International Global Navigation Satellite Systems Society IGNSS Symposium 2013

Outrigger Gold Coast, Australia

16-18 July, 2013

Analysis of Performance Degradation Due to RF Impairments in Quadrature Bandpass Sampling

GNSS Receivers

Vaidhya Mookiah, Ediz Cetin, Andrew G. Dempster University of New South Wales, Australia

Tel: +61415823738 e-mail: v.mookiah@student.unsw.edu.au, e.cetin@unsw.edu.au, a.dempster@unsw.edu.au

ABSTRACT

Radio receiver architectures with Analog-to-Digital Converter (ADC) close

to the antenna can perform reconfigurable band selection in the digital

domain hence resulting in increased integration and improved performance.

Techniques such as Bandpass Sampling (BPS) require a sampling rate of at

least twice the bandwidth of the received signal to sample and downconvert

it to the baseband. Quadrature Bandpass Sampling (QBPS), on the other

hand, accomplishes this with half the sampling rate of BPS, but utilises two

ADCs. QBPS operates on the received Radio Frequency (RF) signal and

uses two ADCs with sampling clocks separated by one quarter of the carrier

signal period, )4/(1 cf , relative to one another. For GPS L1 signal, this delay

corresponds to 158.69 ps, which is not trivial to generate accurately.

The use of QBPS in the analog front-end eliminates the need for expensive

mixers, filters and the impairments associated with them. However,

impairments associated with accurately generating the delay required

between the sampling clocks, along with impairments in the signal paths

between the ADCs result in performance degradation. This paper

investigates the influence of these RF impairments associated with the QBPS

scheme and compares its performance with different traditional RF front-end

architectures in generating in-phase and quadrature signals. A quantitative

comparison of architectures is performed using simulation case studies in

MATLAB environment and their performance with respect to Image

Rejection Ratio (IRR) and Error Vector Magnitude (EVM) is analysed.

Results show that QBPS based architecture outperforms other architectures

as well as resulting in reduced hardware complexity and subsequent reduced

power consumption.

KEYWORDS: software radio, bandpass sampling, RF impairment, image

rejection ratio, quadrature sampling.

1. INTRODUCTION

Radio receivers have been going through a dramatic change in the recent years. The advent of

digital systems has made radio receivers more accurate and compact. However, most radio

receivers use analog components to carry out filtering and frequency translation of the

received Radio Frequency (RF) signals. In order to eliminate the bulky and nonlinear analog

components and to have more flexibility for downconversion, it is desirable to place the

Analog-to-Digital Converter (ADC) as close to the antenna as possible. Similarly the theory

of software radio states that ADC must be close to the antenna to have a single hardware

system that can operate as multiple receivers by software re-programming (Mitola 1995). To

implement this idea, BandPass Sampling (BPS) can be used. BPS has advantages for Global

Navigation Satellite System (GNSS) receivers as it eliminates analog components,

furthermore, the digital part of the receiver can be updated when new GNSS signals are

available and it can be extended for multiple frequency bands. This technique has advantages

over traditional heterodyne GNSS receivers; nevertheless it has implementation difficulties.

There have been a number of techniques developed to implement BPS in GNSS receiver

systems shown by Thombre & Nurmi (2012), but they require high sampling frequency and

larger bandwidth ADCs. This drawback can be overcome by using Quadrature BandPass

Sampling (QBPS) which reduces the strains imposed on the ADCs. The use of QBPS

provides increased flexibility in sampling frequency selection and quadrature

downconversion. The sampling frequencies required by the QBPS can be as small as half the

sampling frequency required by the BPS (Dempster 2011). However, performance of the

QBPS needs to be further investigated for efficient implementation in a GNSS receiver. This

paper looks into the two major parameters: noise folding and RF impairments which affect

the performance of GNSS receiver utilising QBPS and compares the QBPS performance with

other commonly used receiver architectures in terms of Image Rejection Ratio (IRR) and

Error Vector Magnitude (EVM).

The paper is organised as follows: Section 2 provides an overview of different RF front-end

architectures and errors associated with them. Section 3 begins with performance analysis of

QBPS RF front-end, and then details QBPS front-end application in GNSS receiver system.

Section 4 details the theoretical aspects of noise folding and RF impairments. In section 5, the

Matlab model used for performance analysis is described and simulation results evaluation is

given in section 6. Concluding remarks and future work are described in sections 7 and 8

respectively.

