IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 8, AUGUST 2009

1

A New Full Rate Relaying Method for 4G OFDM Systems Afif Osseiran and Andrew Logothetis

Abstract—In this paper, we introduce a new transmit architecture that employs a 2-Dimensional Fourier Transform and a 2-Dimensional Cyclic Prefix (2D-CP) at the base station. In addition, the proposed scheme incorporates relay nodes that forward the received signals with one OFDM symbol delay. The new method introduces artificial frequency, time and spatial diversity, and unlike previously proposed relaying communication systems, the proposed scheme requires only a single transmission phase. Extensive system simulation studies have shown impressive system throughput gain compared to a single hop and conventional 2-hop systems. Index Terms—Cooperative relaying, OFDM, system performance, full rate.

I. I NTRODUCTION

T

HE main driving force in the development of wireless communication networks and systems is to provide, among other aspects, increased coverage or support for higher data rate, or a combination of the two. Until recently the main topology of wireless communication systems has been fairly unchanged for the three existing generations of cellular networks. The dominant topology of wireless communication systems is characterized by the cellular architecture, which consists of fixed radio Base Stations (BS) and User Terminals (UTs) as the only transmitting and receiving entities in the network. Several transmission/radio access technologies have been proposed to increase capacity, flexibility and/or coverage in wireless communication systems. Among those access techniques is Orthogonal Frequency Domain Multiplexing (OFDM). The OFDM receiver is relatively simple, since the multiple data streams are transmitted over a number of parallel flat fading channels, and equalization is done in the frequency domain involving a single tap filter per subcarrier. One way to introduce diversity in the received signal is to utilize multiple antennas at the transmitter and possibly also at the receiver. The use of multiple antennas offers significant diversity and/or multiplexing gains relative to single antenna systems [1], [2], [3]. The spatial diversity offered by Multiple Input Multiple Output (MIMO) can thus improve the link reliability and the spectral efficiency relative to Manuscript received December 29, 2006; revised July 31, 2007, December 20, 2008, and March 23, 2009; accepted June 4, 2009. The associate editor coordinating the review of this paper and approving it for publication was M. Chiang. Part of this work has been performed in the framework of the IST project IST-4-027756 WINNER II, which is partly funded by the EU. The views expressed are those of the authors and do not necessarily represent the project. A. Osseiran is with Ericsson Research, Stockholm, Sweden (e-mail: [email protected]). A. Logothetis is with Airspan Network. He was previously with Ericsson Research (e-mail: [email protected]). Digital Object Identifier 10.1109/TWC.2009.061077

Single Input Single Output (SISO) systems. An alternative approach is to introduce macro-diversity utilizing cooperative relaying. A relaying system is based on a conventional radio network complemented with Relay Nodes (RNs). The RNs communicate wirelessly with other network element (e.g. BS, another RN or a UT). A cooperative relaying system is a relaying system where the information sent to an intended destination is conveyed through various routes and combined at the destination. Each route can consist of one or more hops utilizing the RNs. In addition, the destination may receive the direct signal from the source. Such systems offer possibilities of significantly reduced path loss between communicating entities. Cooperative relaying systems [4] are typically limited to only two (or a limited number) hops. Cooperative relaying systems are generally divided into two categories. A signal may be decoded, re-modulated and re-transmitted, or alternatively simply amplified and retransmitted. The former is known as decode-and-forward, whereas the latter is known as amplify-and-forward. Various aspects of the two approaches are addressed in [5]. The introduction of cooperative relaying systems has the potential of increased macro-diversity gains. This gain comes at an extra cost; in terms of power, hardware and maintenance. There are several well-known schemes that offer such gains: Alamouti diversity based cooperative relaying [6], coherent combining based relaying [7] which offers additional beamforming gain and RCDD1 (Relay Cyclic Delay Diversity) [8], [9]. These schemes require two transmission phases for each DL and UL direction: for instance in the DL, in the first transmission phase the BS transmits to the RN, and in the second transmission phase the RN transmits to the UT. The two phase transmission methods may effectively reduce the data throughput by half. Of course, relaying schemes offer macro diversity gain, and the precise throughput gains can only be computed through extensive system simulation studies. A method that introduces artificial frequency, time and spatial diversity and requires only a single transmission phase for each direction in a cooperative relaying wireless communication system, is proposed here. The artificial selectivity is exploited in conjunction with forward error correction coding to provide coding diversity gain. Each BS transmits data to K RNs and to the desired UT during a predefined period. The RN forwards the information received from the BS to the UT with one symbol delay. Figure 1 illustrates the difference between the 1-hop, classical 2-hop and the 2-Dimensional Cyclic Prefix (2D-CP) 1 In analogy to CDD and in order to provide frequency selectivity and spatial diversity, RCDD consists of using a set of distributed RNs. The set is treated as a single entity composed of multiple antennas where antenna specific cyclic shift is applied to the OFDM symbol.

c 2009 IEEE 1536-1276/09$25.00 

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 8, AUGUST 2009

x2n+1

x2n

BS

BS

UT

(a) 1-hop Slot 2n.

