Frequency Modulated Continuous Wave Radar System at ISM Band for Short Range Indoor Positioning

Frequency modulated continuous wave (FMCW) radar is a technique for obtaining range information from a radar by frequency modulating a continuous signal. The frequency range of FMCW radar varies from 900 MHz to 80 GHz, and one of the applications is human positioning for indoor healthcare scenarios and intelligent housing system. FMCW radar system is becoming more portable, more precise and cheaper. In this thesis, a FMCW radar system at 2.4 GHz ISM band is proposed for intelligent housing system. The thesis proposes an economic and efficient DDS-based PLL frequency synthesizer. It can generate a frequency modulated continuous wave from 2.4 GHz to 2.5 GHz in 1 ms. The thesis uses the ADF4158 phase locked loop (PLL) chip to implement triangle frequency modulation in order to generate the 2.4 GHz continuous wave signal, and in this frequency synthesizer system, a direct digital synthesizer (DDS) chip is used, as the reference frequency of PLL, to analyze crystalbased PLL and DDS based PLL. The PLL frequency synthesizer shows high accuracy and low phase noise, and it is easy to be controlled by PC. The FMCW radar system adopts a homodyne transceiver architecture. The thesis shows effective design of each part of the homodyne receiver, including amplifiers, filters and a mixer. The whole transceiver shows the performance in position estimation and tracking objects within 10 meters with less than 2% error.


Introduction
The word "radar" is an acronym derived from the phrase RAdio Detection And Ranging and it is applied for detecting and tracking objects at certain distances. The basic principle of radar is simple -signals traveling at the speed of light are transmitted, reflected off a target and then returned as an echo.

Research Background
The history of radar dated back to experiments by Heinrich Hertz in 1886 that showed that radio waves were reflected by metallic objects, and in 1900 Tesla described a concept for electromagnetic detection and velocity measurement in an interview, [1].
In 1903 and 1904 , the German engineer Hülsmeyer experimented with ship detection by radio wave reflection, an idea advocated again by Marconi in 1922. In that same year, Taylor and Young of the U.S. Naval Research Laboratory (NRL) demonstrated ship detection by radar and in 1930 Hyland, also of NRL, first detected aircraft (albeit accidentally) by radar, setting off a more substantial investigation that led to a U.S. patent for what would now be called a continuous wave (CW) radar in 1934.
Early radar development was driven by military necessity, including surveillance, navigation, and weapons guidance for ground, sea, air, and space vehicles. And now, radar enjoys an increasing range of applications, [2]. One of the most common is the police traffic radar used for enforcing speed limits. Another is the "weather radar" familiar to every viewer of local television news. Another radar application is found in the air traffic control systems used to guide commercial aircraft. Finally, satellite and airborne radar is an important tool in mapping earth topology and environmental characteristics such as water and ice conditions, forestry conditions, land usage. While this sketch of radar applications is far from exhaustive, it does indicate the breadth of applications of this remarkable technology.
Radar can be classified as primary radar and secondary radar, which is shown in figure 1.1: a primary radar transmits signals with high frequency toward the targets. The transmitted signals are reflected by the target and then received by the same radar. And secondary radar works with active answer signals. is also received and processed continuously. The transmitted signal of unmodulated radar is constant in amplitude and frequency. Transmitting unmodulated power of CW radar can only measure the speed using the Doppler effect, but it cannot measure a range and cannot differ between two reflecting objects. This is achieved in modulated CW radars using the frequency shifting method. In this method, a signal changing in frequency constantly around a fixed reference is used to detect objects. Pulsed radar transmits high power, high-frequency pulses toward the target, then it waits for the echo of the transmitted signal before it transmits a new pulse.
Each method has its advantages over the other. The advantages of pulsed radar include increased range, lower power consumption, and it does not rely on the Doppler Effect to determine movement. Continuous wave radar benefits include a continuous updating of target, higher resolution, and doesn't have the minimum target distance.

