Frequency and Power Estimator for Digital Receivers in Doppler Shift Environments

M. Saber, M. T. A. Khan & Y. Jitsumatsu
Signal Processing: An International Journal (SPIJ), Volume (5) : Issue (5) : 2011 185
Frequency and Power Estimator for Digital Receivers in Doppler
Shift Environments
M. Saber mohsaber@tsubaki.csce.kyushu-u.ac.jp
Department of Informatics
Kyushu University
744 Motooka, Nishi-ku, Fukuoka-shi, 89-0395, Japan
M. T. A. Khan tahir@apu.ac.jp
Ritsumeikan Asia Pacific University, College of Asia Pacific Studies
1-1 Jumonjibaru, Beppu, Oita, 874-8577, Japan
Y. Jitsumatsu jitsumatsu@inf.kyushu-u.ac.jp
Department of Informatics
Kyushu University
744 Motooka, Nishi-ku, Fukuoka-shi, 89-0395, Japan
Abstract
A frequency estimator well suited for digital receivers is proposed. Accurate estimates of
unknown frequency and power of input sinusoidal signal, in the presence of additive white
Gaussian noise (AWGN), are provided. The proposed structure solve the problems of traditional
phase locked loop (PLL) such as, narrow tracking range, overshoot, long settle time, double
frequency ripples in the loop and stability. Proposed method can estimate frequencies up to half
the sampling frequency irrespective of the input signal power. Furthermore, it provides stability
and allows fast tracking for any changes in input frequency. The estimator is also implemented
using field programmable gate array (FPGA), consumes 127 mW and works at a frequency of
225 MHz. Proposed method can estimate the fluctuation in frequency of transmitter’s oscillator,
can be used as a frequency shift keying receiver and can also be applied as a digital receiver in
Doppler shift environment.
Keywords: Digital Phase Locked Loop (DPLL), Frequency Estimator, FPGA.
1. INTRODUCTION
The main objective of a receiver is to generate an accurate replica of the transmitted symbol
sequence. Synchronization is very important for proper detection. It involves recovery of
reference parameters from the received signal and using these parameters to demodulate and
detect data [1]. Synchronization includes carrier recovery and symbol timing recovery. Carrier
recovery is the estimation and compensation of carrier frequency and phase. In case of coherent
detection, knowledge of both frequency and phase of the carrier is necessary. The frequency
offset is generated at the receiver as a result of factors such as variations between the oscillators
at transmitter and receiver, Doppler shift caused by relative motion between transmitter and
receiver and the phase noise generated by other channel impairments [2]. The estimation of
frequency of periodic signals in the presence of noise is also important in many other practical
applications of signal processing.
PLLs are a very important building block in the modern communications. They are used in
synthesizing carrier signals, demodulation and synchronization of frequency and phase of the
received signal. Conventional PLL consists of three components, a phase detector (usually
multiplier), a loop filter which is low pass filter (LPF) and voltage controlled oscillator (VCO)
arranged in feedback manner. Conventional PLL suffers from problems such as high frequency
ripples in the loop, overshoots and narrow tracking range. Higher order loop filters avoid these

problems; However use of higher order loop filters raise the issues such as stability, longer
settling time, and more narrow tracking range [3:8].
We propose a simple design for frequency estimator which can estimate both frequency and
power of received sinusoidal signal in the presence of background noise. Proposed algorithm can
estimate wide range of frequencies up to half the sampling frequency, irrespective of the received
signal power. The structure works in a feedback manner like a PLL and allows fast tracking for
any changes in the received frequency; however, no loop filter is needed. The basic design is
simple and comprises of only a first order system which provides stability. Computer simulations
performed confirm the validity of analytical results. Furthermore, the estimator is modeled with
VHDL and implemented using FPGA. Proposed structure’s hardware implementation consumes
127 mW and works at a frequency of 225 MHz.
This paper is organized as follows: next section explains the working of conventional PLL and
their characteristics. Section 3 presents the proposed method; explain the structure, operation
and mathematical equations of proposed estimator. Computer simulations are presented in
section 4. FPGA implementation is mentioned in section 5 and finally conclusions are given in
section 6.
2. CONVENTIONAL PLL
A conventional PLL as shown in Fig. 1 consists of three main components i.e. a phase detector
(multiplier), loop filter and VCO. PLL receives the input sinusoidal signal with input frequency and
phase. The input signal is multiplied with the generated signal from VCO. Multiplication results in
two signals the first with higher frequency term and the other with lower frequency term. Loop
filter is assumed to remove the high frequency signal. The result output signal from loop filter is
the low frequency signal which represents the frequency and phase difference between input and
generated signals. This difference is used to control the generated phase and frequency from
VCO. When there is no phase difference, VCO generates center frequency only.
FIGURE 1: PLL Block diagram.
Assume an input sinusoidal signal
ω + θυ = = ψi i i i i it(t) A sin( ) A(t in) s (t) , (1)
where ωi is the angular frequency and θi(t) is the unknown phase of input signal. The signal
generated by VCO is
o o oo o ot (t)(t) A cos( ) A (t)s ,coυ = =ω + θ ψ (2)
Loop Filter
VCO
Input signal
υi(t)
Phase
detector
Output signal
o(t)υ
υd(t) υf (t)

