Vinay Kumar Trivedi â, Madhusudan Kumar Sinhaâ , Preetam Kumarâ¡. Department of Electrical Engineering. Indian Institute of Technology Patna-801103, India.
Error Rate Performance of SC-FDMA with Channel Dependent Subcarrier Scheduling Vinay Kumar Trivedi ∗ , Madhusudan Kumar Sinha† , Preetam Kumar‡ Department of Electrical Engineering Indian Institute of Technology Patna-801103, India Email: {∗ vinay.pee14,† madhusudan.mtcm14, ‡ pkumar}@iitp.ac.in
Abstract—Single Carrier Frequency Division Multiple Access (SC-FDMA) is a promising technique compared to Orthogonal Frequency Division Multiple Access (OFDMA) for uplink transmission in 3rd Generation Partnership Project(3GPP) Long Term Evolution(LTE) because of its low peak to average power ratio (PAPR). Being a multiple access technique, resources are required to be distributed among various users. In this paper, we have used Zero Forcing noise amplification factor (βZF ) for scheduling subcarrier allocation in SC-FDMA systems unlike using the summation of amplitude response over different subcarriers. Using βZF for scheduling gives more exact information about channel condition over different subbands for different users. For scheduling purpose we have used, Round Robin, Greedy Chunk and Proportionally Fair algorithms and we have compared the SER results for the different number of users including maximum possible users transmitting simultaneously. The effect on capacity and throughput over error performance has been observed earlier. In this work, the effects of different channeldependent scheduling schemes on error rate performance of SC-FDMA have been evaluated. Index Terms—BER, SER, Ped-A, Veh-A, SC-FDMA, OFDMA, Channel Dependent Scheduling
I. I NTRODUCTION Conventional OFDM serves as an underlying technology and as an attractive option for frequency selective fading environments. The basic advantage of OFDM system is its counteraction to the detrimental effects of fading in wireless channels by dividing the bandwidth available into multiple subcarriers. This property of OFDM eliminates the use of complex time-domain equalizers at the receiver. In addition to this, even though, it may appear to be particularly complicated form of modulation, it lends itself to digital signal processing techniques [1]. On the other hand, OFDM has two major demerits. First, high Peak to average power ratio (PAPR) that can cause power back off for ampliers and distorts the peak. Modifying an amplier to compensate this loss increases cost, size and power consumption. The other
main disadvantage of OFDM is due to closely spaced subcarriers used to minimize the loss due to the cyclic prefix(CP). Because of frequency offset, these closely spaced subcarriers starts to lose orthogonality. Any frequency offset error greater than subcarrier spacing will result in energy of one subcarrier to overlap with another [2], [3]. To overcome the above two demerits of OFDM system, Single carrier FDMA(SC-FDMA) has been appropriately introduced in 3GPP LTE for uplink data transmission in cellular communications. SC-FDMA is the extended version of SC-FDE that allows multiple access with comparable complexity to OFDMA. SC-FDMA is a composite multiple access technology that incorporates the flexible subcarrier allocation of OFDM and low PAPR of single carrier system [4], [5]. With SC-FDMA restricted to the only uplink, complex equalization techniques are only needed at the base station and not at mobile terminals. Channel-Dependent Scheduling in frequency division techniques utilizes frequency diversity and multiuser diversity to obtain performance improvements over broadband multipath channels [6]. For a single user transmission frequency diversity is used to allocate best subcarriers to the user. However with multiple users transmitting simultaneously each spatially dispersed user has different channel response, which allows the use of multiuser diversity along with frequency diversity to obtain performance improvement. Given a particular channel condition for a user terminal, cases may arise when favourable subcarriers are not available. In these cases, we must use a lower baseband modulation scheme to obtain desired error performance. Adaptive modulation utilizes channel information to adjust the baseband modulation scheme to obtain better SER performance on the cost of throughput reduction. In [9], zero forcing noise amplification factor (β ZF ) has been defined and is used to obtain SER performance for
subcarrier de-mapping the received signal is expressed as: YNc = (CL/I )H HCL/I .X + (CL/I )H ηM (5)
symbol-wise slicers. Using the same convention, β ZF can be defined as ! 1 β ZF = mean : k ∈ mapped subcarriers (1) |hk |2
where ηM is the noise vector whose components are i.i.d Gaussian with mean 0 and variance NO . H is M ×M channel frequency matrix for each subcarrier. The recovered symbol after ZF-FDE and inverse pre-coding step is
where hk is obtained by M-point FFT of channel impulse response. Our major contributions in this paper are as follows: we have used βZF for scheduling subcarrier allocation in SC-FDMA systems unlike using the summation of amplitude response over different subcarriers previously. For scheduling purpose we have used, Round Robin, Greedy Chunk and Proportionally Fair algorithms and we have compared the SER results for the different number of users including the case when maximum possible users are transmitting simultaneously.