Research Status of FMCW radar
As the name suggests, frequency modulated continuous wave (FMCW) radar is a technique for obtaining range information from a radar by frequency modulating a continuous signal. The technique has a very long history, but in the past its use has been limited to certain applications, such as radio altimeters. However, there is now renewed interest in the technique for three main reasons, [3]. First, the most general advantage possessed by FMCW radar is that the modulation is readily compatible with a wide variety of solid-state transmitters. Second, the frequency measurement which must be performed to obtain range measurement from such a system can now be performed digitally, for example, using a processor based on the fast Fourier transform (FFT).
Benefits of FMCW over other modulated CW waveforms are: 1) the ability to control the range and to obtain very efficient use of the spectrum; 2) the ease with which the range resolution can be changed, and the way in which very high range resolutions can be obtained without requiring wide IF and video bandwidths.
During the second world war, FMCW radar was used for bomb aiming radars and in 1946 an FMCW surveillance radar was built. This obtained its modulation by "pushing" a magnetron. It did not work very well, and the reason for building it is unclear.
Bamck [4] first discussed the application of moving target indication (MTI) type processing to FMCW radar. In the meantime, Fuller may have been the first to apply FMCW to automotive radar, but in this case the modulation was almost a "side effect" of the use of frequency scanning to scan the beam.
A major step forward was made in the mid 1970's when digital signal processing became available to perform the signal processing to extract the range information from the received signals. Before digital processing became available, many earlier FMCW radars, such as those discussed above, used single band-pass filters to detect signals at a single range, and varied the sweep rate systematically to search all the possible range gates, [5]. This makes very inefficient use of the radar's observation times. On the other hand, FMCW radio altimeters have long used a closed-loop system to adjust the sweep period to keep the beat frequency from the ground within a single range bin. Since only a single range-gate is required, this approach achieves efficient use of the energy without needing to process many range gates. Modern radio altimeters, however, do also use digital (FFT-based) processing as well as this technique. It is now commonplace to use a FFT, or other digital frequency analysis techniques, to analyze the mixture of beat frequencies corresponding to the targets at different ranges.
In 1998, McClanahan and other researchers in United States developed a ranging system based on pulsed radars, of which the center frequency was 3.2 GHz, the error of test data was less than 10%. In 1999, Li developed a FMCW radar obtaining range and angle information of obstacles. Its working frequency was 77 GHz, transmitting signal linearity was better than 0.5%, maximum range was 100 m, range resolution was less than 1m. It had a wide application for vehicle collision avoidance system because of the simple structure.
In 1999, William H. Haydl developed a FMCW radar integrated on a 0.88 2 mm single chip. Its working frequency is 94 GHz, DC input power is 0.7 W, RF power is 10 mW. The receiver had 6 dB noise figure and 10 dB gain. The whole front end included VCO, PA, LNA, mixer and coupler. In 2003, Musch used N-fractional PLL to develop a FMCW radar. The system has high linearity and measurement error was about 0.8 mm, [6].
In 2016, Gitae Pyo [7] and his team developed a CMOS transceiver IC for a singleantenna FMCW radar at K band. The transceiver achieved the output power of −1.6 dBm, phase noise of −105 dBc/Hz at 1 MHz offset, receiver gain of 15.3 dB, and the noise figure of 11.6 dB. including a 1.7 mm × 0.9 mm pad.
Nowadays, FMCW radar is widely used in various fields from civil to military applications. It can be used for imaging purposes. Automotive FMCW radar can be used to record velocity violations on roads. It can also be used as driver intelligence systems to improve driving conditions and avoid collisions. It can be also employed for ship navigation and identification. FMCW radars can also be used target detection under the ground clutter environment, [8]. Some authors presented FMCW radars for geosciences to measure wind speed and directions.
On the other hand, it is frequently used for indoor human tracking for indoor healthcare scenarios, such as fall detection of elderly people or breath detection, and intelligent housing system. FMCW radar for indoor human tracking is becoming more portable, more precise and cheaper. In this work, a FMCW radar system at 2.4 GHz is proposed for intelligent housing systems.