where ωo is the estimation of angular frequency of VCO and θo (t) is the estimated phase of
VCO. Input signal is multiplied by the VCO output, then
d m i vco
i o m i o m
i o i o i o i o
A
)t (
(t) k (
t) (t)) sin(( )t (t) (t))
t) (t)
A A k A k
s n(
2 2
i (
υ = υ × υ
ω − ω + θ − θ + ω + ω + θ += θ
= ψ − ψ + ψ + ψd i o i o[sin( ) sin(k (t) (t) (t) (t))] , (3)
where mk is the gain of phase detector with dimension [1/V] , = i o m
d
A A k
k .
2
In the simplest case
we assume that low-pass filter removes the upper sideband with frequency ω ω+i o but passes
the lower sideband ω ω−i o . VCO’s tuning voltage will be
ψ − ψυ ψ= =f d i o d e(t) k sin( ) sin(t) (t) k (t), (4)
where ψe(t) is the phase difference between input and output VCO signals
ψ ψ − ψ=e i o(t)(t) (t). (5)
This difference will be used to control the frequency and phase generated by VCO. If the error
signal is zero, VCO produces just its free running frequency ( ωc , center frequency). If the error
signal is other than zero, then VCO responds by changing its operating frequency.
+ω = ω υo c o fk(t) (t), (6)
where the constant ok is the gain of VCO. After integration of the above equation and substituting
into (5), the phase difference is
e i c o f
t
(t) k ( dt )( ) .
−∞
ψ ψ − ω τ τ= − υ∫ (7)
This can be rearranged as follows:
e i c o d e
t
(t) t k k sin ( )t d .
−∞
ψ ω − ω ψ τ− τ= ∫ (8)
Differentiating (8) w.r.t. ‘t’ gives
ψ ∆ω= − ψe eKsin
d
(t) (t)
dt
(9)
where i c∆ω = ω − ω and = o dK k k is the gain of PLL. The PLL continues to vary the phase of
VCO ωo until locked, i.e. frequency and phase of the input signal are the same as those
generated by VCO. After getting locked, PLL follows the changes in frequency and phase of input
signal.
It can be concluded from the above analysis that the phase lock arrangement is described by the
non-linear equation (9). Solution of this equation is not known for arbitrary values of ∆ω , and K .
Without an aperiodic solution, the feedback system (PLL) cannot achieve phase stability, i.e.,