UT

(b) 1-hop Slot 2n + 1.

x2n x2n

RN RN

UT

BS

UT

BS (c) 2-hop Slot 2n.

(d) 2-hop Slot 2n + 1.

x2n−1

x2n x2n+1

x2n x2n

x2n+1

RN

BS

UT (e) 2D-CP Slot 2n.

Fig. 1.

RN

BS

UT (f) 2D-CP Slot 2n + 1.

Transmission Phase for 1-hop, 2-hop and 2D-CP.

system. As shown in Figures 1(a) and 1(b), in a 1-hop system the data signal is transmitted to the UT in two consecutive time slots (i.e. 2n and 2n + 1). For instance, the symbol x2n is transmitted at the time slot 2n and is followed by x2n+1 at the next slot. By contrast in a 2-hop system, in order to avoid the BS and RN interfering with each other the transmission is done in two phases (i.e. hops). During the first hop (2n slot in Figure 1(c)) the BS transmits the data signal x2n to the RN. The UT may also receive x2n . During the second hop (2n + 1) the RN retransmits the same data signal x2n to the UT as shown in Figure 1(d). The transmission scheme of the proposed method, is illustrated in Figures 1(e) and 1(f). In contrast to the classical 2-hop system, the transmission now is full duplex. In fact, the BS will transmit during the two consecutive phases (eg. 2n and 2n+1) two different data signals (x2n and x2n+1 , respectively). As shown in Figure 1(e), during time slot 2n, the RN will forward data x2n−1 , which was received from the BS at the previous time slot (2n − 1). During time slot 2n + 1, the RN will forward the signal data x2n (see Figure 1(f)). 2D-CP offers numerous advantages, for instance it provides a substantial data rate increase achieving near full rate transmission. Further it increases the frequency and time selectivity of the channel and additionally does not require relay node antenna specific pilots. The paper is organized as follows: several definitions and notations will be presented first. Section III presents a mathematical model of the proposed scheme. The SINR derivation is also shown. The simulation setup is presented in Section IV. Finally, the results are shown in Section V.

II. D EFINITIONS AND N OTATIONS In this section, we will present the notations and definitions used throughout this article. Notation: Let  and ⊗ denote the Hadamard and the Kronecker product, respectively. (·)T denotes the transpose and (·)H the Hermitian transpose operator. Capital letters represent matrices, and lower case letters represent vectors or scalars. I N is the N × N identity matrix and 0N ×M is an N × M  denotes the 2D-FFT of the matrix matrix of zeros. Finally, X X. Definitions Definition 1: F M denotes the FFT matrix of size M × M . The (n, m)th element of F M , for n, m ∈ {1, 2, . . . , M }, is given by 1 F M (n, m) = √ e−j2π(n−1)(m−1)/M (1) M Definition 2: For an M × 1 vector a = [a(1), a(2), . . . , a(M )]T , the right circulant matrix [10] A  Circ(a) is generated as follows ⎡ ⎤ a(1) a(M ) a(M − 1) . . . a(2) ⎢ a(2) a(1) a(M ) . . . a(3) ⎥ ⎢ ⎥ ⎢ a(3) a(2) a(1) . . . a(4) ⎥ A=⎢ ⎥ (2) ⎢ .. .. .. .. ⎥ ⎣ . . . ... . ⎦ a(M ) a(M − 1) a(M − 2) . . . a(1) The right circulant matrix A is diagonalized using the FFT matrix F M as follows √ (3) A = MF H M D(F M a)F M

OSSEIRAN and LOGOTHETIS: A NEW FULL RATE RELAYING METHOD FOR 4G OFDM SYSTEMS

3

coded input data stream B

Fig. 2.

