FRFT-SCFDMA Scheme for Uplink in 5G Radio Access Networks

ICC2017: WT02-3rd International Workshop on 5G RAN Design

FRFT-SCFDMA Scheme for Uplink in 5G Radio Access Networks Vinay Kumar Trivedi, Student Member, IEEE ∗ and Preetam Kumar, Senior Member, IEEE † Department of Electrical Engineering Indian Institute of Technology Patna-801103, India Email: {∗ vinay.pee14,† 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). However SC-FDMA is very sensitive to carrier frequency offset(CFO), which affects the error rate performance of the system adversely. This paper proposes an efficient signal processing technique known as fractional Fourier transform(FRFT) for Single Carrier Frequency Division Multiplexing(SCFDM) over Nakagami-m fading channel in the presence of CFO. A clear improvement has been shown in symbol error rate(SER) by using FRFT block in place of FFT block. Simulation results confirm that FRFT-SCFDM outperforms FFT-SCFDM as its probability of error can be controlled by varying FRFT angle(α) without significant increase in the complexity. Further, we have compared the FRFT implementations of SCFDM and OFDM and observed a gain of 7 dB for FRFT-SCFDM over FRFT-OFDM at CFO(ε) equals 0.1. Further, no change in PAPR, no significant increase in complexity with improved SER performance or quality of service(QoS) motivates FRFT-SCFDMA to be one of the potential candidates for uplink transmission for 5G radio access networks(RAN). Index Terms—OFDM, Bit error rate; Fourier transforms; Carrier Frequency Offset; SCFDMA; FRFT; RAN; QoS.

I. I NTRODUCTION Conventional OFDM serves as an underlying technology and as an attractive alternative option for frequency selective fading environments. The basic advantages 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 [1], [2]. On the other hand, OFDM has two major demerits. Firstly, high Peak to average power ratio (PAPR) that can cause power backoff for amplifiers and distort the peak. Modifying an amplifier 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 cyclic prefix(CP). Because of frequency offset, these closely spaced subcarriers start to lose orthogonality. Any frequency offset error greater than subcarrier spacing will result in energy of one subcarrier to overlap with another [3], [4]. In the view of these two demerits of OFDM system, Single carrier FDMA(SC-FDMA) has been appropriately used in

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3GPP LTE for uplink data transmission in cellular communications. SC-FDMA is a composite multiple access technology that incorporates the flexible subcarrier allocation of OFDM and low PAPR of single carrier system [5], [6]. Beside the PAPR advantage of SC-FDMA, its high signalling rate causes more complex frequency domain equalization at the receiver compared to OFDMA. With SC-FDMA restricted to only uplink, complex equalization techniques are only needed at the base station and not at mobile terminals. Further, OFDMA is used in downlink, where we have independence in mapping different user data to different subcarriers as this task of scheduling is tough for mobile terminals. SC-FDMA limits resource allocation in downlink. However, in [7], it has been shown that multiuser communication using SC-FDMA can be used in downlink with improved quality of service. Hence, channel carrier frequency should be decomposed perfectly for removing the fading effects of channel at a particular time. Since, channel impulse response will be time varying, the transceiver system should be capable of processing non-stationary signals. Observing above facts, an approximated non-stationary approach has been introduced in [8] using signal basis function well suited for analysis of non stationary signals. In this approach, orthogonal basis signals of chirp type that correspond to FRFT basis signals are used. This particular type of transform are used in various applications in various domains such as signal processing, quantum mechanics, security in optical network. In literature cited in this article, FRFT is defined as the generalization of Fourier transform. In essence, FRFT is a rotation operator in frequency-time plane which rotates with angle α between frequency and time. This aspect of FRFT has drawn significant interest in signal processing research. In [9]- [11] BER analysis of OFDM system with CFO has been presented. Discrete implementation of FRFT basis function has been done in [8]. Using this Discrete FRFT (DFRFT) and Inverse of discrete FRFT (IDFRFT), a multicarrier system known as FRFT-OFDM has been introduced in [12]. Based on this FRFT-OFDM multi-carrier system, several results are already presented in literature. A detailed ICI analysis of FRFT-OFDM system has been discussed in [12]. It is observed that, at α = π/2, FRFT is converted into FFT. FRFT-OFDM system is generalization of conventional OFDM system. It has also been mentioned that, performance of FFT-OFDM and FRFT-OFDM are same over flat fading