output frequency of VCO ωi will never be equal to input frequency ωo . Simplifications are needed
to solve the equation [9]. One solution is the linear solution, in which we assume that, for small
values of ψe(t)
≈ψ ψe esin (t) (t) (10)
The linear model of PLL in the continuous time-domain (S-domain) is shown in Fig. 2 [10]. Since
phase is integral of the angular frequency, the VCO transfer function
=
υ
θo o
f
(s) k
(s) s
(11)
FIGURE 2: Linear model of the PLL.
The transfer function of loop filter is F(s). The closed loop transfer function of a PLL is
o m o
i m o
(s) k k F(s)
H(s) .
(s) s k k F(s)
= =
+
θ
θ
(12)
F(s) will have at least one pole (first order LPF) so the order of PLL always exceeds the order of
loop filter by one. If we assume that the loop filter is first order LPF then the PLL will be a second
order PLL [11].
A PLL has two main operation modes; Acquisition mode in which PLL is either out of lock or just
starts to lock to a signal, the frequency range in which the PLL can acquire the input signal is
called capture range. Tracking mode in which PLL is already locked to the input signal and begins
to follow the changes in frequency and phase of input signal, the frequency range of PLL in which
it can track the input signal is called tracking range. The tracking range is larger than capture
range. The loop filter bandwidth is chosen according to the capture range and tracking range of
PLL. There is a trade-off between the loop filter bandwidth and the noise in PLL. In case the
bandwidth is narrow, the noise level is low but locking time will be long. While larger bandwidth
implies large noise level but provides faster locking time [12:14].
2.1 Drawbacks of PLL
The performance of PLL in estimating and tracking frequency has some limitations such as
1- Double frequency ripples cannot be suppressed easily using first-order LPF, so higher
order LPF is needed. The problem is that stability is not guaranteed for higher order PLLs
[15].
2- All PLLs will exhibit some ringing or settling time. PLLs settling and lock times are
primarily a function of the loop filter bandwidth. There is, in general, a trade off
relationship between stability/noise immunity and settling/lock time [16].
3- The maximum allowable bandwidth of PLL is usually about 10% of the input frequency
i.e. the tracking range for PLL is very limited and must be near the center frequency of
θi(s) mk
θo(s)
θe (s)
υd(s)
F(s)
ok / s

VCO, in case of first-order loop filter this range is vco vcof 0. f1×+ . As the order of LPF
increases tracking range of PLL decreases [17].
3. PROPOSED FREQUENCY ESTIMATOR
The proposed estimator consists of three components, i.e. frequency detector, accumulator and
quadrature numerically controlled oscillator (NCO).The frequency detector component receives
the two input sinusoidal quadrature signals and the two quadrature signals from NCO.
Multiplication between these signals is done to obtain two quadrature signals which represent
frequency difference between the input frequency and NCO signal frequency. These two
sinusoidal signals are passed through a differentiator and squaring circuit to extract the frequency
difference from the argument of sinusoidal signal. The final result from the frequency detector is
the frequency difference term. This difference is directed to the accumulator which accumulates
the differences until no difference is founded between input and generated signal frequencies. At
this point the output of the accumulator represents input radian frequency and the generated
signal from NCO runs at the same input frequency.
We first discuss the design of a digital receiver which can help in understanding our proposed
method. A typical digital receiver structure implemented in software defined radio (SDR), except
the radio frequency (RF) front-end, is shown in Fig. 3 [18]. The analog RF signal is received and
fed through a low noise amplifier (LNA) to a mixer to convert RF to intermediate frequency. Signal
is then passed to an analog to digital converter (ADC). A digital down-converter (DDC) converts
ADC output to digitized real signal centered at zero frequency. DDC consists of direct digital
synthesizer (DDS), low pass filter (LPF) and decimator. In addition to lowering frequency, DDC
decimates the signal to a lower sampling rate allowing application of lower speed processors.
FIGURE 3: Digital receiver structure.
A block diagram of the proposed frequency estimator is given in Fig. 4. It is very similar to a PLL
structure except that the phase detector and loop filter are replaced with a frequency detector and
an accumulator respectively. The estimator receives the quadrature input signal from DDC, which
is then sent to the frequency detector. Frequency detector consists of three components i.e.,
multiplier, differentiator and squaring circuit.
sin
LNA ADC
Decimator
Decimator
Digital
Baseband
processing
I
Q
DDS
cos
Digital down converter (DDC)
Mixer
LPF
LPF

FIGURE 4: Block diagram of proposed estimator.
The block diagram of Fig. 4 can be implemented in analog or digital domain. Since the proposed
estimator is designed mainly for digital receivers, description in the discrete time domain will be
more accurate. Fig. 5 explains the detailed discrete time implementation of the proposed
estimator structure. Mathematical and working details are explained below:
Frequency Detector
FIGURE. 5 Discrete time model of proposed estimator.
Multiplier
Differentiator
Squaring
Circuit
Divider Accumulato
r
Quadrature
Oscillator
Ix (n)
Qx (n)
Iy (n)
Qy (n)
Ir(n)
Qr (n)
a(n)
b(n)
d(n)
c(n)
Estimated
Frequency
Synchronized
Signal
Frequency Detector
I sx (nT )
Q sx (nT )
I sy (nT )
Q sy (nT )
I sr(nT )
Q sr (nT )
sa(nT )
sd(nT )
sc(nT )
−1
z
s
s
a(nT )
b(nT )
−1
z
−1
z
Cos
Sin
µ
ωc
−1
z
−1
z
sb(nT )