2D IFFT

X

2D CP

X'

Column Selection

Up Conv

Example of a 2D cyclic prefix transmission at the BS.

where D(x) denotes a diagonal matrix with x on its main diagonal. Definition 3: The 2-dimensional (2D) FFT of a matrix X of size N × M , is given by  = F N XF M X

xM

(4)

III. T HE P ROPOSED M ETHOD : 2D-CP An example of the proposed transmitter is shown in Figure 2. Let N denote the number of sub-carriers and let B denote a block of data occupying N subcarriers spanning a time window of M OFDM symbols. Unlike conventional OFDM, here a 2D IFFT is applied to the data block B. The output of the IFFT is denoted by X. X is subject to a 2D cyclic prefix operation. This is simply done by pre-appending to X the last column of X. The last rows of the augmented block is copied at the top as shown in Figure 3. In fact, the row-wise cyclic prefixing eliminates the inter-OFDM symbolinterference. Similarly, the column-wise cyclic prefix, as we will show, eliminates the interference from the simultaneous transmission of the data from the BS and RN. Let X  denote the output of the 2D-CP operation. The block X  is subjected to linear operations and is then transmitted. The linear operations simply consist of selecting one column of X  during each OFDM symbol transmission. At the first instant the first column of X  is selected. At the second time instant the second column of X  is selected. This process is repeated until all columns of X  are transmitted. The functional block ”Up Conv” in Figure 2, performs the upconversion of the signals from the baseband into the RF-band. At the UT, data detection can be carried out only when the entire data block has been received. The transmission process of the block data X  at the BS and the RN is illustrated in Figure 4. As shown in the figure, during the first time instant (t = 0), the last symbol xM is transmitted by the BS, and a noisy version of the signal is received by the UT (the received signal is denoted by y 0 ). The RN also receives the signal xM , but forwards it during the subsequent time slot. At time instant (t = 1), the BS transmits the first symbol x1 in the data block and the UT will receive a linear combination of xM from the RN and x1 from the BS. The process is repeated until the BS transmits the entire data sequence in X  . The receiver structure of the UT is shown in Figure 5. For each receive antenna, the data is first down-converted from the RF-band into baseband and then the CP is removed. The data is then subject to a 2D-FFT and equalized. The equalized outputs are then combined to yield the block data estimate B. In the example of Figure 5, the Maximum Ratio Combining (MRC) method was assumed. Contrary to the transmitter of the BS, the receiver and the transmitter of the RN applies onedimensional FFTs and one-dimensional IFFTs, respectively. In

x1

x2

xM-1

xM

N

{ (M+1) OFDM symbols Fig. 3.

Two Dimensional Cyclic Prefix. Block of OFDM symbols

TX at of BS

xM x 1

TX at of RN

RX at of UT y 0

x2

···

xM − 1 xM

xM x 1

x2

···

y1

···

y M− 1 yM

y2

xM − 1

t Fig. 4. A block of M OFDM symbols transmitted at the BS, relayed by the RN and received at the UT.

other words, the RNs employed in this system operate in the same way as the classical 2-hop relaying OFDM systems. Advantages of the proposed scheme: Compared to other relaying communication systems, the proposed 2D-CP method has the following advantages: M−1 • Substantial data rate increase in the order of M+1 , where M denotes the number of OFDM symbols per chunk. For example, if M = 16 then the gain is approximately 88% better than the conventional 2-hop system. • Antenna specific pilots are not required. Unlike the relaying Alamouti and relaying coherent combining schemes, the UT does not need to estimate the channel frequency response from each transmitter. Hence, there is no need to assign unique pilots on each TX antenna. In fact, the UT employing the proposed scheme, observes a combined/effective downlink channel from the BS and its associated RNs, and thus a single pilot pattern on the frequency/time grid is adequate for pilot assisted channel

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 8, AUGUST 2009

M RX antennas Down Conv

Rem CP

2D FFT

2D Equal

2D FFT

2D Equal

RN1

(j)

Down Conv

Rem CP

h1

MRC

(j)

g1

(j) g2

RN2

Bˆ N × M

(j)

gK Down Conv

Rem CP

2D FFT

BS

2D Equal

RNK

Fig. 5.

Example of 2D-FFT Receiver at the UT. Fig. 6.

•

estimation. Frequency and time selectivity of the overall effective channel is increased. The proposed scheme applies a 2dimensional IFFT operation to a block of data symbols and this operation is equivalent to interleaving the data in time. Frequency selectivity is the by-product of spatial diversity. Hence the received signal at the UT will be more robust against bursty errors.

