The level of OOBE can be characterized by the difference between the outside PSD (Power Spectrum Density) of output signal in the case of existing nonlinear HPA and the norm[r]
Trang 1USING THE DISTANCE DEGRADATION TO ESTIMATE THE OUT-OF-BAND EMISSION LEVEL (OBE) CAUSED BY NONLINEAR HIGH POWER
AMPLIFIER IN COMMUNICATION SYSTEMS OF 802-11N STANDARD
Doan Thanh Hai 1* , Nguyen Van Vinh 2
1 University of Technology – TNU,
2 Hung Yen University of Technology and Education
ABSTRACT
In M-QAM-OFDM systems, nonlinear High Power Amplifiers (HPAs) increase dramatically unwanted out-of-band emission that can cause strong Adjacent Channel Interference (ACI) to other systems In this paper, empirical formulae to calculate quickly the level of Out-Of-Band emission (OBE) is found for 16-QAM-OFDM systems of 801-11n standard OBE calculated by this formula would help in defining requirements for the stop-band attenuation of the transmitter
filter in system design to ensure the spectral mask of the system
Keywords: Out-Of-Band Emission, non-linear distortion, High Power Amplifier, OFDM, 802-11n
INTRODUCTION*
The nonlinear distortion mainly caused by the
transmitter HPA in Orthogonal Frequency
Division Multiplexing (OFDM) systems
affects more severely on the system
performance because of the high
Peak-to-Average Power Ratio (PAPR) of OFDM
signals The effects of nonlinear distortion are
not only to degrade dramatically the inband
performance of the system, but also to cause
much higher out-of-band emission that can
violate the required spectral mask and make
Adjacent Channel Interference (ACI) to the
neighbor systems unacceptable
Analysis of out-of-band emission and in-band
interference caused by OFDM techniques as
well as the techniques for compressing
out-of-band radiation have been introduced in [1, 2,
3] However, the authors had not yet taken the
effects of nonlinear HPA and modulation
schemes into account [1] or not yet mentioned
out-of-band emission caused by nonlinear
HPA, but just had completed research on the
in-band performance of the system in the
paper [2]
The parameters described the nonlinearity of
HPAs could be BO (Back-Off), 1
*
compression point, IM3 (third-order InterModulation), IM5 or IP3 (third-order Intercept Point) [2, 3] However, it was difficult to use these parameters to calculate directly Bit Error Rate (BER) or Power Spectrum Density (PSD) analytically If was done, calculated results were too hard to use
in system design calculations or practical applications [3] or those were not monovalent [2] Being considered to be the most feasible system theory method and simulation estimation have been accepted and applied around the world in extremely expensive experimental equipment conditions except giant research corporations So system theory and simulation evaluation are determined in this research
A nominal parameter of HPA’s nonlinearity,
distance degradation dd, had been proposed
since 1995 [4] By using this parameter and simulating systems with many nonlinear HPAs, empirical formulae had been found for estimating the effects of nonlinear distortion
on the system performance in single carrier
M-QAM (M = 16, 64, 256) SISO (Single
Input Single Output) [4-6] or 16-QAM MIMO (Multiple Input Multiple Output) [7] and 16-QAM-OFDM [8] systems
In [9] the parameter of level of Out-Of-Band
emission (OBE) was proposed and the
Trang 2parameter dd was used to find out the
empirical formula for calculating OBE under
the effects of nonlinear HPA for the
16-QAM-OFDM system with some different
numbers of subcarriers [10] The relationship
between OBE and dd, however, depends on
the number of subcarriers, M-ary schemes
Continuous this background and motivated by
the limitations of these above works to
comprehensively estimate the effect of
nonlinear distortion caused by HPA