3.1 Frequency and Power Estimation
We assume the input quadrature signal and the quadrature signal generated by the oscillator are
= ω θ+I s s i s ix (nT ) 2p (nT ) cos( nT ). (13)
= ω θ+Q s s i s ix (nT ) 2p (nT ) sin( nT ). (14)
= θ+ωI s o s oy (nT ) cos( nT ). (15)
= +ω θQ s o s oy (nT ) sin( nT ). (16)
Where sp(nT )is the power of input signal. ωi , ωo , θi and θo are the input and output radian
frequencies and phases respectively, sT is the sampling time.
A. Frequency detector
A.1. Multiplier
It multiplies input quadrature signals with quadrature signals of oscillator. This results in two
quadrature signals I Q(r(n),r (n)) which represent the difference between input frequency and
generated frequency of oscillator.
I s I s I s Q s Q s s sr(nT ) x (nT )y (nT ) x (nT )y (nT ) 2p(nT )c nTos( ),= + = +∆ω ∆θ (17)
Q s I s Q s Q sIs s sr (nT ) x (nT )y (nT ) x (nT )y (nT ) 2p(nT ) s nTin( ).= − − ω +∆ ∆θ= (18)
Where ∆ω = ω ω−i o , ∆θ = θ θ−i o.
A.2. Differentiator
The quadrature signals I Q(r(n),r (n)) pass through a differentiator circuit. This circuit is used to
extract frequency difference from the argument of I Q(r(n),r (n)). The output will be the quadrature
signals multiplied by the frequency difference and amplitude of both signals.
{ }sI t nT I s I s
s
d
r(t) | r(nT ) r(n 1)
Td
1
T
t
= ≈ − − ×
ss s t nT s
d
2p(nT ) ( 2p(t)) |
dt
sin( nT ) cos( nT ),=∆= − + +ω ∆ +ω ∆θ × ∆ω ∆θ (19)
{ }stQ Q QnT s s
s
d
r (t) | r (nT ) r (n 1)
Td
1
T
t
= ≈ − − ×
ss s t nT s
d
2p(nT ) - ( 2p(t)) |
d
cos( nT ) sin( n
t
T ).=∆= ω ∆ω ∆θ ×− + +∆ω ∆θ (20)
s ss Q s I t nT I s t nQ Ta(nT ) r (nT ) (t) |
d d
r r
dt dt
r(nT ) (t) |= =×−×=
2 2
s s s[sin nT2p(nT ) ( ) cos ( nT ])∆ω ∆ω ∆θ ∆ω= + +
s2p(nT ) .= ∆ω (21)

A.3. Squaring circuit
The quadrature signal I s Q s(r(nT ),r (nT )) also passes through squaring circuit. Squaring circuit and
divider eliminate the amplitude term from the result of differentiator. The output of squaring circuit
can be considered as power of input signal.
∆ω ∆θ ∆
=
= +
= + ω+
2 2
s I S Q S
2 2
s s s
s
[si
b(nT ) r (nT ) r (nT )
2p(nT ) ( ) cn nT nT ]
2p(n
o ( )
T
s
).
(22)
A.4. Divider
The divider is used to eliminate the amplitude part from (5). Its output is
= ∆ω=s
s
s
a(nT )
d(nT )
b(nT )
. (23)
B. Accumulator
Frequency difference is passed to the accumulator which accumulates this difference until
saturation which means the input frequency is same as the generated frequency of oscillator. The
accumulator action is given by the following equation
S s Sd (nT ) c(nT ) c(( )n T .1)µ = − − (24)
Where µ is a variable whose value determines the speed of locking and stability of the system.
C. Quadrature oscillator
The oscillator considered in this paper is numerically controlled oscillator (NCO). Output of the
accumulator controls the value of generated frequency of NCO. The feedback loop of the
estimator continues until there is no difference between the input and generated frequency. At
this point, output of the accumulator represents the estimated input radian frequency. NCO
equation is
−
=
= +ω ω ∑o s c
n
k
s
1
0
(nT ) c(kT ). (25)
Where ωc is the center frequency. When the generated frequency from NCO is equal to the input
frequency, the accumulator saturates. Thus at i s o s(nT ) (nT )=ω ω
s i s i sc(nT ) T f2 T=ω π= (26)
3.2 Stability
Stability of the estimator is analyzed in this sub-section. Linear model (z-model) of the system is
built to get system’s transfer function, which is the ratio between output and input signals. Fig. 6
shows z-model of the system. It may be noted that NCO equivalent model is only a delay circuit.
The input is frequency and the output is also frequency so no integration is needed unlike PLL.
Following equations are obtained from Fig. 6.