A. Mathematical Model A 2-hop wireless communication system comprising of one BS and a number of RNs is shown in Figure 6. Each BS and RN is equipped with one receive and one transmit antenna since the 2D-CP operates in a full duplex mode. Furthermore, at the RN, leakage of energy from the transmit antenna to the receive antenna is minimized using antenna isolation (one possibility is to use antennas with high front to back ratios)2 . The OFDM symbols at the RN are received without error and re-transmitted with one OFDM symbol delay. Since the BS and the RNs transmit at the same time, the received symbol y m at the UT is a linear combination of the transmitted symbol (j) xm from the j th BS and the one OFDM delayed symbol (j) xm−1 transmitted from the RNs. Assuming that J BS and their associated RNs are transmitting on the same frequency band, then the received signal of the mth symbol at the UT of interest can be expressed as ym =

J 

(j) (j) (j) H 1 x(j) m + H 2 xm−1 + nm ,

(5)

j=1

where nm denotes the observation noise3 during the mth (j) (j) OFDM symbol period, H 1 = Circ(h1 ) is the channel (j) matrix between the j th BS and the UT, H 2 is the combined channel matrix from all K relays of the j th BS to the UT.

K (j) (j) (j) H 2 can be expressed as: H 2 = k=1 Circ(g k ) = (j) (j) Circ(h2 ), where g k for k ∈ {1, . . . , K}, denotes the channel impulse response from the k th RN of the j th BS (j) to the UT. h2 is the effective channel impulse response and 2 Such techniques are well established in today’s wireless systems employing 2G and 3G repeaters. 3 The noise expression takes into account the effect of noise amplification for the amplify-and-forward case.

The j th cell consisting of one BS and K RNs.

its FFT can be expressed (as shown in [8]) as:  (j) = h 2

K √

(j) N ( g k  eδ(j) ), k

k=1

(6)

(j) where δk is the cyclic shift delay of the k th RN associated with the j th BS, and el is the lth column of I N . Define the following

Y

=

X

(j)

=

H

(j)

= =

N

[y 1 , y 2 , . . . , y M ],

(j) (j) (j) [x1 , x2 , . . . , xM ], (j) (j) [h1 , h2 , 0, . . . , 0],

[n1 , n2 , . . . , nM ].

(7) (8) (9) (10)

Applying a 2D-FFT to the block received data of Eq. (7) yields the following: Y =

J

√ √   , (11) N M H (1) B (1) + N M H (j) B (j) +N j=2

where the first term is the signal of interest (obtained using Theorem 1, which is shown in the Appendix), where B (j) is the transmitted block data and is obtained by taking the 2DIFFT of X (j) . The second term represents the interference observed from other cells (also derived using Theorem 1) and  denotes the thermal noise. The elements of N  are finally N  i.i.d. complex Gaussian random variables. The mean of N H } =  N is 0N ×M and its covariance matrix is Q = E{N H 2 FH E{N N }F = M σ I . The transmitted data block N N N B (j) from the j th BS has an average power given by E{B (j) 2F } = M p(j) , where  · F denotes the Frobenius norm of a matrix, and p(j) denotes the transmitted power per OFDM symbol.

B. Derivation of the SINR Assuming the block data B (j) from different BSs are mutually uncorrelated, and p(j) is equally divided among the N sub-carriers, then the SINR, SINR(n, m), on the nth tone

OSSEIRAN and LOGOTHETIS: A NEW FULL RATE RELAYING METHOD FOR 4G OFDM SYSTEMS

BS RN

4000 11

9

in [11] and is extensively used in the Winner project [12], [13]. The path loss of the extended SCM is given in dB by:

3000 4

5

L = A log10 (d) + B

2

(13)

2000 18

1000

16

10

0

8

3

1

17

−1000

where d is the distance, A and B depend on the radio channel scenario (e.g. for Metropolitan suburban A = 35 and B = 31). Similar radio propagation conditions between the UT the BS and RN are assumed.

14

7

15

21

12

C. Link to System interface

13

−2000 5

The model used for the link to system interface is based on the mutual-information metric which accounts for the modulation alphabet [14]. In order to calculate the Packet Error Rate (PER) the method follows the following steps:

6

−3000 19

20

−4000 −5000

−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

5000

•

Fig. 7.

