A Low Complexity PAR Reduction Technique Using Cyclic Shifted Data Sequences in DS-CDMA Signals

A Low Complexity PAR Reduction Technique Using Cyclic Shifted Data Sequences in DS-CDMA Signals Tarek K. Helaly, Richard M. Dansereau, and Mohamed El-Tanany Dept. of Systems & Computer Engineering Carleton University Ottawa, Ontario, Canada e-mail: {thelaly|rdanse|tanany}@sce.carleton.ca Abstract—Downlink direct sequence-code division multiple access signals have a large dynamic range causing these signals to be distorted by the nonlinear characteristics of the high power amplifier. The signal dynamic range is often characterized by peak-to-average ratio (PAR). Several techniques have been proposed to minimize such forms of distortion by reducing PAR such as partial transmit sequences and selected mapping (SLM), where several representations of the same signal are generated and the one with the minimum PAR is selected for transmission. Such techniques remarkably improve the system performance, but at the expense of an increased system complexity and computational burden. In this paper, we present a low complexity technique to reduce PAR based on cyclic shifts of the users’ data sequences (namely CSS). The search and optimization procedure in the proposed CSS technique is also simplified by adopting a greedy algorithm that selects the best representation sequentially as new users are added to the system. Comparison of the presented technique against SLM shows comparable improvement in terms of PAR reduction and bit error performance but with remarkable complexity reduction. Keywords-CDMA; nonlinear distortion; PAR; predistortion

I.

INTRODUCTION

In downlink direct sequence-code division multiple access (DS-CDMA), the sum of the signals coming from different users forms a signal with a large dynamic range, which could be severely distorted by the nonlinear characteristics of the high power amplifier (HPA). The nonlinear distortion at the transmitter generates interference both inside and outside the signal bandwidth. The in-band component determines a degradation of the system bit error rate (BER) and the system capacity and the out-of-band component produces undesired out-ofband emissions known as spectral regrowth which could affect adjacent systems. To overcome these forms of distortion the input signal to the HPA has to be backed off to prevent the signal vulnerability to the inherent nonlinearity of the HPA. However, increasing the input back-off (IBO) degrades the HPA efficiency. A promising method to minimize the nonlinear distortion due to the

HPA is to insert a predistorter (PD) prior to the HPA, namely PD-HPA [1]. The PD-HPA characteristic is near linear up to a certain amplification, after which it is constant and the signal suffers from clipping. Therefore, there still remains a portion of the signal dynamic range vulnerable to nonlinear distortion (clipping). The signal dynamic range is often characterized by the peak-to-average power ratio (PAR). In order to reduce PAR, various techniques have been proposed for CDMA and orthogonal frequency division multiplexing (OFDM) systems. Clipping of large signal peaks is the most straightforward technique, however, this technique results in performance degradation [2]. Companding techniques have been proposed for OFDM systems [3][4]. Companding achieves improvement in the BER, however in presence of a PD-HPA, the BER is drastically degraded since companding distorts the input signal to the PDHPA. Also, PAR reduction based on Walsh code assignment was proposed in [5][6]. Selected mapping (SLM) [7][8] and partial transmitted sequences (PTS) [9][10] techniques have been originally introduced for OFDM systems. The concept behind SLM and PTS techniques is to generate several representations of the signal to be transmitted and the representation with the smallest PAR is selected for transmission. These techniques effectively reduce the PAR without distorting the signal, but they require much system complexity and computational burden because of the exhaustive search procedure for the optimum representation. In this paper, we propose a low complexity technique to reduce the PAR due to the amplifier chain in DSCDMA systems. The introduced technique is based on cyclically shifting the users’ data sequences to generate different representations of the CDMA signal. Then, among these representations, the signal with the minimum PAR is selected for transmission. Using cyclic shifted sequences (CSS) replaces the multiplications by the phase rotation vector in the conventional SLM techniques, and in turn the computational burden is greatly reduced. Moreover, the search and optimization procedure used in the proposed CSS technique is simplified by adopting a greedy algorithm that selects the best representation

Figure 1. Downlink DS-CDMA transmitter with PD-HPA.

sequentially as new users are added to the system, resulting in noticeable reduction in the system complexity and the computational burden. This paper is organized as follows. In Section II, the considered DS-CDMA system model is described. Section III presents a review on the conventional SLM technique. In Section IV, the proposed CSS technique is explained. The performance of the CSS technique is assessed in Section V through comparison against SLM technique. Section VI summarizes the conclusions drawn from the paper. II.