2. RADIO FREQUENCY FRONT-END FOR SOFTWARE DEFINED RADIO

RF front-end is an important module in any receiver and any development in front-end will

improve the overall performance of the receiver. In order to design an RF front-end which

can support Software Defined Radio (SDR) in an efficient way, it needs to have flexibility

and accuracy. Bandpass signals can be downconverted using In-phase (I) and Quadrature (Q)

mixers or digital downconversion methods. In spite of inflexibility and complexity of

homodyne and heterodyne receivers, they are still the preferred way to downconvert signals

to baseband given the high speed ADC and efficient anti-aliasing bandpass filter

requirements of the digital front-ends. The recent developments in CMOS technology and

innovative methods in sampling have provided flexibility in sampling frequency range for

digital front-ends. The traditional RF front-ends with their RF impairments and noise are

studied in detail in the following sub-sections.

2.1 Direct Downconversion Receiver

The homodyne or zero-IF receiver is a relatively simple architecture which downconverts the

signal in quadrature fashion from RF to baseband without an Intermediate Frequency (IF)

stage. Due to the elimination of IF, image problem doesn’t exist in this architecture. However

RF impairments, DC offset and flicker noise are present which are the major sources

reducing front-end performance (Razavi 1997, Cetin et al. 2007a). Homodyne architecture is

better than heterodyne architecture because it has less analog components which reduces

power consumption and eliminates the major sources of error. However, due to RF

impairments such as phase and gain errors between the I and Q paths, interference might

occur due to overlapping of desired signal and its complex conjugate at the baseband. This

performance of this architecture is taken as the benchmark when comparing different

architectures. Figure 1 shows the RF impairments associated with a homodyne receiver.

Figure 1 Homodyne Quadrature demodulator with phase error

The RF impairments result in image superimposition when downconverting the signal to the

baseband. The IRR is defined as the ratio between the image signal to the desired signal. This

is a function of phase and gain errors ε, φ, and can be given as (Cetin et al. 2007a):

Simpair

Sideal

=1+ε 2 − 2ε cosφ

1+ε 2 + 2ε cosφ (1)

where Simpair is the signal due to RF impairments and Sideal is the desired signal

2.2 BandPass Sampling Receivers

BPS is a simple digital RF front-end design which directly samples the RF signal with a

sampling rate which avoids over lapping of signals at lower-IF or at the baseband. The BPS

receiver samples the signal at a frequency less than twice the upper cut off frequency. The

theoretical minimum sampling rate for any carrier frequency is given in equation (2). For a

bandlimited signal with bandwidth BW=(fu-fl ) the minimum sampling rate derived from the

equation is fs=2BW where: fU and fL are the upper and lower cut-off of the radio signal

0°

90°

LPF

LPF

ADC

ADC

S(t) LO

I(t)

Q(t)

φ

Cos(2πf)

Sin(2πf+φ)

(ε) Gain error

Phase

error

respectively. Factor n is the integer which decides range of sampling frequencies that can be

used and is given in equation (3).

1

22

−≤≤

n

ff

n

f Ls

U (2)

1≤ n ≤ IntegerfU

BW

(3)

Due to intentional aliasing in BPS receiver, the downconverted signal degrades in

performance as the noise level increases as described by Kim et al. (2008) due to noise

folding. When compared with the homodyne architecture, the performance degradation due

to the mixers and filters is eliminated in the BPS receiver. Following on from digitisation,

final frequency translation to the baseband in quadrature form is carried out in the digital

domain. In BPS, the role of the Band Pass Filter (BPF) is important as it filters out nearby

and most of the out of bound noise, limiting the folded-noise contributions hence improving

the overall performance.

The major limitation in BPS receiver design is that it requires high speed ADC and a good

BPF. For 2 MHz bandwidth signal, the ADC must be operating with a minimum sampling

frequency of 4 MHz and the BPF should have a sharp cut-off to avoid overlapping of

neighbouring bands when downconverted. Hence the effects of noise folding, quantization

and jitter must to be analysed for any subsampling front-end (Kim et al. 2008, Ucar et al.

2008). Accordingly the architecture for BPS is shown in Figure 2 which uses Hilbert

transform to generate the I and Q signals. For the purpose of comparison between

architectures, we assume that jitter and quantization noise are not present in the architecture.