Research Status of PLL Frequency Synthesizer
The phase locked loop is a control system that can generate an output signal whose phase is related to the phase of an input signal. While there are several differing types, it is easy to initially visualize as an electronic circuit consisting of a variable frequency oscillator and a phase detector. The oscillator generates a periodic signal, and the phase detector compares the phase of that signal with the phase of the reference signal, adjusting the oscillator to keep the phases matched, [9]. Bringing the output signal back toward the input signal for comparison is called a feedback loop since the output is "fed back" toward the input forming a loop.
PLLs date back to the 1920s, but their popularity and applications took off with the introduction of the monolithic PLL, [10]. The 4046 CMOS Micropower PLL, which RCA introduced in the 1970s, is one of the early PLL ICs. These ICs found use in many applications, including frequency synthesis, FM demodulation and modulation, voltage-to-frequency conversion, and data synchronization. The 4046 integrated two types of phase detectors-a linear mixer and an edge-triggered phase/frequency detector-with a VCO (voltage-controlled oscillator) and an output buffer that allowed designers to use the tuning voltage for demodulation applications.
The most common type of PLL for SOC (system-on-chip) applications is the frequency-multiplying PLL. This type of PLL generates a high-frequency clock from a low-frequency crystal or another reference. Applications for frequency-multiplying PLL are widespread and include logic clocking and RF local-oscillator synthesis.

Thesis Outline
This thesis proposes a FMCW radar at ISM band for indoor human positioning and tracking, including research about DDS-based PLL frequency synthesizer and homodyne receiver architecture. The content of this thesis is organized as follows: In Chapter 2, the thesis presents the working principle and equations of FMCW radar, and parameters of the indoor FMCW radar, including range and velocity information, are given. Then in Microwave Office, the whole radar system is simulated.
In Chapter 3, the thesis designs the frequency synthesizer for the FMCW radar.
The PLL frequency synthesizer is based on a DDS board. In this chapter, the thesis discusses the working principle of DDS and PLL, and gives the measurement and analysis of power spectrum and phase noise of the DDS-based PLL board.
In Chapter 4, the thesis discusses the design of FMCW radar transmitter and homodyne receiver. Test and analysis of each component is given. And the thesis does test and analysis of the whole FMCW radar system. It shows that the whole transceiver has a good performance to position and track objects in 10 meter with 2% error.

FMCW Radar Theory
In the past decade, portable radar systems have experienced tremendous growth.
Such rapid growth has created demand for portable wireless devices that are smaller, lighter, cheaper and of higher performance than ever, and this drives IC designers and engineers to innovate new system architectures and circuit topologies. In this work, we choose frequency modulated continuous wave (FMCW) radar to implement indoor positioning. FMCW radar, it is a type of radar system where a stable frequency continuous-wave radio energy is transmitted and then received from reflecting objects. This work adopts a homodyne architecture in FMCW radar receiver.