Figure 2. Block diagram of the SLM technique.

| | and where are the envelope and phase of , respectively. Finally, the output from the nonlinear device can be expressed as (4)

SYSTEM MODEL

The system under investigation is a downlink DSCDMA system in which the users’ signals are synchronized and have equal power. The block diagram of the transmitter system is depicted in Fig. 1. The complex envelope of the DS-CDMA signal for K active users is defined as [1] (1) is the kth user signal with signal energy where per bit, is the symbol duration, and 1 /√2 is the kth user symbol data for QPSK modulation in the nth symbol duration. Moreover, the symbols are assumed to be independent with zero mean and variance of . In (1), (2) is the spreading waveform obtained with the spreading ,…, , is the spreading factor, / is the chip duration, and is the impulse response of the transmit pulse shaping filter. Therefore, in (1) can be written as code

(3)

where · and Φ · are the AM-AM and AM-PM characteristics of the nonlinear device, respectively. For this paper, we use a PD-HPA as the nonlinear device. The PD-HPA has a zero AM-PM characteristic, and an AMAM characteristic given by [1][6] 0 where

(5)

is the PD-HPA saturation (clipping) threshold. III.

SLM TECHNIQUE

The concept behind the existing SLM technique is based on creating equivalent representations of the same signal by rotating the phases of the symbols. Then, the signal representation that has the minimum PAR [7][8] is selected for transmission. The block diagram of the SLM technique is depicted in Fig. 2. A phase rotation vector ,…, with , 2 / , 1, … , is defined. Each kth user’s data symbol is element-wise multiplied by the vector , resulting in a set of different symbols. These symbols are then multiplied by the corresponding spreading waveform forming different representations for each user as (6) where 1 . Consequently, signal representations are generated by performing all possible combinations of the representations for each kth user signal such that . The PAR is then measured for each representation, where the PAR is defined as

max | |

|

max |

|

|

2

(7)

.

Among the signal representations, the representation that has the minimum PAR is selected for transmission as follows arg min

arg min IV.

max

.

2

(8)

PROPOSED CSS TECHNIQUE

Figure 3. Block diagram of the proposed CSS technique.

The SLM technique remarkably improves the system performance, but at the expense of an increased system complexity and computational burden. The system in this case performs a large number of computations since there ) representations. For instance, for an 8-user exist ( DS-CDMA system with a phase rotation vector consisting in 4 elements, the total number of possible representations is 65536. In this case, the system suffers a tremendous computational burden through performing an increased number of multiplications, in addition to the search and optimization procedures that follow. The issue of computational complexity has been extensively discussed and many approaches have been proposed to reduce the complexity for multiuser systems [11–13, and the references therein]. In the existing search and optimization techniques (SLM or PTS), the multiplication by the phase rotation vector to obtain different representations of the same signal represents the main contributor to the system complexity, especially in multicarrier and OFDM systems, where complexity becomes more severe since they require several inverse fast Fourier transform (FFT) operations to generate different signal representations [11][12][13]. In this paper, we present a low complexity technique for PAR reduction by using cyclically shifted sequences of the users’ data sequences. In the proposed CSS technique, the multiplication operations are replaced by cyclic shifting of the users’ data sequences, which greatly reduces the system complexity. Consider the signal block to be transmitted consisting of N symbols, where the kth user signal has the form .

(9)

The proposed technique is based on creating (M + 1) representations for every user’s data sequence by applying M cyclic shifts to the symbols of that sequence. Hence, the mth representation of the kth user signal can be expressed as

(10) where 0, … , denotes the mth shift assigned to the is the modulo-N kth user data sequence and · operator. In essence, we modify (1) as follows