Figure 2 BPS Hilbert Transform Quadrature Demodulator

Noise folding being the major error source in any subsampling receiver, let us consider noise

folding for BPS after the received signal is bandpass filtered with a filter with bandwidth of

BW, where the SNR for a signal power Sp is dependent on Ni and No, the in-band and out-of-

band noise respectively. The factor that decides the number of folding is given by m and this

directly affects the output SNR values given as:

oi

p

NmN

SSNR

)1( −+= (4)

m =2BW

fs

(5)

It is clear from equations (4) and (5) that the SNR for sub-sampling system depends on the

out-of-band noise and the sampling frequency. If the sampling frequency is higher, then the

effect of noise-folding reduces due to less Nyquist zones being downconverted to the band of

interest. Similarly a better BPF will reduce the out-of-band noise hence improving the overall

performance of the receiver.

Samples at the output of the BPS receiver can then be converted to quadrature signal using

several methods. One of the ways I/Q signals can be generated in the BPS architecture is via

the use of the Hilbert Transform (HT), as depicted in Figure 2. HT converts the signal to

quadrature form at IF and following on the signal is downconverted to the baseband. HT does

not possess RF impairment because it zeros out the negative frequencies, thus eliminating the

problem of self-image interference.

2.3 Quadrature BandPass Sampling Receiver

QBPS is a second order BPS architecture where two ADCs are used to digitise and

downconvert the received RF signal to I/Q samples. With QBPS the ADC sampling clocks

have a delay of cf41 relative to one another. This architecture has greater advantage over

BPS design because the two ADCs provide two samples so that the sampling frequency can

be as low as half the sampling frequency required by BPS. However, there is the cost of an

additional ADC. QBPS receiver architecture is represented in Figure 3.

Figure 3 QBPS Model

With the implementation of two ADCs, the choice of sampling frequency is more flexible

when compared to BPS as described by Dempster (2011). Depending on the chosen sampling

frequency, the signal can be downconverted to lower IF or directly to the baseband. When the

sampling frequency is an integer multiple of the carrier frequency, the RF signal is directly

downconverted to the baseband after sampling. The signal is downconverted to lower IF if

the sampling frequency is chosen to be fraction of the carrier frequency. For the performance

evaluation of QBPS in this paper, RF signal is directly downconverted to the baseband using

the QBPS. Like BPS, QBPS suffers from noise folding. Similarly, for high frequency signals,

delay element accuracy poses challenges which will be investigated in the following sections.

2.4 GNSS RF FRONT-END

The concept of BPS enhanced digital RF front-end designs and analysis of errors like RF

impairment and noise on GNSS receiver system with different digital front-end architectures

will let us develop better front-ends suited for GNSS applications. The traditional homodyne

and heterodyne systems are still used in GNSS receivers; these RF front-ends are bulky and

contain analog components which have nonlinearities associated with them. The new

approach in digital RF front-end architecture based on QBPS for GNSS can improve

performance by eliminating these analog components.

GNSS front-ends with ADCs closer to the antenna help in lowering the hardware complexity

since most of the analog components e.g. mixers are eliminated. Furthermore, GNSS is a

good experimental platform to implement QBPS because we have fixed band and

bandlimited signals. The bands are quite separated so the signals are less affected by

interference. Furthermore, in Psiaki et al. (2003) it is shown that the signal power and carrier

tracking is not influenced by subsampling in GNSS receivers.

3. PERFORMANCE ANALYSIS OF QBPS RF FRONT-END

In QBPS, sampling is the most important process since it downconverts and digitises the

signal in a single step. Due to direct RF sampling, factors like accuracy of sampling

frequency, delay value, BPF and ADC contribute to the performance of the receiver. In this

section, we will look into performance degradation due to noise folding in the absence of

BPF and RF impairments associated with the accuracy of generating the delay between the

sampling clocks of two ADCs. When these errors are considered for GPS L1 signal, the

timing e.g. the accuracy of the delay between the ADCs becomes crucial.