Figure 1: Block diagram of FRFT based Single Carrier FDM (FRFT-SCFDM) system channels. But considerable improvement has been observed in SIR result over frequency selective fading channels. It is important to note that the robustness against CFO is achieved by using FRFT-OFDM system without any increase in implementation complexity compared to FFT based OFDM [14]. Already closed form expression of BER for BPSK in Rayleigh frequency selective channel has been derived in [15]. The

Massive Reduction in Latency Enormous Number of Connected Devices

Massive Throughput

Expected Capabilities of 5G RAN Extreme Device Densities

100% Coverage

Low Energy Consumption

Figure 2: Major challenges for 5G Radio Access Network potential of 5G wireless network access is expected to extend far beyond previous cellular generations. These capabilities shown in Fig.2 includes high data rate, low latency, high reliability, low power consumption, extreme densities etc., and we have expected to full-fill these requirements with the help of combining existing radio access LTE technologies and some new advancements. Future 5G Radio access networks (RAN) will definitely address high traffic growth with improved quality of service with high bandwidth connectivity. Possibly 5G networks will not be based on a particular radio access technology but it will be a portfolio of access and connectivity keys to address the above mentioned requirements. One of the major insight is to look into the inter-operability of existing LTE networks and proposed 5G new radio access technologies and will impact the way people and business operate. Among different important requirements for 5G network architecture such as high data rate, low latency, enormous

number of connected devices, coverage etc., lower power consumption with desirable QoS are crucial and interesting research and development areas to look at [16], [17]. Recently in [18] and [19], possibility of using DFT spread OFDM as a potential 5G candidate with benefits in terms of flexibility, spectrum, latency, and robustness to frequency selective channel has been discussed where the overhead can be tunable according to the frequency selectivity of the channel. Further in [18], it has been discussed that it is easier to extend DFT spread OFDM for MIMO support due to subcarrier wise processing. As for broadband wireless channels conventional time domain complex equalizers are impractical, frequency domain equalizer design as in SC-FDMA serves the purpose. In the direction to improve QoS without more power requirement and without increasing the complexity, SC-FDMA has been extensively studied for terrestrial wireless channels, however FRFT transformed SC-FDMA is never investigated in the existing literature. The above case motivate us for performance evaluation of FRFT-SCFDM over fading channel. Our major contributions in this paper is as follows: We have used FRFT signal processing technique for the BER performance improvement of existing SCFDM for uplink communication in the presence of CFO. Further, we have calculated an optimum value of FRFT rotation operator α which gives lowest BER under a particular value of CFO and SNR. With the help of simulation, it has been shown that the performance of FRFT-SCFDM system is superior compared to FFT-SCFDM system in terms of symbol error rate for different values of FRFT angle parameter α. In the view of results that we have obtained, we are able to nominate FRFT-SCFDMA as a favourable candidate for 5G RAN. The remaining part of this paper is organized as follows: Section II presents the system model for FRFT-SCFDM system subsequently Section III discusses the channel model used for simulation purpose. Section IV presents the important results and Section V concludes the paper. II. S YSTEM M ODEL System model for FRFT-SCFDM can be defined in similar way as traditional FFT-SCFDM system except the change at FFT/IFFT block position as shown in Fig.1. In traditional SCFDM system FFT and IFFT are changed with DFRFT and


IDFRFT respectively. In this paper, conventional SCFDM is introduced as Discrete Fourier transform based SCFDM (FFTSCFDM) for differentiating from another type of SCFDM i.e, fractional Fourier transform based SCFDM system (FRFTSCFDM). First, input data symbols are encoded using M-PSK modulation techniques. χN represents the N × N DFT matrix 2Π with (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 Nx point DFT, we get X = χNx .x in frequency domain, where X = (X0 , X1 , ...., XNx −1 )T . Subcarrier mapping accredits the modulation symbols to available subcarriers [20]. Assume net subcarriers in SCFDM system is N = Z.K. The transmitted signal vector X is then mapped to N orthogonal available subcarriers. (1) W k = CL/I .X 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 ) = IN T

(2)

The subcarriers used for different users do not overlap each other assuring orthogonality among users. 0N , k = j; j k .(CL/I )T = (3) CL/I IN , k = j. Following transmitter section of block diagram, kth transmitted sample can be written as d(k) =