(11) where 1, … , and denotes the total number of signal representations according to the number of shifts assigned to each user data sequence. Among the signal representations , the representation that has the minimum PAR is selected for transmission. Moreover, for the sake of reducing system complexity, the search and optimization procedure itself is performed sequentially as new users are added into the system. This search and optimization procedure is a greedy algorithm that yields a suboptimal selection of the signal to be transmitted. A greedy algorithm is an algorithm that always takes the best immediate, or local, solution while finding an answer at each stage with the hope of finding the global optimum [14]. Using such a greedy algorithm strongly reduces the number of representations among which the system selects the optimum one to be transmitted to 1 . We define the complexity reduction ratio (CRR) in a manner with similarities to that of [15], but using the number of representations generated in each of the optimal and greedy procedures as

TABLE I. K

2

4

8

CRR FOR THE OPTIMAL AND GREEDY ALGORITHMS |

|

2

4

4

0

4

16

6

62.5

8

64

10

84.4

2

16

10

37.5

4

256

16

93.8

M

CRR %

8

4096

28

99.3

2

256

22

91.4

4

65536

36

99.94

8

16777216

64

99.99

CRR %

1

| |

100 %.

(12)

Table I shows the number of representations generated using both the optimal full search procedure | and for different number of users the greedy algorithm | K and different number of representations generated for each user in the system M. The CRR for both procedures is shown as well, where it is evident that a remarkable improvement in complexity reduction in terms of reduced number of representations exists. Finally, the proposed CSS technique for one block is depicted in Fig. 3. It is worth mentioning that the kth receiver must know in order to undo the shifting the number of shifts process for the received data sequence, and hence, the number of shifts should be transmitted as side information. Transmission of the side information is beyond the scope of this paper. However, there are various ways to manage the side information issue, one of which is transmitting the side information about over an overhead channel. V.

PERFORMANCE MEASUREMENT

In this section, we assess the performance of the proposed CSS technique described in Section IV through comparison against the SLM technique. For an 8-user DSCDMA signal with Walsh codes of length L = 64 and filtered using a square root raised cosine filter with rolloff factor of 0.22, four different representations are generated as follows: 1) using SLM with optimal algorithm and = 4, 2) using SLM with greedy algorithm and = 4, 3) using CSS with optimal algorithm and = 4, and 4) using CSS with greedy algorithm and = 4. For each representation, the complementary cumulateive distribution function (CCDF) of the instantaneous power normalized to the average power is computed and plotted in Fig. 4. It is clear from the figure that the PAR reduction achieved by the conventional SLM technique and the proposed CSS technique are similar.

Figure 4. CCDFs of the normalized instantaneous power of an 8-user DS-CDMA signal.

In presence of a PD-HPA pair, we are interested only in the dynamic range where the signal passes linearly, after which the signal is clipped. The PD-HPA clipping threshold can be determined thru the IBO level, which is the ratio of the input power at the PD-HPA clipping threshold to the input signal average. In turn, the horizontal axis in Fig. 4 can be seen as the IBO levels. In search and optimization techniques like SLM or the proposed CSS technique, as the number of users increases, the differences in PAR among different representations tends to vanish since the CDMA signal approaches the Gaussian distribution, which is fixed [5]. Therefore, such techniques are efficient in systems with few users. For an 8-user DS-CDMA signal, an IBO of 4 dB is quite enough to linearly pass most of the signal. For instance, as in Fig. 4, we find that ~96.5% of the input signal passes linearly without clipping using the optimal procedure compared to ~95.5% using the greedy algorithm. In turn, it is clear that although following the optimal procedure offers about 1.25 dB reduction in PAR over the greedy algorithm, at CCDF = 10-4, the PAR reductions achieved using both the optimal procedure and the greedy algorithm are very close at the IBO level of interest (4 dB). Hence, a greedy algorithm is recommended in such cases to offer an acceptable PAR reduction with remarkable complexity reduction. Finally, to assess the ultimate performance of the CSS technique, we use the most desirable performance merit: BER. Fig. 5 shows the measured BER performance over an additive white Gaussian noise channel at different IBO levels for both the SLM and CSS techniques, when a greedy procedure is adopted. It is clear from Fig. 5 that the proposed CSS technique has almost the same performance compared to SLM. VI.

CONCLUSIONS AND FUTURE WORK

Computational complexity represents a major concern in search and optimization techniques like the SLM technique, where several representations of the same

REFERENCES [1]

[2] [3] [4] [5] [6] Figure 5. BER performance of the SLM technique and the CSS technique for K-user DS-CDMA signals at different IBO levels (dB). [7]

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