A PAPR Reduction and Data Decoding for SLM Based ... - IEEE Xplore

A PAPR Reduction and Data Decoding for SLM based OFDM Systems Without SI S. A. Adegbite, Student Member, IEEE, S. G. McMeekin, Member, IEEE, and B. G. Stewart, Member, IEEE Glasgow Caledonian University, United Kingdom {saheed.adegbite, scott.mcmeekin, b.stewart}@gcu.ac.uk Abstract—Selected mapping (SLM) is an effective method for addressing high peak-to-average power ratio (PAPR) issues in orthogonal frequency division multiplexing (OFDM) systems. However, the standard SLM approach introduces additional data decoding challenges in the form of side information (SI) transmission and estimation. In general, SI transmission reduces data throughput and SI estimation normally involves computationally complex procedures, which can increase design costs. To eliminate the need for both SI transmission and SI estimation, this paper presents an investigation into the PAPR reduction and BER performance of a new technique based on a modified SLM approach. It is shown that the proposed method simplifies data decoding through SI cancellation without SI transmission. Results show that the proposed method produces similar PAPR reduction performance and BER performance as standard SLM based OFDM system, which presumes perfect SI estimation, within a frequency non-selective (flat) fading channel. Keywords—orthogonal frequency division multiplexing (OFDM); selected mapping (SLM); side information (SI) estimation; peak-to-average power ratio (PAPR) reduction; Without SI

I.

I NTRODUCTION

Orthogonal frequency division multiplexing (OFDM) is the adopted technology in high speed wireless broadband communication systems including Long Term Evolution (LTE), Digital Video Broadcast (DVB), Wi-Fi and IEEE 802.16 d/e standards, because it offers high data transmission, but unfortunately, it suffers from the problem of high peak-to-average power ratio (PAPR) [1]–[3]. This high PAPR signals often occur at some time instants when there is coherent summation of phases of individual OFDM subcarriers, resulting in peak amplitude signals [4]–[6]. High PAPR levels introduce signal distortion by forcing non-linear operation of power amplifiers (PA) in OFDM transmitters; this increases the bit-error-rate (BER) and thus degrades system performance [7]–[9]. In theory, this PA induced distortion may be eliminated by designing a PA with a large linear region [10]. However, this is impractical because PAs with a large linear region are expensive and often result in poor PA efficiency [11]. This leads to increased power consumption and increased heat dissipation, which reduces battery life of user equipment (UE) terminals. In addition, high PAPR levels require higher resolution specifications of digital-to-analogue (D/A) and analogue-to-digital (A/D) devices, which further increases design costs, and may also put additional constraints on system design [12]. A comprehensive review of common PAPR reduction techniques is presented in [13]–[15]. Amongst these methods, selected mapping (SLM) is widely considered the most at-

tractive solution to the problem of large PAPR in OFDM systems even though it introduces additional challenges in the form of side information (SI) transmission and estimation [16]–[20]. SI is a data overhead while its transmission wastes bandwidth, and may also result in reduced data throughput. In SLM based pilot-assisted OFDM system, studies in [21] and [22] have achieved SI estimation without the need for SI transmission, using pilot-assisted statistical decision criteria. However, since SLM is occasionally implemented, then to perform SI estimation, the receiver must know when SLM is implemented. This requires additional system resources and also introduces additional implementation challenges. In general, SI estimation are prone to errors, particularly in the presence of severe fading channel conditions, and also require highly computationally complex procedures. To eliminate these two challenges i.e. SI transmission and SI estimation, this paper presents a modified SLM approach that facilitate joint PAPR reduction and data decoding without the need for both SI transmission and SI estimation, in a pilot-assisted OFDM system. The proposed method is based on the principle of Embedded Coded Modulation (ECM); a cluster based phase modulation and demodulation approach, first introduced in [23]. Simulations will show that the proposed method produces comparable PAPR reduction and BER performance as the conventional SLM-OFDM method, which presumes perfect SI estimation at the receiver. This paper is organised as follows. Section II gives an overview of a typical SLM based pilot-assisted OFDM system model. Section III describes the proposed modified SLMOFDM method. Section IV presents results and discussions on the comparison of PAPR reduction performance between standard SLM-OFDM and the proposed method for various cluster sizes. It also presents BER performance between the two considered methods, when transmission is over a flat fading channel condition. Finally, conclusions based on the outcomes of the paper are presented in section V. II.

S TANDARD SLM BASED P ILOT- ASSISTED OFDM S YSTEM

This section outlines a standard SLM implementation and associated data decoding procedure for an SLM based pilotaided OFDM system and introduces the concepts of clustered OFDM notations. A. Transmitter Side Consider an OFDM sequence X consisting of Nv subcarriers. Let k for 0 ≤ k ≤ Nv − 1 represent a subcarrier index

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Figure 1: Cluster – data-pilot positions Figure 2: SLM in Pilot-assisted OFDM that corresponds to a subcarrier symbol X[k], where   X = X[0] X[1] . . . X[k] . . . X[Nv − 1] .