N−1

−α (k, m) ∑ d(m)F

(4)

k=0

where N is total number of sub-carriers and d(m) is transmitted symbol on mth sub-carrier. F−α (k, m) is kernel of IDFRFT defined as in [12] − jk2 Ts2 cotα sinα + jcosα × exp F−α (k, m) = × N 2 − jm2 u2 cotα j2πmk exp × exp (5) 2 N where Ts and u are the sampling intervals in time and fractional Fourier domain respectively. α is FRFT angle parameter defined as α = p.π/2, where p is real number varies from 0 to 1. After considering the effect of frequency selective fading channel and CFO, l th sample of FRFT-SCFDM symbol in presence of CFO can be written as in [12] r(l) =

N−1

∑ h(l, l − k)d(k)e j2πε N + w(l) l

(6)

k=0

where h(l, k) is the impulse response of multipath fading channel with k number of paths. w(l) is additive white Gaussian noise (AWGN) with zero mean and variance σ 2 .

In receiver side after DFRFT block, received samples at qth sub-carrier is r(q) =

N−1

∑

q=0

d(m)

N−1 N−1

∑ ∑ Fα (q, l)F−α (k, m)h(l, l − k)e

j2πεl N

l=0 k=0

+w(q)

(7)

where w(q) is AWGN in frequency domain with zero mean and variance, σ 2 and Fα (q, l) is the kernel of DFRFT given in [12] 2 2 jq Ts cotα sinα − jcosα × Fα (q, l) = × N 2 2 2 − j2πlq jl u cotα × (8) 2 N As the transpose of subcarrier mapping matrix is equal to subcarrier de-mapping matrix, which is used at the receiver side following channel estimation and symbol detection. III. C HANNEL M ODEL The Nakagami-m distribution [13] is the probability distribution of the absolute value of a 2m-dimensional Normal random variable with mean 0 and variance Ω. In communications systems the physical significance of Nakagami distribution is to describe the amplitude of the received signal after maximum ratio diversity combining. Generally the fading coefficient is defined as, h = re jφ where the angle φ is uniformly distributed on [−π, π). The amplitude r and phase φ are assumed to be independent. The Nakagami fading distribution is given by m mr2 k 1 2 (9) r2m−1 e− Ω ; r ≥ 0, m ≥ f (r) = Γ(m) Ω 2 where m determines the shape and Ω gives the spread. Nakagami distribution also includes Rayleigh fading as a special case for m = 1 and Rician distribution for m = ∞. IV. S IMULATION AND R ESULTS In this section, SER of BPSK and QPSK for FRFT-SCFDM system has been simulated using Monte Carlo simulation in MATLAB over frequency selective Nakagami-m fading channel under the effect of CFO and compared with FFT based SCFDM system. The extensive simulation parameters are shown in table 1. Fig.3 and Fig.4 introduces the concept Table I: Simulation Parameters Parameters No. of sub-carriers (N) No. of taps (L) Carrier frequency offset(ε) Modulation Subcarrier Mapping FRFT angle parameter (αopt. ) for BPSK FRFT angle parameter (αopt. ) for QPSK Nakagami parameters (m, ω)

Specifications 8 2 0.1, 0.2 BPSK, QPSK Localized FDMA(LFDMA) 1.595 (ε=0.1), 1.620 (ε=0.2) 1.595 (ε=0.1), 1.615 (ε=0.2) m=2,ω=1

of FRFT. These figures show the effect on BER by varying the FRFT angle, α in radians for SNR value of 25 dB. At


0

10

ε=0.1 ε=0.2

−1

10

evaluation of SER versus SNR(dB) for QPSK system. It has been observed that for ε = 0.1 and ε = 0.2 this optimum α is 1.596 and 1.62 respectively for BPSK modulation and 1.596 and 1.615 respectively for QPSK modulation. Fig.5 0

−2

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optimum α=1.62 −4

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optimum α=1.596

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1.56

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1.6 1.61 α (radians)

1.62

1.63

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1.64

FFT, ε=0.1 FFT, ε=0.2 FRFT,ε=0.1, α=1.595

Figure 3: BER vs FRFT angle for BPSK

FRFT,ε=0.2, α=1.621 −4

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20 Eb/No (dB)