Working Principle of FMCW radar
As described above, FMCW radar is a special type of radar sensor which radiates continuous transmission power like a simple continuous wave radar. In contrast to normal CW radar, FMCW radar can change its operating frequency during the measurement: that is, the transmission signal is modulated in frequency (or in phase).
Simple continuous wave radar devices without frequency modulation have the disadvantages [11] that they cannot determine target range because they lack the timing mark necessary to allow the system to time accurately the transmit and receive cycle and to convert this into range. Such a time reference for measuring the distances of stationary objects, but can be generated using frequency modulation of the transmitted signal. In this method, a signal is transmitted, which increases or decreases in the frequency periodically. When an echo signal is received, that change of frequency gets a delay Δt similar to the pulse radar technique. In pulse radar, however, the runtime must be measured directly. For a FMCW radar, the distance measurement is accomplished by comparing the frequency of the received signal to a reference, which is usually the transmission signal. And the duration of the transmission signal is substantially greater than the required receiving time for the installed distance measuring range.
There are several modulation patterns used for different measurement purposes: sawtooth modulation, triangular modulation, square-wave modulation (simple frequency-shift keying, FSK) and stepped modulation (staircase voltage). Sawtooth modulation is used in a large range combined with a negligible influence of Doppler frequency. And for square-wave modulation, it is used for a very precise distance measurement at close range by phase comparison of the two echo signal frequencies.
But the disadvantage is that the echo signals from several targets cannot be separated from each other, and that this process enables only a small unambiguous measuring range. In this thesis, triangular modulation is issued, the carrier signal of the radar is frequency-modulated by triangular waves. The radar transmits and receives signals with a frequency deviation, as shown in figure 2.1. The frequency difference is proportional to the time difference between the transmitted and received signals, which in turn is proportional to the distance between the transmitter and target.
Assuming that the transmitter frequency increases linearly with time and that there is a reflecting object at a distance, the time varing amplitude, frequency and phase is shown below: is the signal amplitude, is the carrier frequency, is the initial phase.
is the sweep rate in Hz. An echo signal will return after the transit time Δt, and the phase of the received signal can be expressed as: The beat frequency component can be written as: where D U is the amplitude of the beat note signal. If there is no Doppler frequency shift, the beat frequency is a measure of the target's range: According to triangle relationship: From equation (2.6) and (2.7), the distance from target can be expressed as: of which the instantaneous phase is Thus, the instantaneous phase of echo signal can be expressed as: (2.14) , the beat frequency is obtained: Since T is much greater than  : As long as we can get the value of two beat frequency , we can get the value of distance and velocity: The frequency range of ISM band is from 2.4 GHz to 2.5 GHz, the maximum bandwidth B is 100 MHz. Since this FMCW radar is used inside building, the detectable distance doesn't need to be very large. In this work, we assume max R is 30 m, it's easy to get delay time for maximum range: The modulation period should be larger than the delay time for the maximum range.
According to papers [31]- [36], most modulation periods of FMCW radar at 2.4 GHz are from 1ms to 10ms. In this thesis, we use ADF4158 PLL synthesizer as frequency source. In ADF4158 chip, the minimum modulation period for 2.4-2.5 GHz is 0.8 ms [14]. In this system, we set the modulation period as 1 ms. According to equation (2.8), the maximum beat frequency can be determined by: According to formula for distance, we can get the formula for velocity resolution ideally as follows, where r f  is frequency resolution of receiver, which depends on the frequency resolution of spectrum analyzer or FFT sampling frequency.
For FFT, the spectrum computed from the sampled signal has a frequency resolution r f  . Calculate the frequency resolution with the following equation: where s T is the acquistion time, N is the number of samples and s f is the sampling frequency. Thus, frequency resolution depends on how long the acquistion time is. And it is necessary to consider the acquistion time becasue we need to calculate distance information before the object moving. We do 25 times FFT and hope the total acquistion time should be less than 0.5s, then frequency resolution should be larger than 50 Hz.
According to equation (2.22), the velocity resolution is larger than 3 m/s, it can be seen that FMCW radar is not a good method to measure human indoor walking velocity because of such high velocity resolution.

Radar Transceiver Architecture
There are three common receiver architectures: heterodyne, homodyne and imagereject, all of which have different advantages and disadvantages. When designing a RF receiver, the choice of architecture is primarily determined by criteria including complexity, cost, power dissipation and the number of external components.
In a homodyne or direct conversion receiver, the incoming RF signal is downconverted to baseband (zero frequency) in one step by mixing with an oscillator output of the same frequency. The output baseband signal is then filtered with a low-pass filter to select the desired channel. This is illustrated in the block diagram in figure 2.3.
Using a homodyne receiver architecture, the difference frequency between the transmitted signal and received signal can be easily obtained if the frequency swept transmit signal is used for the LO down conversion. Consequently, this architecture is the preferred solution. The main advantage of a homodyne receiver [18] is that it solves the image problem because the input RF signal is down-converted directly to baseband without any IF stage. For the image problem, the homodyne receiver shown in figure 2.4 operates with double-sided signals, which overlap the positive and negative parts of the input spectrum. Consequently, the image frequency problem is circumvented because = 0. As a result, no image filter is required.