FIGURE. 6 Z-model of proposed estimator.
1
ic(z) (z) z c(z),−
= −ω (27)
1
d(z) c(z)(1 z ),−
µ = − (28)
(29)
Therefore, transfer function of the proposed estimator
µ
ω
=
− − µ
=
i
c(z)
T(z) .
(z z (1
z
) )
(30)
The variable µ controls stability of the system and its range must be 0 1≥ µ < . For small values
of µ the system is more stable but takes long settle time, for greater values of µ settling time
decreases.
4. COMPUTER SIMULATIONS
Validity of the above mentioned mathematical analysis is checked by performing computer
simulations. In this section we also present a comparison between conventional PLL and
proposed estimator. The results of these simulations are discussed in the sub-sections below.
4.1 Frequency Estimation
We first perform simulations for frequency estimation. The proposed system input frequency is
set at if 500= kHz, sampling frequency s sf 1/ T 10= = MHz with different values of µ . Fig. 7
shows the output of the estimator for each value of µ . It is clear that for small values
of µ frequency locking takes more time compared to that when µ is large. Stability is guaranteed
as µ is in the specified range.
−1
z
−1
z
i (z)ω
d(z)
µ
c(z)
1
1
i
1 z
(z) c(z)(Z ).
−
−
ω = +
µ
−

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 10
-5
0
1
2
3
4
5
6
x 10
6
Time (s)
Frequency(Hz)
µ=0.9
µ=0.2
µ=0.06
FIGURE. 7 Frequency estimation with differentµ .
Following simulations provide a frequency estimation comparison of proposed and conventional
PLL. An input signal with frequency of if 10 kHz= is applied. In these simulations we used two
different loop filters with the PLL; the first loop filter is first order LPF with cut-off frequency 1000
Hz, the other is second order LPF with the same cut-off frequency. The parameters of PLL are:
m o in nco cut sk 1024, f 10 kHz, f1/ 2 1000 Hz, f 100, k 10.5 kHz, Hzf k= = = == = . While the
parameters of proposed estimator are nco sf 100 Hz, f 100 kHz= = .
In Fig. 8 (a) conventional PLL with first-order LPF (second order PLL) did not suppress the double
frequency ripple completely (variance is 665.3610), and overshoot (maximum overshoot
reaches1.06 KHz) occurs, settling time (the time required to reach correct estimated frequency is
about 1 ms) [19]. In Fig. 8 (b) conventional PLL with second-order PLL (third order PLL) the ripple
is suppressed better than the first-order LPF (variance is 1.2759), overshoots (maximum
overshoot reaches1.075 KHz) and ringing occur, settling time (increased to 7.5 ms seconds),
estimation range is reduced and stability becomes critical.
In Fig. 8 (c) the proposed estimator estimates the input frequency at 0.5 ms with no ripples
(Although no loop filter is used system variance is 1.0839e-18), the estimation range is wide from
0 to half the sampling frequency and more stable than PLL. The previous comparison clearly
shows that the proposed estimator is faster, more stable, has a wide range than conventional
PLL. The variance of estimations is also given in Table 1. It can be seen that estimation’s
variance is extremely low in case of the proposed method showing its superiority.