3.1 QBPS ARCHITECTURE

The theoretical expression of QBPS will let us understand more clearly that the output of

QBPS is equivalent to that of a homodyne system. Let us take a cosine wave with amplitude

(A) as our received RF signal:

)2cos()( tfAtS cπ= (6)

After sampling we get two streams of data from the two ADCs. The output of the first ADC

gives the in-phase component, I(nT), when sampled with sampling frequency fs=1/nT :

)2cos()()( nTfAnTSnTI cπ== (7)

The second ADC with sampling time delay ∆t gives the quadrature signal:

))(2cos()()( tnTfAtnTSnTQ c ∆+=∆+= π (8)

Substituting cf

t4

1=∆ in equation (9) we get:

)2sin()( nTfAnTQ cπ−= (9)

From equations (7) and (9), it is evident that QBPS provides us with two streams of data

which are in-phase and quadrature phase component of the received signal. It can also be

recognized that the output of QBPS is equal to the output of the homodyne receiver after

ADC. Also, as can be observed from equation (8), in a QBPS receiver, the accuracy of ∆t is a

major factor in the performance of the receiver. Since the value of ∆t is prone to errors due to

its small value, it can be expressed as εtf

tc

+=∆4

1 where tε is the error in time delay and its

corresponding phase delay will lead to imbalanced quadrature phase as shown in equation

(10):

))(2sin()( επ tnTfAnTQ c +−= (10)

To model this we will consider the case of single band signal with centre frequency of GPS

L1 (1575.42 MHz). Corresponding Matlab models are developed to generate oversampled

high frequency signals to emulate the analog signal. The received signal is then

downconverted using sampling frequency greater than the bandwidth of the transmitted

signal. Similarly, another stream of samples is downconverted to generate samples with a

time delay of ∆t. The major parameters to be considered are the delay ∆t and the sampling

frequency fs. Keeping the sampling frequency fixed, we will carry out different simulations to

find out the image rejection performance due to ∆t, knowing the fact that error in ∆t is same

as the phase error φ for a homodyne receiver. The phase mismatch creates the same

attenuation effects as observed in the homodyne system and will be discussed in detail in the

later section. From these facts it is quite understandable that the phase error and RF

impairments will affect the SNR of the signal.

3.2 Noise Folding

Subsampling of signals will cause the frequency spectrum to fold. This increases the noise

level. QBPS system uses two streams of data, each with a minimum sampling period equal to

the bandwidth of the signal; hence, effect of noise folding is going to affect the SNR heavily.

When the sampling frequency is equal to the signal bandwidth i.e. fs=BW, the SNR of I and Q

samples can be given as:

oi

p

NN

SISNR

+=_ (11)

oi

p

NN

SQSNR

+=_ (12)

Where Ni and No are the in-band and out-of-band noise respectively. This means that each

stream has its own noise folding, which has higher SNR when compared to the I/Q mixer

architecture in the Homodyne receiver.

Assuming Ni = No =N, were N is the total noise after passing through a BPF, the noise floor is

folded 2BW/fs times if m>1 given in equation (5). So considering each I and Q streams the

noise level is higher when compared to BPS, but when combined the noise level will remain

equal to BPS.

Noise in a homodyne system is mainly due to analog mixer circuit Nm and the thermal noise

Nd. The SNR for the mixer can be expressed as:

+

=

d

md

pm

N

NN

SSNR

21

1 (13)

From the comparison we get to know that factor governing noise level for QBPS is directly

influenced by the sampling frequency, the higher the sampling frequency the better the SNR

value and the lower the EVM. For the I/Q mixer SNR mainly depends on the mixer noise

figure.

3.3 RF Impairments

Receiver architectures with quadrature signal processing are susceptible to mismatch in phase

and amplitude. In QBPS, the phase mismatch corresponds to the error in delay element

needed to generate the 1/4fc delay. To analyse the performance degradation due to delay error,

the amplitude mismatch is not considered. If the delay of the Q phase ADC is distorted, then

it creates an imbalance and thus degrades the performance of the receiver which can be

measured using IRR and EVM. Based on Cetin et al. (2003, 2007a), the performance

degradation due to I/Q impairment for a homodyne system is calculated. In these papers

authors evaluate the bit error rate and image rejection ratio for the system which uses

quadrature demodulation. Similarly, QBPS performance can be evaluated in terms of image

rejection ratio and EVM for changes in the phase error. Taking the homodyne receiver

performance as a reference for the RF impairments, the performance of the QBPS receiver

can be compared.

For QBPS, the phase error ϕ depends on the error in time delay, tε, of the second ADC.

