Automatic Gain Control Scheme for M-PAM Receiver with Precision-limited ADC Yu Ye, Jiangyun Zhou, IEEE student Member, Jianhao Hu, IEEE Member, National key Lab. of Communications University of Electronic Science and Technology ofehina, Chengdu, China
[email protected],
[email protected] Abstract-In this paper, we study on the automatic gain control (AGC)
scheme for
pulse amplitude modulation
(PAM) with
low-precision analog-to-digital converters (ADCs). For M-PAM communication systems, we investigate the problem of AGC schemes under the assumption that low precision ADCs (e.g., 1-4 bits) are used at the receiver end. We adopt blind approach to estimate the amplitude of an unknown sequence by analyzing the distribution characteristics of corresponding quantized samples. For the fixed thresholds ADCs, and altering the gain to ADC input,
we
propose
an
algorithm
based
on
ADC
output's
distribution-function to adjust the gain of the amplifier in front of the ADC. The sequence used in the proposed algorithm can be training sequence or the transmitted data symbols. Different from the existing solutions, our method doesn't use the dither signal for SNR increasing to achieve acceptable estimation performance. Thus, the complexity of the receiver can be reduced. Moreover we find that the NMSE performance of our algorithm can be better when SNR is larger. As a result, the proposed scheme can obtain better BER performance than the dither signal based schemes. Meanwhile we apply our AGC scheme to track the time-varying signal and achieve a good result as well.
Keywords-. low precision ADCs, M-PAM, A GC scheme
I.
INTRODUCTION
The analogy-to-digital converter (ADC) is a key component in the digital receivers. It converts analog signal into its digital format and directly affects the entire receiver performance. As the demand for speed and bandwidth of communication system is increasing, the power consumption and conversion rate of ADCs become a bottleneck for the development of modem receiver. In order to meet the requirements for fast speed of communication and low power consumption, low precision ADCs are adopted. Thus, how to design the receiver with low precision ADC becomes one of the urgent issues for digital receiver designs. According to information-theoretic analysis for the AWGN channel in [2]-[5] show that the capacity loss caused by low-precision ADCs can be acceptable when the signal-to-noise ratio (SNR) is moderately high. The enhancements for the channel estimation [9] and synchronization [6] are proposed for PSK modulation schemes, when ADC precision is dramatic reduced. But AGC is a critical issue for pulse amplitude modulation (PAM) with low-precision ADC, which is studied over the AWGN channel with the goal to align the ADC thresholds with the maximum likelihood (ML) decision regions in [7]. It requires the signal amplitude estimation from the quantized ADC output corresponding to an unknown symbol sequence. According to the work in [7], we This work was supported by the National Natural Science Foundation of China under Grant 61371104, and National High Technology Project of China under Grant 20 I I AAO I 020 I
propose a new algorithm which is based on distribution characteristics of quantized symbol sequence in this paper. The proposed AGC scheme can achieve better performance than that in [7]. AGC is a component of receiver to ensure communication system to get optimized performance when the thresholds of ADC quantization are fixed. When the amplitude of signal is unknown, we need a blind approach to estimate the amplitude and adjust the gain of the AGC. According to the results in [5], digital receiver can achieve near-optimal performance when M-Ievel ADC quantization is used for M-point PAM transmission system over AWGN channel. In this paper, the problem of AGC can be attributed to that of estimating a single amplitude parameter based on the low precision quantized output corresponding to the received noisy signals. Then the proper scale factor can be applied to amplifier in front of the ADC input. The maximum likelihood (ML) estimator of the signal amplitude in [7] can be expressed as the minimum of the Kullback-Leibler (KL) divergence between the expected probability distribution and the empirical probability distribution of the quantized output by setting the gain of AGC. It is observed that the performance of the ML estimator will degrade when SNR increases for low precision ADC receiver. For these receivers, dither signal is added to compensate the severe nonlinearity induced by low-precision quantization, which was investigated in work [10]-[13] illustrated in Fig.I. According to our study, dither signal can cause performance degradation when SNR is high.