0 0.01 0.02 0.03 0.04 0.05
1
1.02
1.04
1.06
1.08
x 10
4
Time (s)
(a)
Frequency(Hz)
0 0.01 0.02 0.03 0.04 0.05
1
1.02
1.04
1.06
1.08
x 10
4
Time (s)
(b)
Frequency(Hz)
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
0
5000
10000
15000
Time (s)
(c)
Frequency(Hz)
FIGURE. 8 Frequency estimation curves of (a) Conventional PLL with first-order loop filter, (b) Conventional
PLL with second-order loop filter, (c) Proposed Estimator.
TABLE 1: Comparison between PLL and proposed estimator.
4.2 Frequency Estimation With AWGN
In practical situations the received input signal is corrupted with AWGN and this will affect the
results. Some design modifications are performed to take care of this situation. Block diagram of
the modified design is shown in Fig. 15. Two moving average filters (MAF) with length of 10
stages are used for I and Q phase input signals. Another filter is used for smoothing the output.
The MAF is a low pass finite impulse response (FIR) filter commonly used for smoothing an array
of sampled data/signal. It takes M samples of input at a time and computes the average of those
samples and produces a single output point. As the filter length (number of delays) increases the
smoothness of output increases [20].
The following simulations are performed to investigate the effect of AWGN on both conventional
DPLL (second and third order DPLL) and proposed estimator. MAF with the same lengths are
added to both architectures. An input signal is applied to three architectures with different
frequencies 5.05E4, 5.15E4, 5.25E4 Hz and SNR 0, 5, 10 dB at sampling frequency of 10 MHz.
Architecture Variance Settling
time
Max.
overshoots
Tracking
range
Second order PLL 665.3610 1 ms 1.06 kHz 8950:11050 HZ
Third order PLL 1.2759 7.5 ms 1.075 KHz 9095:10904 Hz
Proposed estimator 1.0839E-18 0.5 ms - 0:50 kHz

Fig. 9 shows estimations of the second order DPLL with different frequencies and SNRs. At
frequency of 5.05E4 and SNR =0 dB (green line) the noise level affected the estimation and
variance is 2.2728E4. At frequency of 5.15E4 and SNR= 5 dB (blue line) the noise level is reduced and
variance is 6.6063E3. At frequency of 5.25E4 and SNR=10 dB (red line) a higher reduction in noise level
causes the variance to further reduce to 3.1311E3.
The estimations are improved using third order DPLL as shown in Fig. 10. The proposed
estimator results are shown in Fig. 11. Variance of estimates of each architecture is summarized
in Table. 2 it can be seen that, the proposed architecture produces the smallest values for each
estimated frequency although loop filter is not used.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
4.9
4.95
5
5.05
5.1
5.15
5.2
5.25
5.3
x 10
4
Time (s)
Frequency(Hz)
SNR= 0 dB
SNR= 5 dB
SNR= 10 dB
FIGURE. 9 Frequency estimation with different SNRs using second order DPLL.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
4.9
4.95
5
5.05
5.1
5.15
5.2
5.25
5.3
x 10
4
Time (s)
Frequency(Hz)
SNR= 0 dB
SNR=5 dB
SNR= 10 dB
FIGURE. 10 Frequency estimation with different SNRs using third order DPLL.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
4.9
4.95
5
5.05
5.1
5.15
5.2
5.25
5.3
x 10
4
Time (s)
Ferquency(Hz)
SNR= 0 dB
SNR= 5 dB
SNR= 10 dB
FIGURE. 11 Frequency estimation with different SNRs using proposed estimator.
TABLE 2: Comparison between PLL and proposed estimator with different SNR.
4.3 Tracking Performance
We also checked performance of the proposed method in tracking frequency changes and
estimating amplitude/power variations. Frequency of the input sinusoidal signal is varied
randomly within the range 10 kHz-60 kHz. The input signal power is also randomly varied within
the range 0.06125-0.21125 watt. The simulations are performed with SNR 10 dB and sampling
frequency of 1 MHz. Fig. 12 shows the tracking of the input frequency while Fig. 13 gives
estimation of power. It can be seen that the estimator tracks changes in input frequency and
amplitude very fast.
Architecture SNR Variance
Second order PLL 0 dB 2.2728E4
5 dB 6.6063E3
10 dB 3.1311E3
Third order PLL 0 dB 1.7288E4
5 dB 4.1194E3
10 dB 1.6340E3
Proposed estimator 0 dB 3.4036E-4
5 dB 3.5282E-4
10 dB 3.6620E-4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
1
2
3
4
5
6
x 10
4
Time (s)
Frequency(Hz)
Ideal
Estimated
FIGURE. 12 Frequency tracking.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Time(s)
Power(Watt)
Estimated
Ideal
FIGURE. 13 Power estimation.
In order to investigate the performance of conventional PLL to track the frequency change, we
have to change the previous estimation range because it exceeds PLL capabilities. A signal with
input frequency changed from 10.3-10.9 kHz with sampling frequency of 100 kHz without AWGN
is applied to conventional PLL with second-order LPF with ncof =10 kHz. As shown in Fig. 14 for
each tracked frequency the overshooting and ringing occurred. The situation becomes worst
when the input signal have AWGN. As a result of using second-order LPF the estimation range is
reduced to 10:10.9 kHz.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
1
1.05
1.1
x 10
4
Time (s)
(a)
Frequency(Hz)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
1
1.05
1.1
x 10
4
Time (s)
(b)
Frequency(Hz)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
1
1.05
1.1
x 10
4
Time (s)
(c)
Freqyency(Hz)
FIGURE. 14 Frequency tracking using
[1] Conventional second order DPLL. b) Conventional third order DPLL. c) Proposed estimator.
5. FPGA IMPLEMENTATION
The estimator is modeled using Xilinx system generator tool [21,22]. VHDL code is used to
describe the proposed estimator. Fig. 15 shows the system model used to generate the VHDL
code [23, 24]. All signals of the estimator model are fixed point signals with 16 bits.
FIGURE. 15. System generator model of proposed estimator.
The model receives quadrature input signal with AWGN then the signals are passed to the
moving average filter (MAF) to generate signals named ‘xi’ and ‘xq’. The generated quadrature
signals from NCO are ‘yi’ and ‘yq’. These two quadrature signals are directed to the frequency
detector block whose output is the signal ‘d’. This signal enters the accumulator block to generate