XbNc = χNHc (H H H)−1 H H HX + χNHc (H H H)−1 H H η
where η = (CL/I )H ηM is a vector whose values are corresponding noise values. Hence, the expression for k-th received symbol after ZF-FDE can be written as Nc
b j,k = xk + η ek xbk = xk + ∑ η
II. S YSTEM M ODEL
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b j,k = hj,k and each received symbol is the result where η j ek to the original of adding an effective noise term η transmitted symbol [6]. This effective noise is as a b j,k or result of the sum of elementary noise term η enhanced gaussian noise for each subcarrier. Each of those elementary noise terms is equivalent to noise in the OFDM with ZF-FDE. In [9], the noise characteristic of SC-FDMA system has been shown to depend on βZF , which can be used to better utilize scheduling algorithms for subcarrier allocations. In SC-FDMA and OFDMA systems, the main idea behind Channel-Dependent Scheduling is to map the transmission of each user to a set of favourable subcarriers. Ideally, each user terminal inspects its own frequency response and transmits the information about the channel to the scheduler at the base station, which monitors the frequency response for each user and does the mapping accordingly. This method is a bit impractical due to long control head required and due to the need for higher computational power. To shorten the length of the control word from each user and also to ease the computation at the scheduler, the subcarriers are assigned in chunks as in IFDMA or LFDMA scheme. For a system with the total number of subcarriers M, and the number of subcarriers assigned to a single user Nc , the number of available subbands is given by Q = M/Nc . If subcarriers are assigned individually we need to send information about M subcarriers from the user terminal to the base station and we need to find the best Nc subcarriers out of M subcarriers at the base station. However, with subcarriers assigned as chunks, the user terminal is required to transmit information of Q subbands and scheduler has to find one subband out of Q subbands. With multiple users
(2)
Where CL/I is N × Z mapping matrix containing 0 and 1 depending on whether IFDMA or LFDMA is used as subcarrier mapping method. Also, the transpose of mapping matrix is equal to de-mapping matrix used at the receiver side. CL/I .(CL/I )H = IM
(7)
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For a given user, the collection of transmitted bits is mapped to the complex symbols (BPSK, QPSK, MQAM). The resulting sequence X is then mapped to a Nc point DFT before being distributed to Nc allocated subcarriers out of M independent subcarriers. Firstly, input data symbols are encoded using M-PSK modulation techniques. χN represents the N × N DFT matrix with 2Π (x, y)th element being √1N e j N (x−1)(y−1) . Assume x = (x0 , x1 , ......, xNx −1 )T is data symbol set to be transmitted. After Nc point DFT, we get XNc = χNc .x in frequency domain, where X = (X0 , X1 , ...., XNc −1 )T . Subcarrier mapping assigns frequency domain modulation symbols to available subcarriers [4]. Assume net subcarriers in SCFDMA system is M = Z.K. The transmitted signal vector X is then mapped to M orthogonal available subcarriers. The transmitted signal vector X is then mapped to M orthogonal available subcarriers. W k = CL/I .X
(6)
(3)
The subcarriers used for different users do not overlap each other assuring orthogonality among users. 0M , k 6= j; j k T CL/I .(CL/I ) = (4) IM , k = j. At the receiver, perfect estimation and synchronization have been assumed. After cyclic prefix suppression and
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Figure 1: Transmitter and Receiver schematic of SC-FDMA scheme with Channel Dependent Scheduling transmitting simultaneously the computation required at the base station by using subcarrier assignment as chunks becomes much less than the case when subcarriers are assigned individually. For SC-FDMA systems with single user transmission, the task of CDS reduces to finding the best subband for transmission. However, with multiple users transmitting simultaneously each user has different channel response and some scheduling algorithm is required to distribute Q subbands among Q users in order to minimize the overall SER of the system.
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We have used two sets of channels based on Pedestrian A channel and Vehicular A channel for the study of scheduling techniques. Fig.2 and Fig.3 show the amplitude response for different users for all 512 subcarriers over channels derived from Vehicular-A and PedestrianA channel model. For 5 MHz system bandwidth 3GPP TS 25.104 [9] based Pedestrian and Vehicular channels are given by 10
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and vehAchannel = [1 0 10−1/20 0 10−9/20 10−10/20 0 0 0 10−15/20 0 0 0 10−20/20 ]
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To obtain a different channel for different users we have multiplied each tap with a Normal random variable. Tapped-delay line model is used to define the impulse response of channel in various standards and are used to compare various communication schemes. Since β ZF is the average value of 1/|hk |2 overall mapped subcarriers it can be easily seen that for LFDMA, the subbands with the lower value of amplitude response will have higher effective noise and hence degraded SER performance. However, such observation cannot be made directly from amplitude response plot of the channel response for
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Figure 3: Amplitude response of 32 users for 512 subcarriers over channel derived from Ped-A channel model IFDMA mapping scheme because for IFDMA mapping, subcarriers are allocated over entire channel bandwidth.