Cell plan. •

of the mth OFDM symbol is given by:  2  √   E  N M H (1) (n, m)B (1) (n, m)

•

 2  √ 

J  (j) (j)   E  N M j=2 H (n, m)B (n, m) + N (n, m)  p(1) |H (1) (n, m)|2  (j) (j) |H (n, m)|2 + σ 2 j=2 p

= J

(12)

Note that the (post-filtering) SINR expression in Eq. (12) is calculated at the input of the constellation de-mapper, and is valid for the match filter, the zero forcing equalizer and the MMSE receiver, since for each n and m the signal model is an SISO flat fading channel. IV. S YSTEM M ODELING AND A SSUMPTIONS In this section the air interface characteristics and the system assumptions for the evaluation of the 2D-CP method are described. The most relevant parameters that characterizes the air interface are summarized in Table I. Note that only the downlink connection (when the UT is receiving) is considered. A. BS and RN deployment The simulated cell plan consists of seven sites, each site comprises of three sectors forming a regular hexagonal deployment topology as shown in Figure 7. The BSs are represented by circles and are placed where the three hexagons intersect. The RNs are placed on a circular arc around the BSs. Three RNs per cell are assumed (see Figure 7 where the RN is represented by a star sign). B. Path Loss and Channel The radio propagation channel and distance path loss model is an extension of the Spatial Channel Model (SCM) proposed

The user SINR of a specific chunk (the smallest addressable contiguous area in time and frequency) is calculated after receiver processing. For each chunk, the average mutual information per bit (MIB) is calculated depending on the modulation used. The MIB is mapped to a PER depending on the channel coding type and rate.

D. Radio Network Algorithms The most relevant Radio Network Algorithms (RNA) are described in this section. Handover & Link Adaptation Only hard handover is considered. In order to avoid ping-pong effects a handover margin of 3 dB is used. Modulation and channel coding were adapted to the channel conditions, which can be considered as an alternative and preferred method to power control. Scheduling In order to fully exploit the 2D-CP concept, Max-SINR scheduling is used. The frequency bandwidth is divided into several chunks, the user having the highest SINR for a given chunk, is scheduled. For instance, if the bandwidth is divided into 10 chunks then up to 10 users can be scheduled for the whole available bandwidth. Note that the SINR per chunk (or an equivalent measure, e.g. channel quality information) is available at the BS. Radio Node Selection The UT connects to the preferred BS and RNs based on long term averaging of the received signal (i.e. path loss and shadow fading). Note that for the reference case, only one out of three RNs will retransmit data to the scheduled users during the second transmission phase. The impact of the number of active RNs and their positions on the performance is addressed in Section V.

E. Evaluations Criteria Cell throughput is used as a measure to evaluate all the methods simulated in this paper. The cell throughput is the average number of correctly received bits over the entire simulation time divided by the simulation time and the number of cells.

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 8, AUGUST 2009

TABLE I A IR I NTERFACE PARAMETERS . Parameter Carrier Frequency Bandwidth Modulation Type Number of Subcarrier Number of Data Subcarriers Sub Carrier Spacing Symbol Period Frame Length Super Frame Length Coding Rate Power Control Handover Scheduling Relaying Decoding Method

Value 5.0 20 [4 16 64 256 512] 512 416 39.062 28.8 8 2 [1/3 1/2 2/3 8/9] None Hard Max-SINR amplify-and-forward

TABLE III C ELL T HROUGHPUT LOSS WITH CSI IMPAIRMENTS . Unit/Type GHz MHz QAM

kHz µs OFDM symbol Frame Turbo

TABLE II S IMULATION PARAMETERS . Parameter Number of Sites Number of Sectors per Site Wrap Around BS power RN power BS Antenna Gain RN Antenna Gain UT Antenna Gain UT Speed UT Noise Figure Shadow Fading Variance, LOS Shadow Fading Variance, NLOS

Value 7 3 Yes 43 37 14 10 0 3 9 3.5 8

Unit/Type

Add. Info

Modeled dBm dBm dBi dBi dBi m/s dB dB dB

3-Sector Omni Omni

Line Of Sight Non LOS

V. E NVIRONMENT D ESCRIPTION AND R ESULTS The evaluation is carried out using a dynamic system simulator. An average number of 10 UTs per sector is generated. A simple data traffic model is used since the interest is in the relative performance of the simulated schemes and not in the traffic modeling performance per se. Generated users have full buffers, ready to transmit when they are scheduled. The radio network cell plan is simulated over a certain number of snapshots. Each snapshot consists of a large number of super-frames which itself is composed of a certain number of radio frames. Each radio frame consists of a number of OFDM symbols. A set of new users is generated at the start of each super-frame, placed in the cell plan and associated to one BS. On the frame level, first the users will move according to the chosen mobility model and then the propagation channel conditions will be generated (i.e. path loss, slow and fast fading). Thereafter, the traffic model will generate the data packets for all active users. Then, the scheduler will decide which users will be scheduled according to the channel quality measure. The users’ modulation and coding schemes will be decided by the link adaption algorithm. The link to system interface derives the block error rate taking into account the interference of all BSs and RNs. The entire process will be repeated until the desired number of snapshots is reached. The most relevant simulation parameters are described in Table II. The cdf of the received SINR of 1-hop and 2-hop systems for a cell radius of 1km is shown in Figure 8. The proposed method, yields 9 dB SINR gain at the median value relative to the single-hop system. On the other hand, the conventional 2-hop system offers slightly higher SINR gain (11 dB) at the expense of doubling the latency (two transmission phases are