Fig. 1 The architecture of low precision quantization digital receiver
However, we change the method of how to get the signal amplitude distribution for AGC adjusting. We redesign the architecture of AGC and propose a new algorithm to estimate amplitude without dither signal. In this paper the dither signal is not needed and the complexity is also reduced. From simulation study, we find that the proposed scheme can get better NMSE and the BER performance than that in [7] under the same condition. Meanwhile, we also apply our algorithm to good estimation performance for time varying amplitude signals. The rest of the paper is organized as follows. Section II
M
analysis model and relate work are introduced. The proposed estimation algorithm based on quantized output and strategy for tracking the slowly varying signal are provided in section III. Section IV presents simulation and numerical results. We conclude the paper in section V. II.
a = p(Yj,zl)
(
Q
( ��ry:i ) ) t
(3)
+
(4)
Lemma 1: In (4), f(a) is a non-decreasing function of a and only when a = A we have f(A)= 0 no matter how much is the (7.
1} and the parameter T is fixed. In addition, we define
= -00 and tM = 00. It is depicted in [5] that the quantizer thresholds to be the mid-points of the constellation points to get near optimal performance. If Q(.) stands for quantization process, then we get the quantized received signal: X
_
,
.
+
to
where i.i.d.
'
( I ) P (Y�+1'1 I a ) ) a ) a p(YM,zl) - ( p(Y1,zl)
f() a = p Y�'1 a
z
= 1, 2, ...,N
t
We define the distribution equation
We consider linear modulation over an AWGN channel. Transmitted symbols are uniform M-PAM signals and I bit quantization is applied, where M = 21. Assume the signal constellation is X := {XdXi = (2i - M - ) 1 A, i = 1,2, ..., M}, in which the amplitude scaling parameter is A. The thresholds Zi-M · 1= 1, 2, ..., M of quantlzer are set to T:= ti ti = --T, .
n
�
=
�
ANAYLSIS MODEL
{I
L P( yJ· p(Yj,zlyJ i 1 � ( Q ( j � ; Yi )
Proof: We first prove that f(A)= 0 when a = A. In this case 1 . 2,i = 1,2, ..., M} and P := {f3i lf3i =(2i - M - ) (Zi-M-1}(M-Z). for ,1= 1,2, ..., M y:= Yi Yi = Z(M-1)
{I
(1) Q
= {XvXz, ..., XN} are transmitted signal which are
t!f-f3!f
from an M-PAM constellation Xn E {xvxz, ..., XM} and the occurrence probability of each symbol is equal. X can be treated as training sequence or data symbols whose length is N. W = {WvWz, ..., WN} is the white Gaussian noise N(,O (JZ), and '1 is the VGA gain adjusting factor. Y = {YvYz, ..., YN} denotes the quantized output and each samples Yn E {yv Yz, ..., YM}, Yn = Yj if
Q
( ) ( (J"'r]1
and
samples
_
}
t!f+1 -f3!f
so
(J"'r]1
on,
=Q
) (
((
( I)
P Y�+1'1 A = z
_
(J"'r]1
Q
t!f-f3!f+1
) (
) ( )) can
tj-1 -f3!f
I) �
(
(J"'r]1
we
. IM M Q P Y2M,1 A = 2. M ]=2 Similarly
t!f-l -f3!f+1
_
and
Q
)
(J"'r]1
easily
trf3!f (J"'r]1
hence
get
= ..2... ZM
( I)
P Y�'1 A
(
I)
When
a < A we can prove P YM,1 a
z
M-Z
'1z = -, we can get Yn ' 1 = Q((Xn + Wn)''11) and Z(M-1)a I(A) = P�'1(A) + P�+1'1(A) - P1,2(A) + PM,z(A) Yn,z = Q ((Xn + Wn)''1z) respectively, where Wn . =0 ( 5) '11�N(O,((7 ''11)) Z . Define Z and Wn ''1z�N(,O ((7 ''1z)) 1 A . '1vi = 1,2, ..., M} and y:= P := {f3df3i = (2i - M - ) The A which makes formula (5) equal to 0 is the estimated {ydYi = (2i - M - ) 1 A ''1z, i = 1,2, ..., M} then the value of parameter A. In order to find the , we can make use A
(
corresponding distribution of quantized outputs are M
a = P(Yj,ll)
)
(
)
of searching-based method. During the searching process, we need to change the values of '11 and '1z according to previous probabilities of Yi' Obviously it is complex for hard implementation if we use the whole symbol sequence Y in every searching step. In order to reduce hardware complexity, we can use different receiving signal Yb whose length is N i. We first initialize the searching range [a, f3] to ensure a < A < f3 and f3 - a > E where the E is a constant for error tolerance. We propose an algorithm as described below
L P( f3i)' p(Yj,lIf3J i 1 =
2
Input:{YvYz, ... Yi, ...}, a, {3(a Output:A