Equation for phase error corresponding to timing error is related to each other for a given

carrier frequency and can be given as:

� = 2���(�) (14)

Considering these errors for the GPS L1 signal, the time delay must be in the order of

6.347x10-10

seconds which is not trivial to generate. A 1° phase error corresponds to a time

delay of 1.763x10-12

seconds, it means that the receiver sampling delay should have accuracy

in the scale of picoseconds. IRR due to the phase imbalance in L1 signal can be calculated as:

��� = 20��� �1 − ����1 + �����

Here the IRR is calculated as the ratio of image signal, due to the phase error, to the actual

signal. This IRR provides an insight into how well the image signal is attenuated and is given

as the ratio of the self-image signal power to the desired signal power. Figure 4, depicts the

IRR for varying delay errors, tε. As can be observed from Figure 4, as the time delay error in

∆t increases, the IRR reduces. This clearly explains that if the tε=0 there is no leakage of

inphase component in the quadrature component and vice versa. There is no image

component in the IRR whereas when tε= 90° the image signal is equal to the desired signal.

Therefore, controlling the delay error tε becomes vital in a QBPS receiver.

(15)

Figure 4 IRR for QBPS for GPS L1 frequency

4. COMPARISON BETWEEN ARCHITECTURES

In this section, performance analysis of QBPS in comparison to other approaches detailed in

the previous sections is provided. There has to be a solid comparison between the existing

methods and QBPS to prove that it can provide better solution to replace the inflexible RF

front-end. Experimental comparison is made between homodyne, BPS with HT and QBPS

architectures, as detailed in the previous sections, using Matlab simulation case studies. The

Matlab model consists of a BPSK transmitted signal, SNR varying AWGN channel, and the

receiver models. Figure 5 shows this evaluation set-up. As it can be observed from Figure 5,

the receiver models have a common received signal after passing through the BPF with cut-

off frequency equal to the bandwidth of the signal. Signals are downconverted and

demodulated to baseband to recover the data. The Matlab model design is developed to

generate an oversampled BPSK signal at the GPS L1 frequency to establish how crucial the

delay error and BPF can affect the QBPS system in a GNSS receiver. Channel is modelled as

an Additive White Gaussian Noise (AWGN), and the system is considered to be free from

interference or any fading.

First, the BPF with bandwidth equal to the bandwidth of the signal is used to filter the signal

and the samples are demodulated without introducing any phase error. The corresponding

EVMs are measured for different SNR values. EVM is calculated as: (Arslan 2009)

������ = � !∑ |�$%&'(,*+�,&'-,*|.!*/ !∑ 0�$%&'(,*0!*/ . 1

. (16)

Further experiments are carried out to establish how the performance of EVM is affected by

the absence of the BPF. Finally evaluation of the phase error keeping the BPF at an optimum

design is simulated to find the image rejection performance of the architectures. These

experiments are carried out assuming that there aren’t any interference or transmitter errors.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

x 10-10

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

IRR

(d

B)

Time delay offset in seconds (0 to 90 deg)

IRR vs delay error for QBPS

Figure 5 Matlab Model representation

5. EXPERIMENTAL EVALUATION

To represent the analog domain and ADC conversion, Matlab models are constructed with

very high sampling rate. As per the experimental setup detailed in the previous section, a

BPSK signal is generated with 100 symbols. Following this the baseband signal is

upconverted to GPS L1 frequency of 1575.42 MHz and additive white Gaussian noise is

added to the transmitted signal. This signal is then fed to all three architectures under

evaluation for downconverting and demodulation, as shown in Figure 5. The results of the

experiment where the BPF is not present is shown in Figure 6. As can be observed from

Figure 6, QBPS has a performance close to that of the homodyne receiver when the SNR

values are high, but as SNR decreases the EVM percentage difference between the QBPS and

homodyne increases. The QBPS has higher EVM value than homodyne system because of

the noise folding in both of the I and Q streams. The out-of-band noise does not affect the

homodyne system but it is clearly seen from Figure 7 that the output of QBPS heavily

effected by the noise folding.

Figure 6 EVM for Matlab models without BPF

Even though BPF is absent the noise does not affect the Homodyne receiver as much as

QBPS. Thus this architecture has lower EVM values than QBPS.

