 1 at the UE and the Receiver Antenna at the eNB is modeled as {h1 (n)} 1 Note

that this antenna configuration is just for the purpose of describing various OLTD schemes concisely. The proposed schemes in this paper can be applied to any antenna configuration such as 2x2 which is actually used in the simulations in Section IV.

:= [h1 (0), ..., h1 (L − 1), 0, ..., 0]T , := [h2 (0), ..., h2 (L − 1), 0, ..., 0]T ;

(1) (2)

CP Removal: this block is responsible for removing the cyclic prefix from the discrete output of the receiver analog front end. Under the assumption of perfect timing and that the CP size exceeds the channel delay spread, after CP removal, we have the following important relationship, which is also the key equation for OFDM communication: for n = 0, 1, ..., N − 1, y(n) = x1 (n) ⊗N h1 (n) + x2 (n) ⊗N h2 (n) + w(n),

(3)

where ⊗N represents N -point circular convolution operation −1 2 and {w(n)}N n=0 are iid Gaussian noise with variance σ ; N-Point FFT: after performing N -point FFT to the received signal yT = [y(0), y(1), ..., y(N −1)], i.e., Y = FN ·y, we can obtain the following relation, which is another key equation for OFDM communication: for k = 0, 1, ..., N − 1, Y (k) = H1 (k)X1 (k) + H2 (k)X2 (k) + W (k),

(4)

where := [Y (0), Y (1), ..., Y (N − 1)]T ,

Y H1 H2 W

√ N FN · h1 , √ T := [H2 (0), H2 (1), ..., H2 (N − 1)] = N FN · h2 , := [W (0), W (1), ..., W (N − 1)]T = FN · w. := [H1 (0), H1 (1), ..., H1 (N − 1)]T =

−1 Since FN is a unitary matrix, {W (k)}N k=0 are iid with 2 variance σ . Tone De-Mapping: this block is to extract the tones of interest and form the M × 1 receive vector R as:

R := [Y (0), Y (1), ..., Y (M − 1)]T .

(5)

Now we have the end-to-end relation: R(k) = H1 (k)X1 (k) + H2 (k)X2 (k) + W (k) = H1 (k)S1 (k) + H2 (k)S2 (k) + W (k),

(6)

for k = 0, 1, ..., M − 1, where R := [R(0), R(1), ..., R(M − 1)]T . Receiver Processing: this block performs equalization, demodulation, and decoding tasks and will be our main focus in the following section. III. ACHIEVING D IVERSITY WITHIN S INGLE SC-FDM S YMBOL : O NE S YMBOL STBC In this section, we will show how to achieve full transmit diversity within a single SC-FDM symbol. From eq. (5) and (6), by defining: † · R, r := FM

˜1 h ˜2 h

:= :=

† FM † FM

(7)

· [H1 (0), ..., H1 (M − 1)] ,

(8)

· [H2 (0), ..., H2 (M − 1)]T ,

(9)

T

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

where

r := ˜ h1 := ˜ 2 := h

[r(0), ..., r(M − 1)]T , ˜ 1 (0), ..., h ˜ 1 (M − 1)]T , [h ˜ 2 (0), ..., h ˜ 2 (M − 1)]T , [h

we have: r(n)

Cyclic Prefix: P1

Data 1

Cyclic Prefix : P1 Data 2 Cyclic Postfix : P2 Data 2

Cyclic Postfix : P2

Cyclic Prefix: P1

Cyclic Prefix : P1 Data 1 Vector of M Time Domain Symbols

Cyclic Postfix : P2

1 ˜ 1 ˜ = √ h h2 (n) ⊗M s2 (n) 1 (n) ⊗M s1 (n) + √ M M +w(n), ˜ (10)

where ⊗M stands for M -point circular convolution, s1 (n) and s2 (n) are the transmitted time domain complex modM −1 ulation symbols, and {w(n)} ˜ n=0 is the M -point IDFT of M −1 {W (k)}k=0 . ˜ 2 (n)}. ˜ 1 (n)} and {h Now, we can take a closer look at {h −1 as: By defining {φ(n)}N n=0 [φ(0), ..., φ(N − 1)]T = † · [H1 (0), ..., H1 (M − 1), 0, ..., 0]T , FN   

(11)