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Figure 5: BER of BPSK for FRFT-SCFDM over Nakagami-m (m=1) or Rayleigh frequency selective channel

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1.59 1.6 1.61 α (radians)

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1.64

Figure 4: SER vs FRFT angle for QPSK

Bit Error Rate

10

−2

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−3

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FFT, ε=0.1 FFT, ε=0.2

α = 1.57, FRFT is turned into FFT. In another way, FRFT can be understood as generalization of FFT. α represents the angle between frequency and time axis. Fig.3 represents BER versus α plot for BPSK modulation scheme at different values of CFO (ε). From the plot it can be observed that, lower BER can be achieved at α other than π/2 i.e., FFTSCFDM system. Here a particular α termed as optimum α at which the lowest BER is achieved. This optimum α has been used in simulation result of BPSK for FRFT-OFDM system. Similarly, Fig.4 shows the SER versus α for QPSK modulation scheme at different CFOs. Again, it also shows an optimum α other than π/2 at which the lower SER is achieved and this optimum α has been used for the performance

FRFT,ε=0.1, α=1.596 FRFT,ε=0.2, α=1.620 −4

10

0

5

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15

20 Eb/No (dB)

25

30

35

40

Figure 6: BER of BPSK for FRFT-SCFDM over Nakagami-m (m=2) frequency selective channel presents the BER versus SNR(dB) of FRFT-SCFDM system at optimum FRFT angle α, 1.595 and 1.621 for CFO(ε) 0.1 and 0.2 respectively over Rayleigh frequency selective channel or m = 1 [15]. The figure clearly shows the BER performance degradation with increasing value of CFO and SNR gain in case of FRFT implementation. Fig.6 and Fig.7 presents the


0

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−1

−1

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Bit Error Rate

Symbol Error Rate

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FFT, ε=0.1 FFT, ε=0.2

SCFDM, ε=0.1 SCFDM, ε=0.2 OFDM, ε=0.2 OFDM, ε=0.1

FRFT,ε=0.1, α=1.596 FRFT,ε=0.2, α=1.615 −4

0

5

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20 Eb/No (dB)

25

30

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Figure 7: SER of QPSK for FRFT-SCFDM over Nakagami-m (m=2) frequency selective channel BER versus SNR(dB) of FRFT-SCFDM system at optimum α for BPSK and QPSK modulation scheme over Nakagami-m frequency selective environment respectively. It is obvious that at higher values of CFO, BER will be higher. At each value of CFO, different values of optimum α has been given. The figure clearly shows the SNR gain in case of FRFT-SCFDM system. Similarly Fig.7 shows the SER versus SNR(dB) for QPSK modulation. Again, at each CFO, two results have been shown: one is for FRFT-SCFDM(at αopt ) and another at (α = π/2). A clear improvement has been shown in SER, by using FRFT block in place of FFT block in traditional SCFDM system, especially at high SNR region, where the error floor is reduced by more than an order of magnitude. It is important to note that the robustness against CFO is achieved by using FRFT-SCFDM system without any increase in implementation complexity compared to FFT based SCFDM [14]. A. Comparison of FRFT-OFDM and FRFT-SCFDM In this section, FRFT implementations of both SCFDM and OFDM has been compared in terms of BER over Nakagami frequency selective channel. In Fig.8, BER performance of FFT-SCFDM and FFT-OFDM has been presented at ε, 0.1 and 0.2 respectively. It is clear from the figure that SCFDM outperforms OFDM in terms of error rate. Similarly, FRFTSCFDM outperforms FRFT-OFDM as shown in Fig.9. It has been observed that SNR gain of 7 dB is observed for FRFTSCFDM compared to FRFT-OFDM at CFO(ε) equals 0.1. A clear reduction in error floor by more than an order of magnitude has been observed. Table II discusses different waveform candidates relevant to the work discussed in the paper with a comparison on the basis of some important characteristics and desirable features that are expected to evolve while moving from existing LTE

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Figure 8: BER of BPSK for FFT-SCFDM and FFT-OFDM over Nakagami-m (m=2) frequency selective channel 0