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10 -2 error rate of a user over a tapped delay line Since channel depends on βZF , each user sends values of βZF for different subbands to the base station. At the base station,10-3a matrix is formed containing the values of βZF whose column corresponds to individual users and rows correspond to different subbands [9]. βZF,matrix is used 10 -4 algorithms for SC-FDMA subcarrier allocation in CDS using LFDMA and IFDMA chunk allocation. Chunk
size is equal to the number of subcarriers assigned to a user so that each user is assigned a single chunk as 10 -2 per LFDMA or IFDMA subcarrier mapping scheme [7], [8]. Following scheduling algorithms has been studied in -3this work: 10
A. Round Robin based scheduling Each user is assigned subcarrier chunk in equal proportions and in the circular fashion. Assigned subcarriers 10 -4
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Figure 4.1: plots of SER performance of Round Robin, Greedy Chunk and Proportionally fair scheduling Schemes with number of users=1,2 and 4 over Pedestrian A and Vehicular A channel
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Figure 5: Plots SER performance of Round Robin, Greedy Robin, Chunk and Proportionally Schemes Figure 4.2:ofplots of SER performance of Round Greedy Chunk Fair andscheduling Proportionwith number of users = 16 and 32 over Pedestrian A and Vehicular A channel ally fair scheduling Schemes with number of users=8,16 and 32 over Pedes-
trian A and Vehicular A channel are rotated over entire bandwidth in circular fashion based on time division fashion.
3. Delete jth user and ith subband. 4. Repeat steps 1,2,3 till all users are assigned subbands.
B. Greedy chunk based scheduling This scheduling algorithm is based on the idea of assigning best chunk first in order to minimize SER.44 Following algorithm is used in this work for Greedy chunk based scheduling algorithm. 1. Find the minimum value of βZF(i, j) from βZF,matrix . 2. Assign ith subband to the jth user.
C. Proportionally fair based scheduling It is based on the idea of assigning best subcarrier chunks to the user with worst conditions first in order to minimize SER. Following algorithm is used in this work for Proportionally fair based scheduling algorithm. 1. Find the minimum value of βZF(i, j) from βZF,matrix along each column i.e. minimum value of βZF(i, j) for
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among localized contiguous subcarriers. As the number of users in the system rises towards the full capacity of the system the SNR gain of the LFDMA system with fair scheduling becomes more prominent.
each user j. Let the vector containing minimum values of βZF(i, j) be denoted as βZF(min, j) . 2. Find the maximum value of βZF(min, j) . Let the max value be denoted by max(βZF(min, j) ) 3. Assign ith subband to the jth user corresponding to max(βZF(min, j) ). 4. Delete jth user and ith subband. 5. Repeat steps 1,2,3 till all users are assigned subbands.
VI. C ONCLUSIONS In this paper, the effects of different channeldependent scheduling schemes on error rate performance of SC-FDMA have been evaluated. Zero Forcing noise amplification factor (βZF ) is used for scheduling subcarrier allocation in SC-FDMA systems, as it gives more exact information about channel condition over different subbands for different users. For scheduling purpose, we have used: Round Robin, Greedy Chunk and Proportionally Fair algorithms and compared the overall SER results for the different number of users. When the number of users is small, Proportionally Fair and Greedy Chunk scheduling algorithms give similar overall SER performance. As the number of users increases, Proportionally Fair algorithm outperforms Greedy Chunk scheduling algorithm. LFDMA mapping with Proportionally Fair scheduling has best overall performance in all cases due to inherent multi-user diversity. The results presented in this paper can be used to better utilize the channel dependent scheduling for SC-FDMA systems maintaining the quality of service (QoS) of communication.
V. S IMULATION AND R ESULTS Extensive simulation parameters used in this work is given in table 1. Number of subcarriers is taken as 512 and one block size is 16 symbols. We have considered tapped delay line channels i.e. Ped-A and Veh-A discussed in section III for which values of βZF is calculated from corresponding values of hk . Table I: Simulation Parameters Parameters Modulation DFT precoder size (Nc ) Total no. of Subcarriers (M) SC-FDMA input block size Cyclic Prefix length Channel Equalization No. of Subcarriers per user
Specifications QPSK 16 512 16 20 Ped-A and Veh-A Zero Forcing FDE 16
From Fig.4 and Fig.5, it is interesting to note that when the number of users is small, the Greedy Chunk scheduling algorithm and Proportionally fair scheduling algorithm has essentially same performance over both Pedestrian A and Vehicular A channel. This results from the availability of multiple subbands with good channel response (or low βZF ) for each user for subband selection. As the number of users increases Greedy Chunk scheduling results starts deviating from that of the Proportionally fair scheduling algorithm. The Proportionally Fair scheduling algorithm outperforms the Greedy Chunk scheduling algorithm with increasing number of users. Round Robin scheduling algorithm has worst performance among all as it doesn’t use channel information for scheduling. Better performance of Proportionally fair scheduling for large number of users arise from the fact that with increasing number of users, Greedy Chunk scheduler assigns worse resources to the users, whereas Proportionally Fair scheduling aims at providing better service to users under worst channel conditions. LFDMA has better or same SER performance than IFDMA in both Greedy Chunk and Proportionally Fair Scheduling algorithm, due to better multi-user diversity
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