N −M

and assuming mod (N, M ) = 0 and K = N/M , we have the following equation: √ ˜ 1 (n) = Kφ(nK), ∀n ∈ {0, ..., M − 1}, (12) h ˜ 1 (n) is simply down-sampled φ(n). Meanwhich means h while, we have: [φ(0), ..., φ(N − 1)]T = † · [H1 (0)Ψ(0), ..., H1 (N − 1)Ψ(N − 1)]T , (13) FN

where [Ψ(0), ..., Ψ(N − 1)] = [1, ..., 1, 0, ..., 0]    M

is a length-M rectangular window function. Then we have: φ(n) = h1 (n) ⊗N ψ(n),

(14)

where ψ(n) is N -point IDFT of the windowing function {Ψ(n)}: [ψ(0), ..., ψ(N − 1)] = FN · [Ψ(0), ..., Ψ(N − 1)] . T

T

It can be verified that: 1 sin(πM n/N ) j π(M −1)n N e ψ(n) = √ , N sin(πn/N )

(15)

with one-sided mainlobe width equal to N/M = K. Since {h1 (n)} has L non-zero taps and {φ(n)} is the circular convolution of {h1 (n)} and {ψ(n)}, it is easily seen that {φ(n)} has about L + 2K taps of significant energy, i.e. {φ(0), ..., φ(L + K)} and {φ(N − K), ..., φ(N − 1)}. From eq. (12), if we define ν as: ν := L/K + 1, (16) ˜ 1 (n)} concentrates over we conclude that the energy of {h ˜ 1 (ν)} and h ˜ 1 (M − 1). Similarly, the energy ˜ 1 (0), ..., h taps {h ˜ 2 (0), ..., h ˜ 2 (ν)} and ˜ 2 (n)} concentrates over taps {h of {h ˜ 2 (M − 1). h

Fig. 2.

Cyclic Postfix : P2

s1 (n)

s2(n)

Time domain signal structure.

Now, we can let the transmitted time domain signals s1 (n) and s2 (n) exhibit the following structure (see also Fig. 2):  s1 = a(Q − P1 ), ..., a(Q − 1), a(0), ..., a(Q − 1), a(0), ..., a(P2 − 1), b(Q − P1 ), ..., b(Q − 1),  (17) b(0), ..., b(Q − 1), b(0), ..., b(P2 − 1) ,  s2 = ˜b(Q − P1 ), ..., ˜b(Q − 1), ˜b(0), ..., ˜b(Q − 1), ˜b(0), ..., ˜b(P2 − 1), −˜ a(Q − P1 ), ..., −˜ a(Q − 1),  −˜ a(0), ..., −˜ a(Q − 1), −˜ a(0), ..., −˜ a(P2 − 1) , (18) where a ˜(n) = a∗ ( mod (−n, Q)), ˜b(n) = b∗ ( mod (−n, Q)), ∀n ∈ {0, ..., Q − 1}, and {a(n)}, {b(n)} are information bearing modulation symbols. Clearly, we have: 2(Q+P1 +P2 ) = M . It is because the time domain vectors s1 and s2 have the above structures that we call this transmission scheme “One Symbol STBC”. Choosing P1 and P2 judiciously such that P1 ≥ ν and P2 ≥ 1, we can now extract two Q-by-1 vectors from {r(n)} defined in eq. (10) as follows: r1 r2

:= :=

[r(P1 ), r(P1 + 1), ..., r(P 1 + Q − 1)]T , (19) [r(2P1 + P2 + Q), r(2P1 + P2 + Q + 1), ..., r(2P1 + P2 + 2Q − 1)]T . (20)

˜ 1 (n)} Since the time domain energy spread of the channels {h ˜ 2 (n)} are limited to ν + 1 taps, we can define two and {h shortened channels as: [λ1 (0), ..., λ1 (Q − 1)] = ˜ 1 (ν), 0, ..., 0, h ˜ (M − 1)], ˜ 1 (0), ..., h [h    1

(21)

Q−ν−2

[λ2 (0), ..., λ2 (Q − 1)] = ˜ 2 (ν), 0, ..., 0, h ˜ (M − 1)], . ˜ 2 (0), ..., h [h    2

(22)

Q−ν−2

From (10), (17), (18), (19), and (20), the following relationship can be established: λ1 (n) λ2 (n) ⊗Q a(n) + √ ⊗Q ˜b(n) + w1 (n),(23) r1 (n) = √ M M λ1 (n) λ2 (n) ⊗Q b(n) − √ ⊗Q a ˜(n) + w2 (n),(24) r2 (n) = √ M M