SNR loss due to CSI impairments

Method

0dB

3dB

7dB

1-hop 2-hop 2D-CP

Γ0 (2) Γ0 (3) Γ0

0.7Γ0 (2) 0.9Γ0 (3) 0.9Γ0

0.4Γ0 (2) 0.7Γ0 (3) 0.7Γ0

(1)

(1)

(1)

TABLE IV C ELL THROUGHPUT FOR VARIOUS RN DISTANCES .

Method

R/2

2-hop 2D-CP

Γ0 (3) Γ0

(2)

RN distance √

R

(2)

1.14Γ0 (3) 1.10Γ0

2R

(2)

0.99Γ0 (3) 1.02Γ0

required). Although the interference increases when the 2D-CP method (BS and RNs simultaneously transmit) is employed, the SINR gain of the proposed method translates into a substantial cell throughput gain as shown in Figure 9. In fact, for a cell size ranging from 0.5km to 2km, 2D-CP yields up to 2 times cell throughput gain compared to the 1-hop system. The conventional 2-hop system at best provides 30% increase in cell throughput. In the following subsections we will investigate the impact on the performance of various deployment strategies (i.e. RN positions), the number of active RNs associated with each BS, and finally, the channels impairments (i.e. Channel State (1) (2) (3) Information (CSI) errors). Let Γ0 , Γ0 and Γ0 denote the reference cell throughput for the 1-hop, conventional 2-hop and the 2D-CP method, respectively. The above mentioned throughput values were computed under the following assumptions: perfect CSI, cell radius of 1km, a single active RN per cell, and each RN is placed at 0.5km from the BS. A. CSI impairments The cell throughput was computed using different levels of CSI impairments and is summarized in Table III. The 1hop system is more vulnerable to channel estimation than the conventional 2-hop and 2D-CP methods. In fact, the throughput is more than halved in the 1-hop system compared to relaying. The benefit of macro-diversity (i.e. path loss gain) is clearly evident. Of course, as the CSI error variance increases, the performance degrades. The system throughput degradation using the two relay schemes is approximately 30% even for high level of impairments. B. RN deployment strategies The conventional 2-hop and the 2D-CP method are evaluated for three RNs deployment strategies. Each deployment consists of placing 3 RNs on an arc√of a circle with center the BS site and radius Rd ∈ {R/2, R, 2R}. R denotes the cell radius. Note the BS site-to-site distance is 3R. From Table IV we conclude that the RNs positions have a minor impact on the performance for both the 2D-CP and the 2-hop conventional systems. C. Number of active RNs Simultaneously utilizing more than one RN per cell will result in the rise of the interference originating from other

OSSEIRAN and LOGOTHETIS: A NEW FULL RATE RELAYING METHOD FOR 4G OFDM SYSTEMS

TABLE V C ELL THROUGHPUT VERSUS THE NUMBER OF ACTIVE RN S .

45

Number of Active RNs 2 3 (2) (2) (2) Γ0 0.94Γ0 0.88Γ0 (3) (3) (3) Γ0 0.95Γ0 0.90Γ0

40

System throughput [Mbps/cell]

1

Method 2-hop 2D-CP

7

100

90

80

35

1−hop 2−hop 2D−CP

30

25

70 20

cdf

60

50 15 500

1000

1500

40

Fig. 9. Cell throughput versus the cell radius R for 1-hop, 2-hop and the 2D-CP scheme√assuming perfect CSI, a single active RN per BS and each RN placed at 2R meters from the BS.

30

20 1−hop ,R=1000m 2−hop ,R=1000m 2D−CP ,R=1000m

10

0 −10

2000

Cell Raduis [m]

−5

0

5

10

15 SINR [dB]

20

25

30

35

40

Fig. 8. cdf of the SINR for 1-hop, 2-hop and 2D-CP schemes for a cell radius of 1km.

A PPENDIX (j) Let y m denote the signal received from the j th BS and its associated RNs, i.e. (j)

cells. Both the conventional 2-hop and the proposed 2DCP method will be affected and the cell throughput will be reduced. The degradation is in the same order for the two methods as shown in Table V. It should be clear that increasing the number of active RNs for transmission results in increasing the frequency selectivity of the effective channel observed at the UT. Clearly, the improvement in selectivity and the use of the Max-SINR scheduler cannot offset the inter-cell interference increase.