Figure 2.4 Simple homodyne receiver working principle
Another advantage is that it is easy to implement. Since it does not require any high frequency band-pass filters, which are usually implemented off-chip in a superheterodyne receiver for appropriate selectivity, the homodyne requires less number of external components. However, the homodyne architecture does suffer DC offsets. Also, since the mixer output is a baseband signal, it can easily be corrupted by the large flicker noise of the mixer, especially when the incoming RF signal is weak.
LO leakage can result in DC offset, when the isolation between the LO port and the inputs of the mixer and the LNA is not infinite. The leakage signal appearing at the inputs of the LNA and mixer is mixed with the LO signal, which provide a DC component at the output of the mixer. This phenomenon is called self-mixing. Another phenomenon arises if a large interferer leaks from the LNA or mixer input to the LO ports and is multiplied by itself. The principle is similar with self-mixing. And it is exacerbated if self-mixing varies with time.
Even-order nonlinearity is also a problem in homodyne down conversion systems.
[19] Two strong interferers will generate a low-frequency beat. Because mixers exhibit a finite isolation from the RF input to the IF output due to asymmetry in the mixing core, the low-frequency beat will appear in the IF port. Besides, the mixer RF port may also suffer from even-order distortion, requiring special attention in the design.
Next, some basic parameters of FMCW radar system are shown below: (1) Working Frequency: The working frequency of a transmitter and a receiver includes center frequency and bandwidth. In this thesis, the FMCW radar uses industrial, scientific and medical (ISM) radio bands, which is reserved internationally for the use of radio frequency (RF) energy for industrial, scientific and medical purposes other than telecommunications. The working frequency is from 2.4 GHz to 2.5 GHz, so the center frequency is 2.45 GHz and bandwidth is 100 MHz.
(4) Receiver Sensitivity: Sensitivity in a receiver is normally taken as the minimum input signal required to produce a specified output signal having a specified SNR and is defined as the minimum signal-to-noise ratio times the mean noise power. For a signal impinging on the antenna, sensitivity is known as minimum operational sensitivity (MOS): where k is Boltzmann's constant, o T is effective noise temperature of the receiver input and G is system gain.
According to equation (

Summary
After talking about the history and development of FMCW radar in chapter 1. In  [20] In this thesis, we use a DDS-based PLL synthesizer as frequency source of FMCW radar transceiver. It offers very many advantages, including high levels of stability and accuracy. It is also easy to be controlled from digital circuitry such as microprocessors.