the signal ‘c’. Another MAF is used to enhance the output signal ‘fout’. The model of quadrature
NCO as shown in Fig. 16 consists of accumulator and two read only memory (ROM), one ROM
stores sine waveform samples and the other stores cosine waveform samples. The accumulator
receives the signal ‘c’ and generates both signals ‘yi’ and ‘yq’. One rotation of the accumulator
represents one complete cycle of sine or cosine waveform.
FIGURE. 16. System generator model of NCO.
The estimator was implemented using XCSD1800A-4FG676C Spartan-3A DSP board. Fig. 17
shows simulation results of the VHDL model when input and sampling frequencies are 1 MHz and
10 MHz respectively. It can be seen that the hardware model results agree with the simulations in
locking time and stability. FPGA resources utilization for proposed architecture, which indicates
how many hardware components are used by the model, is provided in Table 3. It can be seen
that the proposed method requires fewer hardware resources. Implementation results indicate
that the proposed design provides fast operation and low power consumption. Furthermore, it can
be observed that the method has a simple design and avoids complexities.
0
1
xi
-1
0
1
yq
0 1 2 3 4 5
x 10
-5
0
5
10
x 10
5
Time (s)
fout
FIGURE. 17. VHDL simulation results.

TABLE 1: This is Table 1. All tables must be aligned Centered.
TABLE 3: FPGA resources utilization.
6. CONCLUSIONS
PLL is wide used in communication application such as frequency tracking. Conventional PLL has
many drawbacks such as overshot, ringing, limited tracking range and instability. The aim of this
paper is to present a proposed estimator solve limitation in conventional PLL. The proposed
estimator accurately estimates unknown frequency and power of input sinusoidal signal
simultaneously. Proposed method worked well even in the presence of AWGN. The estimator
rapidly tracked any changes in input signal frequency and amplitude. Operation of the proposed
structure is similar to that of a PLL. The phase detector component and the low pass filter in PLL
have been replaced with frequency detector and accumulator. Computer simulations performed
showed promising results. The paper also discussed hardware implementation of the system.
The proposed architecture is designed and modeled using VHDL and implemented using FPGA
circuit. Implementation results indicate that the estimator has a simple design, faster operation
and low power consumption.
7. ACKNOWLEDGEMENT
This research is partially supported by Grant-in-Aid for scientific Research (B) no.20360174, and
the Aihara Project, the FIRST program from JSPS, initiated by CSTP.
8. REFERENCES
[1] B. Sklar. Digital Communications: Fundamentals and Applications. Prentice Hall Inc.,2001.
[2] J. G. Proakis, M. Salehi. Digital Communications. Mcgraw-Hill., 2008.
[3] D. Green. “Lock-In, Tracking, and acquisition of AGC-aided phase-locked loops.” IEEE
Transaction on Ciruits and Systems, vol. 32, pp. 559-568,1985.
[4] S. Changhong, C. Zhongze, Z. Lijun, L. Yong. “Design and Implementation of Bandwidth
Adaptable Third-order All digital Phase-Locked Loops,” in Proc. WICOM, 2010, pp.1-4.
[5] P. Hanumolu. “W Gu-Yeon, M. un-ku, A Wide- Tracking Range clock and Data recovery
Circuit.” IEEE Transaction on Solid state circuits, vol. 43, pp. 425:439, 2008.
[6] X. hongbing, G. Peiyuan, L. Shiyi. “Modeling and simulation of Higher-order PLL rotation
tracking system in GNSS receiver,” in Proc. ICMA, 2009, pp. 1128-1133.
[7] A. Carlosena, A. Manuel- Lazaro. “Design of Higher-Order Phase-Lock Loops.” IEEE
Transaction on Circuits and systems II, vol. 54, pp. 9-13, 2007.
[8] B. Razavi, Monolithic Phase-Locked Loops and clock recovery circuits: Theory and Design,
Wiley-IEEE Press, 1996.
Component used Avilable Utilization
Number of slice flip flops 76 33280 1%
Value Number of 4 input LUTs 583 33280 1%
Number of occupied slices 320 16640 1%
Number of DSP48As 6 84 7%
Number of Bonded IOBs 81 519 15%
Maximum frequency 225 MHz
Power consumption 127 mW