(j)

(j)

(j) y (j) m = H 1 xm + H 2 xm−1

(14)

Rearranging Eq. (14) into a matrix form yields the received (j) (j) (j) data matrix Y (j) = [y 1 , y 2 , . . . , y M ], Y (j)

=

2

(j)

H l X (j) P l ,

(15)

l=1 (j)

VI. C ONCLUSION In this paper a novel method that employs a 2-dimensional FFT in conjunction with a 2-dimensional cyclic prefix (2DCP) at the BS transmitter was proposed. The proposed scheme also incorporates relay nodes that forward the received signals with one OFDM symbol delay. The 2D-CP method introduces artificial frequency, time and spatial diversity and requires only a single transmission phase for each direction in a cooperative relaying wireless communication system. The proposed scheme was analyzed, evaluated and compared with a conventional 2-hop system in a dynamic system simulator. The proposed method provided numerous advantages, for instance relay node antenna specific pilots are not required, additionally it provides a substantial data rate increase achieving near full rate transmission. Further, it was shown that the 2D-CP method yields an impressive 9 dB SINR gain compared to a 1-hop system. The SINR gain translates into a substantial cell throughput gain. Extensive simulation studies have shown that the 2D-CP method yields 100% and 70% cell throughput gain compared to a 1-hop and a conventional 2-hop systems, respectively.

where H l and X (j) are defined in Eq. (9) and (8), respectively. The permutation matrices P l are given by: P1 P2

= IM = [eM , e1 , . . . , eM−1 ]

(16) (17)

Theorem 1: The 2-dimensional Fourier transform of Y (j) is given by √   Y (j) = N M H (j)  B (j) (18) where B (j) denotes the transmitted data block from BS j and  H (j) is the 2D-FFT of the channel matrix H (j) . Proof: Taking the 2-dimensional Discrete Fourier Transform of Y (j) , diagonalizing H (j) and P l , yields  Y (j)

=

2 

√ (j) F N X (j) F M NM D F N hl l=1

D (F M el )

(19)

8

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 8, AUGUST 2009

= =

√ √

M

NM

 (j)  D F N hl XD (F M el )

l=1 M 

NM

(j)

11×M ⊗ F N hl



(20)

  X (j) 

l=1   1N ×1 ⊗ eTl F M √  N M X (j)  F N H (j) F M = √   N M H (j)  X (j) = √  N M H (j)  B (j) =

(21) (22) (23) (24)

(j) hl

Eq. (20) is valid since = 0N ×1 for l > 2. Eq. (21) is derived by replacing the product of a matrix and a diagonal matrix by a function of Hadamard and Kronecker products [15]. Eq. (22) is derived using Lemma 1 and Eq. (23) follows from the definition of the 2D-FFT. Finally as stated in Section III, the transmitted block data B (j) is obtained by taking the 2D-IFFT of X (j) . Lemma 1: Let A = [a1 , a2 , . . . , aM ] be an N ×M matrix, and B = [b1 , b2 , . . . , bM ] an M × M symmetric matrix. Then AB =

M

 (11×M ⊗ am )  1N ×1 ⊗ bTm

(25)

m=1

Proof: Let C be given by C=

M

 (11×M ⊗ am )  1N ×1 ⊗ bTm

(26)