B. Receiver Side (1)

Assuming a pilot-assisted OFDM, this OFDM sequence X may consists of Nd data and Np pilot components such that Nv = Nd + Np . For an equi-spaced pilots with L as the pilot spacing, and by letting c and l respectively represent arbitrary indices for 0 ≤ c ≤ Np − 1 and 0 ≤ l ≤ L − 1, each subcarrier X[k] is represented through (e.g. [21]) X[k] = X[cL + l], for 0 ≤ l ≤ L − 1  X p [c], l = lp = 0 = X d [cL + l], otherwise, l = ld ,

(2)

where the terms X p [c] and X d [cL + l] respectively represent the pilot and data components. Also, for a given value of c, both lp and ld represent indices for pilot and the data respectively. For 0 ≤ n ≤ N − 1 where N represents the length of a time-domain OFDM signal x[n], expressed by x[n] =

N v −1

X[k] exp(j2πnk/N ).

(3)

k=0

max{|x[n]|2 } , E{|x[n]|2 }

Y¯ [k] = H[k]X[k]B u¯ [k] + V [k],

(4)

where E{·} denotes the expectation function. Alternatively, X[k] may also be represented using a clustered notation (see Fig. 1) as follows: X[k] = X c [l] = Ac [l] exp(jθc [l])  X c [lp ] = X p [c] = X c [ld ] = X d [cL + l], where Ac [l] and θc [l] respectively represent the amplitude and the phase component of X c [l]. Fig. 2 shows a block diagram representation of an SLM based pilot-assisted OFDM (SLMOFDM) system. Let B uc [l] = B u [k] represent a set of SLM phase rotation sequences for u = 1, 2, . . . U where U is the number of SLM sequence vectors. SLM creates U alternative OFDM signals from which one of the modified signals with the lowest PAPR value is selected for transmission [16].

(5)

where V [k] represent a complex-valued additive white Gaussian noise (AWGN) component. Similar to X[k], the expression in (5) can also be represented in clustered form as Y¯ c [l] = H c [l]X c [l]B uc¯ [l] + V c [l],

(6)

where Y¯ c [l], H c [l], B uc¯ [l] and V c [l] respectively represents the clustered representations of Y¯ [k], H[k], B u¯ [k] and V [k]. Let u ˆ represent an SI estimate, then in the case of perfect SI estimation i.e. u ˆ=u ¯. The initial stage of the data decoding process in an SLM based OFDM receiver normally involves using the value of u ˆ for sequence de-mapping to produce Y c [l] as follows Y c [l] = Y¯ c [l]B ucˆ [l]∗ .

The PAPR of x[n] may be defined by the ratio P AP R{x[n]} =

Consider an OFDM transmission over a multipath fading channel with frequency response H[k]. Then, after the implementation of SLM, the received OFDM sequence Y¯ [k] may be expressed through

(7)

Assuming a true flat (frequency non-selective) fading channel condition where H c [ld ] ≈ H c [lp ] ≈ H c . Then channel equalization may be achieved through a subcarrier level (i.e. element by element) division procedure given as ˆ c, Yˆ c [ld ] = Y c [ld ]/H

(8)

ˆ c represents the pilot sub-channel estimate obtained where H from a subcarrier level division procedure written as ˆc = H ˆ c [lp ] = Y c [lp ]/X c [lp ] . H

(9)

This means even though channel estimation (through interpolation) is not required since the considered channel is frequency non-selective, SI estimation is however still necessary, to enable successful data reception in this channel condition. The final stage of data reception usually produces an

estimated constellation point nearest to Yˆ c [ld ] using a form of Maximum Likelihood (ML) detection defined in [22] through  2 ˆ c [ld ] = min Yˆ c [ld ] − D[q] , X (10)

1 SLM Proposed

D[q]∈Q

ˆ c [ld ] ∈ Q and Q is a set of Q constellation points where X D[q] for 1 ≤ q ≤ Q. III.

CCDF(γ)

0.1

0.01

P ROPOSED M ETHOD

This section introduces the new approach that facilitates joint PAPR reduction and data decoding in SLM based OFDM systems, but without the need for SI transmission and SI estimation.

original OFDM U=4 U = 16

0.001

0.0001 6.5

7.5

8.5

Modified SLM

10.5

11.5

1 SLM Proposed

(11)

0.1

CCDF(γ)

where αuc represents the uth phase rotation component for cluster c i.e. the phase component of J uc . Let J uc¯ = exp(jΘc ) represent the optimum vector that produces the transmitted signal with the lowest PAPR, in a similar manner as in standard SLM [16].