Working Principle of Direct Digital Synthesizer
As the name suggests this form of synthesis generates the waveform directly using digital techniques. This is different from the more familiar indirect synthesizers that use a phase locked loop as the basis of their operation.
A direct digital synthesizer operates by storing the points of a waveform in digital format, and then recalling them to generate the waveform. The rate at which the synthesizer completes one waveform then governs the frequency. The overall block diagram is shown below, but before looking at the detailed operation of the synthesizer it is necessary to look at the basic concept behind the system.
The operation can be envisaged more easily by looking at the way that phase progresses over the course of one cycle of the waveform, [21]. This can be envisaged as the phase progressing around a circle. As the phase advances around the circle, this corresponds to advances in the waveform. As the phase advances around the circle this corresponds to advances in the waveform, i.e. the greater the number corresponding to the phase, the greater the point is along the waveform. By successively advancing the number corresponding to the phase it is possible to move further along the waveform cycle.
The digital number representing the phase is held in the phase accumulator. The number held here corresponds to the phase of the FM signal and is increased at regular intervals, [21]. In this way, it can be seen that the phase accumulator is basically a form of counter. When it is clocked, it adds a preset number to the one already held. When it fills up, it resets and starts counting from zero again. In other words, this corresponds to reaching one complete circle on the phase diagram and restarting again. Once the phase has been determined it is necessary to convert this into a digital representation of the waveform. This is accomplished using a waveform map. This is a memory which stores a number corresponding to the voltage required for each value of phase on the waveform. In the case of a synthesizer of this nature it is a sine look up table as a sine wave is required. In most cases the memory is either a read only memory (ROM) or programmable read only memory (PROM), [22]. This contains a vast number of points on the waveform, very many more than are accessed each cycle.
The next stage in the process is to convert the digital numbers coming from the sine look up table into an analogue voltage. This is achieved using a digital to analogue converter (DAC). This signal is filtered to remove any unwanted signals and amplified to give the required level as necessary.
Tuning is accomplished by increasing or decreasing the size of the step or phase increment between sample points. A larger increment at each update to the phase accumulator will mean that the phase reaches the full cycle value faster and the frequency is correspondingly high. Smaller increments to the phase accumulator value means that it takes longer to increase the full cycle value and a correspondingly low value of frequency. In this way, it is possible to control the frequency. It can also be seen that frequency changes can be made instantly by simply changing the increment value. There is no need to a settling time as in the case of phase locked loop based synthesizer.
These synthesizers do have some disadvantages, [23].  Higher order harmonics also fall within the Nyquist bandwidth.
Another source of spurs [25] is switching transients that arise within the internal

Phase-locked Loop Frequency Synthesizer
A Phase Locked Loop (PLL) is a fundamental part of radio, wireless and telecommunication technology. It is a simple negative feedback architecture that allows economic multiplication of crystal frequencies by large variable numbers. By studying the loop components and their reaction to various noise sources, we will show that PLL is uniquely suited for generation of stable, low noise tunable RF signals for radio, timing and wireless applications.

Working Principle of PLL Synthesizer
The phase locked loop is a closed- The basic method of an integer-N phase-locked frequency synthesis is: the phase locked loop locks a high stable reference oscillator, and a programmable divider is in the loop. We change the divider ratio by programming to get stable output frequency which is N times the reference frequency.  Fractional PLL technology has made it possible to alter the relationship between N, r F , and the channel spacing of the synthesizer. [28] It is now possible to achieve frequency resolution that is a fractional portion of the phase detector frequency. This is accomplished by adding internal circuitry that enables the value of N to change dynamically during the locked state. If the value of the divider is "switched" between N and N+1 in the correct proportion, an average division ratio can be realized that is N plus some arbitrary fraction, K/F. This allows the phase detectors to run at a frequency that is higher than the synthesizer channel spacing.
where, F = the fractional modulus of the circuit, K = the fractional channel of operation.

Phase Noise Analysis
Phase noise of PLL is a random process. Although we can use simulation software such as ADIsimPLL for analysis, we need to begin with the linearized PLL model, which is shown in figure 3.8 [29] : We take the reference crystal oscillator as an example to derive the transfer function of each noise source: assume ( ) is phase noise generated by reference crystal oscillator and ignore the input of other noise sources: According to the equations of forward gain and reverse gain, the transfer function of reference crystal oscillator can be written as:   MHz, the multiplication ratio is 10,000 and the corruption in phase noise will be 80 dB.
When divided down by a digital divider, the divider improves jitter by N times or ) ( log 20 10 N in noise power.
In this thesis, we choose ADF4158 PLL chip, it is fractional-N PLL frequency synthesizer, of which RF bandwidth is up to 6.1 GHz, and it contains a 25-bit fixed modulus allowing subhertz resolution at 2.4 GHz.    Compared to TCXO, a major advantage of a DDS system is that its output frequency and phase can be precisely and rapidly manipulated under digital processor control. so that we can choose a high PFD frequency with good power spectrum for PLL. can be written as:

DDS-based PLL Synthesizer
We can find that with the increase of N, loop bandwidth decreases.    are correlated and as a result, the phase noise will partially cancels out due to range correlation effects as shown in [24]. So in chapter 4, the thesis will focus on how receiver system noise and gain influence the performance of the radar transceiver.