[4] J. N. Laneman, “Cooperative diversity in wireless networks: algorithms and architectures,” Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA, Aug. 2002. [5] J. N. Laneman and G. W. Wornell, “An efficient protocol for realizing distributed spatial diversity in wireless ad-hoc networks,” in ARL FedLab Symposium on Advanced Telecommunications and Information Distribution (ATIRP-2001), College Park, MD, Mar. 2001. [6] Anghel et al., “Distributed space-time coding in cooperative networks,” in Proc. IEEE Vehicular Technology Conference, Spring, Norway, Oct. 2002, pp. 9–10. [7] P. Larsson, “Large-scale cooperative relay network with optimal coherent combining under aggregate relay power constraints,” in Proc.. Future Telecommunications Conference, Beijing, China, Dec. 2003, pp. 166–170. [8] A. Osseiran, “Advanced antennas in wireless communications: colocated and distributed,” Ph.D. dissertation, Royal Institute of Technology, Stockholm, Sweden, May 2006. [9] A. Osseiran, A. Logothetis, S. B. Slimane, and P. Larsson, “Relay cyclic delay diversity: modeling and system performance.” in IEEE International Conference on Signal Processing and Communication (ICSPC07), Dubai, UAE, Nov. 2007. [10] R. M. Gray, Toeplitz and Circulant Matices: A Review. http://wwwee.stanford.edu/∼gray/toeplitz.pdf, 2002, Stanford, California. [11] 3GPP, “Spatial channel model for multiple input multiple output (mimo) simulations, tech. rep. 3GPP TR 25.996 V6.1.0, Sept. 2003, http://www.3gpp.org/ftp/Specs/html-info/25996.htm. [12] J. Meinil¨a, ed., IST-2003-507581 WINNER I, D5.4, Final report on link level and system level channel models, 2005, no. v1, http://projects.celtic-initiative.org/winner+. [13] ——, IST-2003-507581 WINNER I, D5.2, etermination of Propagation Scenario, 2005, no. v1, http://projects.celtic-initiative.org/winner+. [14] K. Brueninghaus et al., “Link performance models for system level simulations of broadband radio access systems,” in IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Berlin, Germany, Sept. 2005. [15] H. Lutkepohl, Handbook of Matrices. West Sussex, England: John Wiley& Sons Ltd, 1996.

m=1

The (k, l)th element of the C, which is denoted by C(k, l), is obtained by multiplying Equation (25) left and right by eH k and el , respectively, C(k, l) =

M

m=1

=

= =

  T (1 el eH ⊗ a )  1 ⊗ b 1×M m N ×1 m k ⎡

⎛

⎜ ⎜ eH k ⎜ am ⎝ m=1 M

M

m=1 M

am

am (k)bTm el =

. . . am



⎢ ⎢ ⎢ ⎣

bTm bTm .. .

⎤⎞ ⎥⎟ ⎥⎟ ⎥ ⎟ el ⎦⎠

bTm M

am (k)bm (l)

m=1

A(k, m)B(m, l)

Afif Osseiran [M’06] received a B.Sc.E.E degree in Electrical Engineering from Universit´e de Rennes I and INSA Rennes in 1997, and a M.A.Sc. degree in Electrical and Communication Engineering from ´ Ecole Polytechnique de Montr´eal, Canada, in 1999 ; and a Ph.D from the Royal Institute of Technology (KTH) in Stockholm, in 2006. Since 1999, he has worked for Ericsson, Sweden. In 2004, as one of Ericssons representatives, he joined the European project WINNER funded under the 6th Framework Programme. During 2006 and 2007, he led the spatial temporal processing (i.e. MIMO) task, which mainly deals with multiple antenna techniques for future generations. Since April 2008, he has been the technical manager of the Eureka Celtic project WINNER+. He is also the leader of the System Concept Design Work Package in WINNER+. His research interests include many aspects of wireless communications with a special emphasis on advanced antenna systems for the third generation and future generations (IMT - Advanced), on radio resource management, network coding and cooperative communications.

m=1

Since the (k, l)th element of the product AB is given

M by m=1 A(k, m)B(m, l), for ∀k ∈ {1, . . . , N }, ∀l ∈ {1, . . . , M }, it necessarily follows that C = AB. R EFERENCES [1] S. M. Alamouti, “A simple transmit diversity technique for wireless communication,” IEEE J. Select. Areas Commun., vol. 16, pp. 1451– 1458, Oct. 1998. [2] V. Tarokh, N. Seshadri, and A. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,” IEEE Trans. Inform. Theory, vol. 44, no. 2, pp. 744–765, Mar. 1998. [3] L. Zheng and D. Tse, “Diversity and multiplexing: a fundamental tradeoff in multiple antenna channels,” IEEE Trans. Inform. Theory, vol. 49, no. 5, pp. 1073–1096, May 2003.

Andrew Logothetis [M’00] was born in Melbourne, Australia, 1970. He received his Bachelor of Science (Computer) in 1993, Bachelor of Engineering (Electrical) in 1994, Master of Science Engineering in 1995 and Ph.D. in 1998, all from University of Melbourne, Australia. In 2005, he joined Airspan Networks in the UK as principal engineer. From 2000 to 2005 he was with Antenna Systems and Propagation department at Ericsson Research in Sweden. In 1999, he was a Research Associate at the Department of Electrical Engineering, Princeton University, USA. In 1998, he was a Research Fellow at the Department of Signals, Sensors, and Systems, Royal Institute of Technology, Sweden. His research interests include statistical signal processing in communication systems, hidden Markov models, time-series analysis and advanced antenna systems.