[9] V.F. Kroupa. Phase Lock Loops and Frequency Synthesis. John Wiley & Sons, 2003.
[10] F.M Gardner. Phase lock techniques. Wiley-Interscience, 2005.
[11] R. E. Best. Phase locked loops Design, simulation, and Application. Mcgraw-Hill, 2007.
[12] L. Kyoohyun, C. Seunghee, K. Bemsup. “Optimal loop bandwidth design for low noise PLL
applications,” in Proc. ASP-DAC,1997, pp. 425-428.
[13] W. Ping-Ying, F. Chia-Huang. “All digital modulation bandwidth extension technique for
narrow bandwidth analog fractional-N PLL,” in Proc. ESSCIRC,2010, pp. 270-273.
[14] J.Roche, W. Rahadjandrabey, L. Zady, G. Bracmard, D. Fronte. “A PLL with loop
bandwidth enhancement for low-noise and fast-settling clock recovery,” in Proc. ICECS,
2008, pp. 802-805.
[15] M. Saber, Y. Jitsumatsu, M.T.A. Khan. “Design and Implementation of Low Ripple Low
Power Digital Phase-Locked Loop.'' Signal Processing: An international journal (SPIJ), vol.
4, pp. 304-317, Feb. 2011.
[16] M. Min, V. Mannama, T. Paavle.”Settling time minimization in PLL frequency synthesizer,”
in Proc. ICCSC, 2005, pp. 366-369.
[17] L. Verrazzani . ”Pull-In Time and Range of Any Order Generalized PLL. “ IEEE Transaction
on Aerospace and Electronic systems, vol. AES14, pp.329-333, 2007.
[18] M. Dillinger, K. Madani, N. Alonistioti. Software Defined radio: Architectures, Systems, and
Functions. Wiley, 2003.
[19] M. J.Roberts, R.A. Riccardo. Student's Guide to Analysis of Variance. Routledge, 1999.
[20] W.S. Steven. The Scientist & Engineer's Guide to Digital Signal Processing. California
Technical Pub,1997.
[21] P. Pong Chu. RTL Hardware Design Using VHDL: Coding for Efficiency, Portability and
Scalability. Wiley-IEEE Press, 2006.
[22] Xilinx Inc. system generator for DSP user guide. Xilinx, 2009.
[23] W.Y. Yang. Matlab/Simulink for digital communication. A-Jin, 2009.
[24] Pong p. chu. FPGA Prototyping by VHDL Examples: Xilinx Spartan-3 Version. Wiley-
Interscience, 2008.

Frequency and Power Estimator for Digital Receivers in Doppler Shift Environments

More Related Content

What's hot (20)

Viewers also liked (12)

Similar to Frequency and Power Estimator for Digital Receivers in Doppler Shift Environments (20)

Recently uploaded (20)

Frequency and Power Estimator for Digital Receivers in Doppler Shift Environments