Figure 7 (Left) Scatterplot for QBPS receiver (Right) Scatterplot for homodyne receiver

However, for the second experiment which incorporates a BPF in the model, which

eliminates the out-of-band noise, QBPS performance shows significant improvements as

depicted in Figure 8. It can be concluded that an optimum BPF with sharp cut-off frequency

and good noise attenuation can improve the quality of QBPS receiver. Theoretically, reducing

the out-of-band noise using a good BPF does improve the performance of QBPS receiver.

From the theory it is known that both inphase and quadrature phase components are heavily

affected by noise folding in QBPS, whereas in homodyne the quadrature component isn’t

affected much as it is a BPSK.

As it can be observed from Figure 8, that IQ mixer performs much better when SNR values

are low, but both HT receiver and QBPS still suffer noise folding effect slightly even after

filtering. The effect of noise still persists in the quadrature component of the receiver and this

-5 0 5 10 15 20 250

20

40

60

80

100

120

140

160

180

SNR (dB)

EV

M (

%)

QBPS

Homodyne

Hilbert

is the reason the homodyne architecture performs slightly better than QBPS. Without a phase

error it is obvious that homodyne has better advantage than QBPS. Figure 9 shows the EVM

performance when a 5° of phase error is introduced to both of the homodyne and QBPS

receivers.

Figure 8 EVM vs SNR without a BPF

Figure 9 EVM vs SNR with 5° phase error

As it can be observed from Figure 9, when a 5° of phase error is introduced to both of the

homodyne and QBPS receivers, the EVM value increases in both of the systems. There is a

10% increase in the EVM value for a 5° of phase error for both QBPS and homodyne. The

main noticeable change is that both homodyne and QBPS EVM performance tend to move

closer to each other as the SNR increases. The gap between the QBPS and homodyne systems

is closer which shows that when the phase error increases the receivers behave quite

-5 0 5 10 15 20 250

20

40

60

80

100

120

140

160

180

SNR (dB)

EV

M (

%)

QBPS

Homodyne

Hilbert

-5 0 5 10 15 20 250

10

20

30

40

50

60

70

SNR (dB)

EV

M (

%)

QBPS

Homodyne

Hilbert

similarly. The advantage of QBPS receiver is that the delay error can be controlled making

the system more flexible for error rectification, also in case of phase error compensation,

image rejection filter can be used without any modifications as normal receiver. Thus, QBPS

architecture has several advantages over homodyne system. Further investigations on gain

imbalance and RF impairment will help in exploring ways to utilize QBPS for multiband

operation. QBPS has not only advantage over eliminating the analog components but can be

used with the same impairment mitigation methods designed for quadrature receivers.

6. FUTURE WORK

The purpose of this study is to understand how QBPS can be used for future low-complexity

GNSS receivers. To understand the operation of QBPS for processing multiband signals we

need to know how the ∆t needs to be varied so that it can provide a better signal acquisition.

The phase error indicates that if the design is made to downconvert multiband GPS L1 and

L2 signals, the choice of ∆t cannot have a specific value for L1 or L2 frequency. The problem

of image and phase imbalance can cause attenuation to either of the signal. This raises the

question of performance degradation on the corresponding band when downconverting

multiband signals. However, for a multiband operation, the influence of ∆t on different bands

can be calculated and appropriate correction mechanisms can be put in place to deal with

them. However, time varying errors in ∆t will require an adaptive system that will estimate

these errors and compensate for them while the system is operating. We are currently

working on such adaptive approaches to enhance the performance of QBPS. Furthermore,

future work is needed to utilize the full potential of QBPS to downconvert and digitize more

than one band simultaneously.

8. CONCLUDING REMARKS

The paper has investigated the performance analysis of QBPS RF front-end architecture on

SDR. To have an efficient and flexible RF front-end the major sources of error were

investigated and experiments were carried out to come to a conclusion that QBPS will

perform equally well as the traditional homodyne receiver but with the benefit of reduced

analog components count as the mixers and filters are eliminated. Furthermore, QBPS

introduces more flexibility to the RF front-end. From the simulation case studies, it is

observed that a good BPF will make the QBPS receiver performance quite similar to that of

the homodyne receiver. To have a flexible and simple digital RF front-end for GNSS

receivers, QBPS will be more appropriate choice for a SDR. QBPS will provide more

flexibility and control to the front-end for processing not only single band but also multiband

for future system.

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