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

where ⊗Q means Q-point circular convolution operation and ˜ w1 (n), w2 (n) are the corresponding noise samples from w(n) in eq. (10). Applying Q-point DFT to both sides of eq. (23) and eq. (24), we can get: √ √ Q Q R1 (k) = √ Λ1 (k)A(k) + √ Λ2 (k)B ∗ (k) + W1 (k), (25) √M √M Q Q R2 (k) = √ Λ1 (k)B(k) − √ Λ2 (k)A∗ (k) + W2 (k), (26) M M for k = 0, 1, ..., Q − 1, where [R1 (0), ..., R1 (Q − 1)]T = FQ · [r1 (0), ..., r1 (Q − 1)]T , [R2 (0), ..., R2 (Q − 1)]T = FQ · [r2 (0), ..., r2 (Q − 1)]T , [Λ1 (0), ..., Λ1 (Q − 1)]T = FQ · [λ1 (0), ..., λ1 (Q − 1)]T , [Λ2 (0), ..., Λ2 (Q − 1)]T = FQ · [λ2 (0), ..., λ2 (Q − 1)]T , [A(0), ..., A(Q − 1)]T = FQ · [a(0), ..., a(Q − 1)]T , [B(0), ..., B(Q − 1)]T = FQ · [b(0), ..., b(Q − 1)]T .

Now it is clear that standard Alamouti STBC processing can be applied and we get: (28) Λ∗1 (k)R1 (k) − Λ2 (k)R2∗ (k) = √ Q √ (|Λ1 (k)|2+|Λ2 (k)|2 )A(k)+Λ∗1 (k)W1 (k)−Λ2 (k)W2∗ (k), M Λ2 (k)R1∗ (k) + Λ∗1 (k)R2 (k) = (29) √ Q √ (|Λ1 (k)|2+|Λ2 (k)|2 )B(k)+Λ2 (k)W1∗ (k)+Λ∗1 (k)W2 (k). M From the above equations, it is clear that full transmit diversity is indeed achieved with the transmission scheme described in (17) and (18) (see also Fig. 2). Furthermore, if we assume the fading channels in (1) and (2) have been normalized, i.e., the average total power is 1, we know the average total power of {φ(n)} in (13) is M . After down-sampling in (12), we ˜ 1 (n)} is still about M . know the average total power of {h The same conclusion can be made for {λ1 (n)} in (21) and {λ2 (n)} in (22). By letting the symbol power be E[|s1 (n)|2 ] = E[|s2 (n)|2 ] = P/2 at each transmit antenna, the signal-tonoise ratio averaged over fading channels in eq. (28) (same for (29)) can be calculated as: Q 2 M E[|Λ1 (k)|

+ |Λ2 (k)|2 ]E[|A(k)|2 ] P = 2. σ2 σ

† S2 , is not a vector It turns out that the IDFT of S2 , i.e. FM composed of complex modulation symbols from constellations such as QPSK, 16QAM, 64QAM and so on. Thus, when applying SFBC, the waveform from the second transmit antenna is not SC-FDM anymore. Following the same signal paths as depicted in Fig. 1, after Tone De-Mapping, from eq. (6), we can get:

R(2k)

= H1 (2k)S1 (2k) + H2 (2k)S2 (2k) + W (2k) (32) = H1 (2k)S1 (2k) + H2 (2k)S1∗ (2k + 1) + W (2k),

and similarly, we have: R(2k + 1)

=

H1 (2k + 1)S1 (2k + 1) − H2 (2k + 1)S1∗ (2k) +W (2k + 1).

We can rewrite (25) and (26) in the following matrix vector format: √     Q Λ1 (k) Λ2 (k) A(k) W1 (k) R1 (k) =√ + . (27) ∗ ∗ ∗ R2∗ (k) W2∗ (k) M −Λ2 (k) Λ1 (k) B (k)

SN R =

domain signal for the second transmit antenna can be directly constructed from S1 as follows: for n = 0, 1, ..., M/2 − 1,

S2 (2n) = S1 (2n + 1)∗ , (31) S2 (2n + 1) = −S1 (2n)∗ .

(30)

Now, let us deviate from “One Symbol STBC” temporarily and take a look at how conventional SFBC will perform when there was no single-carrier waveform constraint. In case of SFBC, we will not need the M-Point DFT block for the second transmit antenna in Fig. 1 and the frequency

(33)

Under the assumption that the channel can be regarded flat between adjacent tones, i.e. H1 (2k) = H1 (2k + 1) and H2 (2k) = H2 (2k + 1), from (32) and (33), we can obtain: H1∗ (2k)R(2k) − H2 (2k)R∗ (2k + 1) =

(|H1 (2k)|2 + |H2 (2k)|2 )S1 (2k) +

H2 (2k)R



H1∗ (2k)W (2k) − H2 (2k)W ∗ (2k + 1),

(2k) + H1∗ (2k)R(2k + 1) = (|H1 (2k)|2 + |H2 (2k)|2 )S1 (2k + 1) + H2 (2k)W ∗ (2k) + H1∗ (2k)W (2k + 1).