9.5

Figure 3: CCDF comparisons (L = 4)

Unlike conventional SLM, in the proposed method, a modified form of phase rotation sequences called SLM by clustering (SLMC) are defined. For 1 ≤ u ≤ U where U represents the number of alternative signal representations, the proposed phase rotation sequences are defined by u u J uc [lp ] = J uc [ld ] = J u c [l] = J c = exp(jαc )

γ (dB)

0.01

original OFDM U=4 U = 16

0.001

Channel Equalization ¯ c [l] is repreIn this case, the received OFDM sequence Z sented as ¯ c [l] = H c [l]X c [l]J uc¯ + V c [l] . Z (12) Now assume a flat or very slow fading channel condition where

0.0001 6.5

7.5

8.5

γ (dB)

9.5

10.5

11.5

Figure 4: CCDF comparisons (L = 8)

H c [l] ≈ H c [ld ] ≈ H c [lp ] ≈ H c . Given that the pilots X c [lp ] are usually known at the receiver, data decoding may be directly achieved through a channel cancellation procedure. This involves a simple subcarrier level division, and can be expressed as   ˆ c [ld ] = Z ¯ c [ld ]/Z ¯ c [lp ] × X c [lp ] Z H c Ac [ld ] exp{j(θc [ld ] + Θc )} × X c [lp ] = H c X c [lp ] exp(jΘc ) ≈ X c [ld ]. (13) This procedure (the division process) cancels out the phase term Θc , without the need for the receiver to know its value. In this way, SI cancellation is possible because the modulating phase component Θc is common to all subcarriers in each cluster; thus successful data recovery is achieved without SI estimation at the receiver or separate SI transmission. This suggests data recovery can be achieved even if Θc is randomly generated.

IV.

S IMULATION R ESULTS

This section presents comparisons of PAPR reduction and BER performance between the standard SLM based OFDM and the proposed method. Simulations use QPSK modulated pilot sequences and the following standard LTE parameters: OFDM subcarrier spacing of 15 KHz, guard interval of 5.21 μs, sampling frequency of 30.72 MHz and with values of [N and Nv ] set to [2048 and 1200] respectively using randomly generated 64-QAM complex-valued data symbols and using as an example, randomly generated phase rotation sequences chosen from the set [0, 2π) within SLM. Simulations also consider transmission over a single tap frequency-flat fading channel. The PAPR reduction performance is measured by evaluating the well known complementary cumulative distribution function (CCDF). The CCDF gives the probability of a calculated PAPR value P AP R (dB) exceeding a certain threshold

1

1 SLM Proposed

SLM Proposed 0.1

CCDF(γ)

CCDF(γ)

0.1

original OFDM U=4 U = 16

0.01

0.001

7.5

8.5

γ (dB)

9.5

10.5

11.5

Figure 5: CCDF comparisons (L = 12)

with perfect SI Proposed 0.1

0.01 16QAM 64QAM 0.001

3

6

9

12

15 18 SNR (dB)

21

24

27

30

Figure 7: BER – standard SLM-OFDM (presumes perfect SI estimation) vs. proposed method (without SI estimation)

level denoted by γ dB; thus defined in [8] as CCDF{γ} = P rob(P AP R > γ) .

0.0001 6.5

7.5

8.5

γ (dB)

9.5

10.5

11.5

Figure 6: CCDF comparisons (L = 24)

1

BER

original OFDM U=4 U = 16

0.001

0.0001 6.5

0.0001 0

0.01

correlation values. In addition, with U set to 4, and L set to 6, the BER is evaluated when transmission occurs over a flat (frequency non-selective) fading channel in order to demonstrate, through simulation, the data decoding capability of the proposed method. Fig. 7 shows the comparison of BER between the proposed method (without SI estimation) and the standard SLM-OFDM method (with perfect SI estimation). This clearly shows that even though SI estimation is avoided within the proposed method, it gives similar performance when compared to a standard SLM-OFDM system, which presumes perfect SI estimation. This is expected because in this case the channel condition is assumed to be flat, and the channel equalization ˆ c [ld ] in the proposed method (13) and Yˆ c [ld ] in terms i.e. Z the standard method (which presumed perfect SI) in (8), are both similar. This shows that even with randomly generated phase rotation sequences, the proposed method can produce successful reception of payload data information without the need for both SI transmission and SI estimation, and without resulting in BER degradation. Furthermore, the proposed method may be extended to enable data decoding in the presence of a frequency selective fading channel, through some form of channel estimation and equalization, but without SI estimation and SI transmission.

(14)

With U set to 4 and 16, Figs. 3 to 6 show comparisons of CCDF curves between the original OFDM (before PAPR reduction) and when PAPR reduction is performed using conventional SLM and the proposed method for L set to 4, 8, 12 and 24 respectively. Results in Figs. 3 to 6 show that the proposed method produces nearly identical PAPR distributions as standard SLM. This is because with a large value of N , the proposed phase rotation sequences maintains an intrinsic low correlation comparable to standard SLM. This agrees with recent study in [24], which has indicated that phase rotation sequences with low correlation values have good PAPR reduction capabilities than sequences, which have higher

V.

C ONCLUSIONS

This paper has introduced a modified SLM-OFDM approach, which facilitates joint PAPR reduction and data decoding (over a flat fading channel), without the need for SI estimation or SI transmission, thereby resulting in a significant reduction in the complexity of OFDM receivers. The proposed method achieves comparable PAPR reduction performance as standard phase rotation sequences. In addition, the proposed method produces similar BER performance when compared to standard SLM based OFDM system, which presumes perfect SI. Though, the presented implementation of the proposed approach assumed a flat fading channel condition, it may be

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