out-of-band of the 802-11n system, the relationship
between OBE and was investigated and
empirical formulae to calculate OBE as a
function of dd were presented in this paper
The paper, after the introduction, is organized
as follows: The main conceptions (Model of
system to be considered, Definition of the
nonlinearity parameter dd, Level of
Out-Of-Band emission OBE) are presented in Section
2; Simulation results for a number of unintentionally chosen TWT (Traveling-Wave Tube) HPAs and the empirical
formulae between OBE and subcarrier
number are given in Section 3, Section 4 is used for the conclusion and discussions MAIN CONCEPTIONS
System Model
The M-QAM-OFDM system of 802-11n
standard to be considered as modeled in Fig 1a Single Carrier (SC) system also as depicted in Fig 1b The transmitter nonlinear HPA is taken into account In addition, the pulse shaping filters (square-root raised cosine filters) are also included in the simulation system
(a)
Figure 1 (a) Model of M-QAM-OFDM system of 802-11n with HPA
(b) Model of M-QAM-SC system with HPA
HPA is described by the curves of AM/AM and AM/PM conversions If the input symbol is
j
sre , the output signal can be expressed in polar coordinates as:
( )
ˆ ( ) j r j ,
s A r e e (1) where rand are the amplitude and phase of input signal, respectively;A r( )and ( ) r are the AM/AM and AM/PM conversions [10]:
Trang 3
2
p a
r r
where a, aand p, pare the parameters of Saleh model These parameters of 3 HPAs selected unintentionally [1, 4 ] are listed in Table 1
Table 1 The parameter of HPA according to Saleh model
Distance Degradation (dd)
HPA causes the signal state displacements,
the higher nonlinearity of the HPA, the
greater displacements of the signal points
Under the effects of the displacements, the
signal states are shifted closely to the decision
boundaries on the M-QAM signal
constellation and the BER becomes higher
The degradation of the distance from the
signal states to the nearest decision boundary
averaging on all of signal set is defined as
distance degradation, dd, and can be
calculated from the HPA’s characteristics as
follows [4]:
dd
M
4
1
2
, ,
/
(3)
Figure 2.Defining d 22 (for symmetry, only a
quadrant of signal constellation is shown)
where dd i,j = 1 d i,j , the distance d i,j from the
signal point [i, j] to the nearest boundary can
be calculated directly from the characteristics
of HPA and a given BO, For each HPA, the
characteristics of gain decrease G(P out) and phase rotation (P out) as functions of output
power P out are given by the manufacturer
From these characteristics and the given BO,
G ij and ij for every signal point [i, j] can be easily determined and by using geometry, dd i,j
can be easily calculated, i, j = 1, 2,…, M / 2
, as shown in Figure 2
Figure 3 Explaination of calculating OBE Level of Out-Of-Band Emission (OBE)
The frequency components in the OFDM signal are intermixed by HPA's nonlinearity and then the output signal spectrum is expanded Amplitude characteristics of an HPA can always be expressed by a Taylor series, its even-order terms cause the products far-outside the signal spectrum and these products can be neglected The odd-order inter-modulation products, however, on the one hand will fall into the signal band, causing nonlinear noise, and cause spurious radiation outside the signal bandwidth on the
Trang 4other hand This out-of-band emission can
interfere the adjacent channels (the so-called
ACI) In general, the Taylor series of HPA
characteristics can be truncated to the 3rd order
and the output signal spectrum is often 3
times-wider than the one of the input signal It
means that at the output, the signal spectrum is
added a signal bandwidth to both sides
We called the normalized out-of-band
emission (OOBE) bandwidth as B oob-norm [9]