(34)

(35)

The signal to noise ratio averaged over fading channels can be found to be P/σ 2 , which is the same as the SNR computed in eq. (30). Comparing eqs. (28), (29) with eqs. (34), (35), it should be evident that our proposed “One Symbol STBC” achieves the same diversity performance as the conventional SFBC whereas SFBC scheme can not maintain single-carrier waveform at the second transmit antenna. Our proposed scheme transmits SCFDM waveform at both transmit antennas. In the next section, we will provide some simulated performance of our proposed OLTD scheme and compare our scheme with several other candidates which also preserve single-carrier waveform at each transmit antenna. IV. S IMULATED P ERFORMANCE In this section, we simulated our scheme in the context of the LTE uplink with normal cyclic prefix configuration according to [2]. For all the following simulations, we will assume there are 2 transmit antennas at the UE and 2 receive antennas at the eNB, and we will adopt the 6-path typical urban (TU) channel model as described in [5]. The powerdelay profile is plotted in Fig. 3. The UE speed is assumed to be v = 3km/h and the channel fading Doppler spectrum is assumed to be the classical one [5]: S(f ) = A/ 1 − (f /fd )2 , f ∈ (−fd , fd ), where fd is the maximum Doppler frequency.

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

Typical Urban Channel

QPSK, Rate=1/2, 10RB, Ideal Channel

0

0

10 Path 2

One Symbol STBC: −a: 0% OH, P1=0, P2=0 −b: 10% OH, P1=5, P2=1 −c: 20% OH, P1=10, P2=2

−1

−3

10

Path 1 −2

−4

10 FER

Relative power (dB)

−1

Path 3

−2

−5 Path 4

−3

−6

10

−7 Path 5

−4

−8

10

−9 Path 6 −10

−5

0

1

Fig. 3.

2

3 Relative time (μs)

4

5

10

6

Power-Delay profile of TU channel.

−4

Fig. 5.

Large Delay CDD SFBC FSTD One Symbol STBC − a One Symbol STBC − b One Symbol STBC − c SIMO −2

6

8

FER performance with perfect channel knowledge.

QPSK, Rate=1/2, 10RB, Estimated Channel

0

0

0 2 4 Tone SNR per Rx Ant (dB)

10

One Symbol STBC: −a: 0% OH, P1=0, P2=0 −b: 10% OH, P1=5, P2=1 −c: 20% OH, P1=10, P2=2

−5 −1

10

−2

10

−15

~ |h (n)|2

FER

Relative Power (dB)

−10

1

−20

−3

10

−25 −4

10 −30

−35

−5

0

20

Fig. 4.

40

60 Channel Tap: n

80

100

120

Energy concentration in time domain.

At carrier frequency 2.0GHz, the Doppler frequency can be found as: fd = fc v/c = 5.6Hz. The system bandwidth is 5MHz and the FFT size in Fig. 1 is N = 512. Tone spacing used here is 15kHz. Thus, the sampling frequency after the receive filter is F s = 512 × 15 = 7.68MHz. From Fig. 3, we know the number of channel taps in (1) can be set to L = 40 > 5 × 7.68. The allocated uplink transmission bandwidth is 1.8MHz (corresponding to M = 120 tones). Clearly, we have ν = LM/N + 1 = 10 from eq. (16). In ˜ 1 (n)} as Fig. 4, we show one realization of the channel {h defined in (8), which verifies our approximation in (21). With QPSK modulation and rate-1/2 Turbo coding, the performance of different transmit diversity schemes for LTE-Adv uplink is shown in Fig. 5 with perfect receiver side channel knowledge, and in Fig. 6 with estimated channel knowledge at the receiver by exploiting an IDFT-based channel estimation algorithm. In Fig. 5 and 6, “FSTD” stands for frequency

10

−4

Fig. 6.

Large Delay CDD SFBC FSTD One Symbol STBC − a One Symbol STBC − b One Symbol STBC − c SIMO −2

0 2 4 Tone SNR per Rx Ant (dB)

6

8

FER performance with estimated channel knowledge.

switch transmit diversity and “CDD” stands for cyclic delay diversity, and “One Symbol STBC” denotes the proposed diversity scheme in the current paper. Fig. 7 illustrates how the scheme “FSTD” works. While simulating CDD, we have used a large delay value of 128 samples (wrt the FFT size: 512). Note that, unlike “SFBC”, “FSTD”, “CDD”, and “One Symbol STBC” all preserve the single-carrier waveform at both transmit antennas. Clearly, with 10% overhead (P1 = 5, P2 = 1), our proposed “One Symbol STBC” can achieve the same FER performance as “SFBC” and performs much better than “FSTD” and “CDD”. The complementary CDFs of the PAPR of the transmitted waveform at each transmit antenna for each diversity scheme are plotted in Fig. 8, from which we see clearly the PAPR advantage of our proposed scheme. The other related configuration parameters in the simulations are listed below:

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

S1

V. C ONCLUSION

S2 S3 S4

M/2-DFT

S1

0

S2

0

S3

0

S4 Q1 M/2-DFT

N-IFFT

Ant1

N-IFFT

Ant2

0

FSTD

0

Q2

0

Q3

0 0

Q4

Q1 Q2 Q3 Q4

Fig. 7.