10

FRFT−OFDM, ε=0.1, α=1.595 FRFT−OFDM, ε=0.2, α=1.623 FRFT−SCFDM, ε=0.1, α=1.596 FRFT−SCFDM, ε=0.2, α=1.62

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Figure 9: BER of BPSK for FRFT-SCFDM and FRFT-OFDM over Nakagami-m (m=2) frequency selective channel

to 5G radio access technologies. Based on the components presented in table, it is very easy to draw the conclusion that compared to all other waveform candidates, FRFT-SCFDMA is very much suitable in terms of low complexity, low PAPR, improved QoS etc. without losing anything in terms of latency, MIMO-support and reliability of communication link. V. C ONCLUSIONS Performance Evaluation and comparison of probability of error for BPSK and QPSK modulation for FRFT based


Characteristics and desirable features

OFDM

Complexity

FFT/IFFT at transmitter and receiver.Tap equalization

PAPR

High PAPR as a major disadvantage for uplink

Low latency MIMO Support Multiple access

QoS

Enabled by using short symbols Direct. MIMO enabled due to subcarrier wise processing Enabled using high subcarrier spacing Good, due to robustness against frequency selectivity of channel

SC-FDMA DFT+IFFT/FFT+IDFT at transmitter and receiver. Tap equalization in frequency domain Low PAPR compared to OFDM (desirable in uplink) Enabled by using short symbols Direct. MIMO enabled due to subcarrier wise processing Enabled using high subcarrier spacing Excellent, frequency and multi-user diversity due to different subcarrier schemes i.e. LFDMA, IFDMA

FRFT-OFDM IDFRFT/DFRFT at transmitter and receiver. Tap equalization (No change in complexity)

FRFT-SCFDMA DFT+IDFRFT/DFRFT+IDFT at transmitter and receiver. Frequency domain equalization (No change in complexity)

High PAPR

Same PAPR as SC-FDMA

Enabled by using short symbols Direct. MIMO enabled due to subcarrier wise processing Enabled using high subcarrier spacing

Enabled by using short symbols Direct. MIMO enabled due to subcarrier wise processing Enabled using high subcarrier spacing

Good

Excellent

Table II: Different waveform candidates: comparison on the basis of some important characteristics and desirable features SCFDM system has been done over Nakagami-m frequency selective channel for any arbitrary m under the effect of CFO. At α = π/2, the performance of FRFT-SCFDM is similar to that of FFT-SCFDM. A clear improvement has been shown in SER by using FRFT block in place of FFT block in traditional SCFDM system especially at high SNR region, where the error floor is reduced by more than an order of magnitude. The results confirm that FRFT based SCFDM outperforms FFT based SCFDM as its error rate can be controlled by varying FRFT angle (α). It is important to note that this improvement is achieved without significant increase in implementation complexity compared to FFT based SCFDM or conventional SCFDM. At optimum α, which is different for different values of CFO, minimum error rate is achieved. As using fractional Fourier transform do not introduce any changes in PAPR calculations, PAPR of FRFT-SCFDM is same as FFTSCFDM. Al-together low PAPR, no change in complexity and improved QoS lead to nominate FRFT-SCFDMA as a probable candidate for uplink transmission in 5G-RAN. R EFERENCES [1] G. L. Stuber, J. R. Barry, S. W. McLaughlin, Ye Li, M. A. Ingram and T. G. Pratt, ”Broadband MIMO-OFDM wireless communications,” in Proceedings of the IEEE, vol. 92, no. 2, pp. 271-294, Feb. 2004. [2] M. K. Simon and M. S. Alouini, ”Digital Communication over Fading Channels”(2005, Wiley). [3] Z. Wang and G. B. Giannakis: ”Wireless multicarrier communications”, IEEE Signal Processing Magazine, vol. 17, no. 3, pp. 29-48, May 2000. [4] Shaoping Chen and Cuitao Zhu, ”ICI and ISI analysis and mitigation for OFDM systems with insufficient cyclic prefix in time-varying channels,” in IEEE Transactions on Consumer Electronics, vol. 50, no. 1, pp. 78-83, Feb. 2004. [5] H. G. Myung, J. Lim and D. J. Goodman, ”Single carrier FDMA for uplink wireless transmission,” in IEEE Vehicular Technology Magazine, vol. 1, no. 3, pp. 30-38, Sept. 2006. [6] H. G. Myung, J. Lim and D. J. Goodman, ”Peak-To-Average Power Ratio of Single Carrier FDMA Signals with Pulse Shaping,” 2006 IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications, Helsinki, 2006, pp. 1-5.

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