B oob-norm is determined from the point from
which the signal spectrum starts to extend
comparing to the case of completely linear
system, and the width of normalized OOBE
B oob-norm equals to the normalized in-band
bandwidth B ib-norm (Fig 3) B ib-norm depends on
M and the number of subcarriers
The level of OBE
The magnitude of OOBE depends on dd The
larger dd, the more nonlinear HPA, then the
greater is the radiation power of OOBE due to
nonlinear distortion The level of OOBE can
be characterized by the difference between
the outside PSD (Power Spectrum Density) of
output signal in the case of existing nonlinear
HPA and the normalized in-band PSD (PSD
ib-norm) of linear system Because PSD is not a
constant in the frequency range of OOBE, in
[9] we recommended taking the difference
between PSDib-norm and the average PSD over
the OOBE range (PSDmean-oob-norm, Fig 3) as a
parameter characterized for OBE:
ib norm mean oob norm mean oob norm
[dB] (4)
Of course, the greater dd, the higher the
HPA’s nonlinearity, the higher the
out-of-band emission, and the smaller is the OBE
SIMULATION RESULTS Many simulations are performed to estimate
BER and calculate OBE in the practical range
of nonlinear distortion dd Configuration of
system is shown in Fig.3 802-11n system has
a length of IFFT/FFT equal to 64; the number
of subcarriers=52, the length of cyclic prefix
is 1/5 of integral period Square-root raised cosine filters at the transmitter and receiver: Delay = 10, Rolloff factor = 0.5, in/output sampling rates Fd = 1, Fs = 8 (in order to ensure no spectrum distortion in calculation when the output signal spectrum is expanded
at least 3 times) Because we investigate only the impact of nonlinear distortion, the channel
is AWGN, synchronization of the system is assumed to be perfect The amplifiers have parameters of Saleh model as shown in Table
1 The BO is taken according to the peak power (called Ppeak) of HPA’s input signal
Range of dd corresponding to the useful range of IBO
With the same values IBO (input BO), different HPAs express different nonlinearities Given smaller IBO, the HPA operates in area closer to the saturation point
then distortion is greater and dd is higher
With large enough IBO, HPA can be considered as linear The investigated and
useful ranges of IBO and dd are listed in
Table 2 for OFDM systems of 802-11n standard and Table 3 for SC systems The useful range of IBO (and thus the normal
range of dd) is the range, in which the system
is not outaged (BER ≤ 10-3
), but OBE is still
not too high (HPA is not too linear)
Table 2 Ranges of dd and IBO, IBOs are taken with steps of 0.5 dB in 802-11n system
Investigated range of IBO:
Range of dd corresponding to the
useful range of IBO 0.0386 – 0.3294 0.0381 - 0.2954 0.0307 - 0.2661
Trang 5Table 3 Ranges of dd and IBO, IBOs are taken with steps of 0.5 dB in SC system
Investigated range of IBO: IBOmin
Range of dd corresponding to the
useful range of IBO 0.0215 – 0.1247 0.0190 - 0.1687 0.0217 - 0.1782
The bit error rate BER and PSD of systems
Figure 4 (a) Simulated BER performance and (b) Simulated PSD of the QAM of HPA 1373
Simulated BER (see Fig 3a) and PSD (see Fig
3b) are compare with system without the
effects of HPA
The empirical formula between OBE and
number of subcarriers
PAPR in M-QAM-OFDM systems is very
high because it includes the PAPR of OFDM
modulation scheme and the inherent PAPR of
M-QAM signal When the number of
modulation level M and the number of
subcarriers vary, resulting in changes in
PAPR, OBE will change
16-QAM-OFDM systems of 802-11n
standard
The OBE caused by nonlinear HPA in
16-QAM-OFDM systems of 802-11n standard
when the subcarrier number N c equal to 64 dd
changes in the useful range (Table 2) with 35
calculated points
From our investigation, this relationship is