FSTD transmit diversity scheme.

0

10

−1

In this paper, we have described a novel open-loop transmit diversity scheme: “One Symbol STBC”, which enjoys the following advantageous features: - low PAPR SC-FDM waveform transmission at both transmit antennas; - single SC-FDM symbol operation; - being able to achieve similar diversity performance as SFBC. The salient enabling idea for this scheme is the time domain transmitted modulation symbols before the DFT spreading block at each transmit antenna are arranged in the way shown in eq. (17), (18), and Fig. 2 so that one SC-FDM symbol is effectively split into two shorter single-carrier symbols in time domain. Note that the cyclic prefix size P1 , the cyclic postfix size P2 , and the overhead incurred by “One Symbol STBC”, i.e. 2(P1 +P2 )/M , can be flexibly configured according to the channel delay spread and the desired performance requirement.

10 CCDF

R EFERENCES

CDD, Tx Ant 1 CDD, Tx Ant 2 FSTD, Tx Ant 1 FSTD, Tx Ant 2 SFBC, Tx Ant 1 SFBC, Tx Ant 2 One Symbol STBC, Tx Ant 1 One Symbol STBC, Tx Ant 2

−2

10

−3

10

4

5

6

7

8

9

PAPR (dB)

Fig. 8.

PAPR comparisons of different diversity schemes.

Prefix(Postfix) size P1 (P2 ) in eq. (17): 0(0): 0% overhead, 5(1): 10% overhead, 10(2): 20% overhead; Symbol detector: first carrying out MMSE equalization in frequency domain [8], [12], then performing symbol detection in time domain; Turbo decoder: max-Log-MAP algorithm with maximum 8 iterations; Slot boundary frequency hopping: no; Pilot sequences for different tx antennas: different cyclic shifts of a common Zadoff-Chu sequence [2]; Channel estimation: averaging two pilots within one subframe of length 1ms.

[1] 3GPP Technical Report 25.913, ver. 8.0.0, “Requirements for Evolved UTRA (E-UTRA) and Evolved UTRAN (E-UTRAN),” Dec. 2008. [2] 3GPP Techinical Specification 36.211, ver. 8.4.0, “Physical channels and modulation,” Sept. 2008. [3] 3GPP Techinical Specification 36.212, ver. 8.4.0, “Multiplexing and channel coding,” Sept. 2008. [4] 3GPP Technical Report 36.913, ver. 8.0.0, “Requirements for further advancements for E-UTRA,” Jun. 2008. [5] 3GPP Technical Specification 45.005, ver. 8.3.0, “Radio transmission and reception,” Nov. 2008. [6] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE Journal on Selected Areas in Communications, vol. 16, pp. 1451-1458, Oct. 1998. [7] Alcatel Shanghai Bell, Alcatel-Lucent, “STBC-II scheme for uplink transmit diversity in LTE-Advanced,” 3GPP TSG RAN WG1 #53bis, R1-082500, Jun. 2008. [8] D. Falconer, S. L. Ariyavisitakul, et al, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Communications Magazine, pp. 58-66, Apr. 2002. [9] K. F. Lee and D. B. Williams, “A space-frequency transmitter diversity technique for OFDM systems,” in Proc. 2000 IEEE Global Communications Conference, pp. 1473-1477, Dec. 2000. [10] H. G. Myung, J. Lim, and D. J. Goodman, “Single carrier FDMA for uplink wireless transmission,” IEEE Vehicular Technology Magazine, pp. 30-38, Sept. 2006. [11] H. G. Myung, J. Lim, and D. J. Goodman, “Peak-to-average power ratio of single carrier FDMA signals with pulse shaping,” in Proc. 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), pp. 1-5, Sep. 2006. [12] T. Shi, S. Zhou, and Y. Yao, “Capacity of single carrier systems with frequency-domain equalization,” in Proc. IEEE 6th CAS Symposium on Emerging Technologies: Mobile and Wireless Comm., pp. 429-432, May 2004.

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.