shown in Fig.5, OBE is a 1st-order function of
dd when the BO is taken according to Pmax of
HPA’s input signal:
16, 6452 45, 4064
This relationship between OBE and dd is shown in Fig.6, OBE is a 1st-order function of
dd when the BO is taken according to the
average power (Pmean) of HPA’s input signal:
227, 4411 45,1890
RMSE=0,37 (6)
16-QAM-SC systems
This relationship between OBE caused by
nonlinear HPA in 16-QAM-SC systems and
dd is shown in Fig.6, OBE is a 1st-order
function of dd when the BO is taken
according to Pmax of HPA’s input signal:
42, 2967 46, 2572
RMSE=0,29 (7)
This relationship between OBE caused by
nonlinear HPA in 16-QAM-SC systems and
dd is shown in Fig.6, OBE is a 1st-order
function of dd when the BO is taken
according to Pmean of HPA’s input signal:
RMSE=0,30 (8)
Trang 6Figure 5 The relationship between OBE and dd
when IBO is taken according to P mean
Figure 6 The relationship between OBE and dd
when IBO is taken according to P max
It is easy to see that in the case of BO taken according to Pmean of HPA’s input signal (system
operating in nonlinear condition) the OBE of 802-11n system is worse (belower) than that of the
SC system (Fig 5) In a position on the other side of OBE in case of BO taken according to Pmax of
HPA’s input signal (system operating in linear condition) the OBE of SC system is worse
(belower) than that of the 802-11n system (Fig 6)
In addition, OBE and dd can be approximated by a polynomial function of 2nd order with smaller errors as shown in Table 4
Table 4 Relationship between OBE and dd by a polynomial function of 2 nd order in SC and 802-11 systems
when BO is taken according to Pmax or P mean of HPA’s input signal
Relationship in systems 0-order coe 1st-order coe 2nd-order coe RMSE
CONCLUSION AND DISCUSSION
In this paper, the empirical formulae to
determine the zero- and first-order
coefficients of the relationship between OBE
and dd in 16-QAM-OFDM in 802-11n
standard are found by simulation These
coefficients of polynomial are listed in
formulae (5-8) for 1st order function and 2nd
ones in Table 4 The nominal parameter of
HPA’s nonlinearity, dd, which can be
determined if BO is given and the
characteristics of HPA are provided by the
manufacturer
Depending on the required accuracy, we can
use the 1st or 2nd order polynomial to calculate
OBE In order to evaluate separately the effect
of the nonlinear HPA, it is possible to
investigate the 802-11n system under BO
conditions taking into account the average power of HPA’s input signal
OBE of the 16-QAM-OFDM system of
802-11n standard can be calculated simply and
quickly by those formulae OBE calculated by
this way would help in system design (for determining the stop-band attenuation of the transmitter filter to ensure the spectral mask
of the system)
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TÓM TẮT
SỬ DỤNG LƯỢNG THIỆT HẠI KHOẢNG CÁCH ĐỂ ƯỚC LƯỢNG MỨC BỨC
XẠ NGOÀI BĂNG GÂY BỞI BỘ KHUẾCH ĐẠI CÔNG SUẤT LỚN PHI TUYẾN TRONG CÁC HỆ THỐNG TRUYỀN THÔNG CỦA CHUẨN 802-11N
Đoàn Thanh Hải 1* , Nguyễn Văn Vĩnh 2
1 Trường Đại học Kỹ thuật Công nghiệp – ĐH Thái Nguyên;
2 Trường Đại học Sư phạm Kỹ thuật Hưng Yên
Trong cá hệ thống M-QAM-OFDM, Các bộ khuếch đại công suất phi tuyến làm tăng nghiêm trọng bức xạ không mong muốn ở ngoài băng tần của hệ thống gây nhiễu kênh lân cận lớn tới các hệ thống khác Trong bài báo này, các công thức thực nghiệm nhằm ước lượng nhanh mức bức xạ ngoài băng được xác định cho các hệ thống 16-QAM-OFDM của chuẩn 802-11n Mức bức xạ ngoài băng tính theo công thức này đặt ra các yêu cầu về tiêu hao băng chắn của mạch lọc máy phát trong thiết kế hệ thống để đảm bảo mặt nạ phổ của hệ thống
Từ khóa: Out-Of-Band Emission, méo phi tuyến, HPA, OFDM, 802-11n
Ngày nhận bài: 27/8/2018; Ngày phản biện: 17/9/2018; Ngày duyệt đăng: 12/10/2018
*