Summary
The comparative discussion consists of PLL, DDS and DDS-based PLL. We discuss the working principle of DDS and PLL, and a DDS-driven PLL frequency synthesizer architecture is given in this chapter. We also talk about some main parameters for frequency synthesizer, particularly phase noise and spurs.

FMCW Radar System Design and Test
In this thesis, we use a homodyne receiver with one output signal. After being amplified by a power amplifier, the transmitting signal is received by the homodyne receiver: incoming RF signal is down-converted to baseband (zero frequency) in one step by mixing with an oscillator output of the same frequency. The resulting baseband signal is then filtered with a low-pass filter to select the desired channel. To improve the input and output matching of LNA, we add two isolators in the receiver. This is

LNA design and test
In this thesis, we describe how to design a microwave LNA at 2.

Filter design and test
The low pass filter only allows low frequency signals from 0 Hz to its cut-off frequency to pass while blocking those any higher. In this thesis, we design a maximally flat low-pass filter with a cutoff frequency of 40 kHz, impedance of 50 Ohm, and at least 10 dB insertion loss at 50 kHz and 40 dB insertion loss at 100 kHz.
The high pass filter only allows high frequency signals from its cut-off frequency, while blocking those any lower. And the band pass filter allows signals falling within a certain frequency band setup between two points to pass through while blocking both the lower and higher frequencies either side of this frequency band, [25]. The parallel coupled transmission lines are used to construct band-pass filter, whose the passband is

Mixer Test
A mixer is a three-port device that uses a nonlinear or time-varying element to achieve frequency conversion. An ideal mixer produces an output consisting of the sum and difference frequencies of its two input signals. Operation of practical RF and microwave mixers is usually based on the nonlinearity provided by either a diode or a transistor. In this thesis, we need a frequency down-conversion mixer in the radar receiver, the desired IF output in a receiver is the difference frequency, which can be easily selected by low-pass filtering: This work adopts a double-balanced mixer, which uses two hybrid junctions or transformers, and provides good isolation between all three ports, as well as rejection of all even harmonics of the RF and LO signals. [30] This leads to very good conversion loss, but less than ideal input matching at the RF port. The double-balanced mixer also provides a higher third-order intercept point than either a single-ended mixer or a balanced mixer.
An important figure of merit for a mixer is therefore the conversion loss, which is defined as the ratio of available RF input power to the available IF output power, expressed in dB: In this thesis, we use LTC5548 microwave double balanced passive mixer, its main parameters are shown in table 4.1:

Antenna Test
In this radar system, we adopt two monopole antennas as transmitting and receiving antennas. Main parameters of the antennas are shown in Return loss (dB) <-6 <-6 <-6

Radar Components Summary
In this chapter, we designed each component of the homodyne radar receiver, including low-noise amplifier, band-pass filter, low-pass filter, mixer and power amplifier, the summary is shown in

Figure 4.7 Radar test in the aisle in Thornton Hal
The radar receiver is tested in the aisle in Thornton Hall, and the attenuation and reflection of wall and electrical devices will affect the results, particularly when the transmitting signal is weak.
In this test, we use a power spectrum analyzer Agilent E4440A to measurement.
The measurement range is from -5-40 kHz and there are 600 samples in this range. (1) Receiver mismatch: The input and output return loss of LNA is not very good, which means that signal may bounce between LNA and BPF. Such oscillation means there will be more than one RF frequency for the mixer RF input, and finally results in inter-modulation of the mixer. Besides, the receiver may suffer even-order distortion.
When there are two strong frequencies 1  and 2  at the input of LNA, it will generate a low-frequency beat 2 1    . Since the isolation is finite from the RF input to the IF output, such low-frequency beat will appear in the IF port.
When the LNA is removed, we can find that spurs still exist but are decreased significantly. Besides, when we use lossless cables to replace antennas and objects, the power of spurs increases. If we add an attenuator at the input of BPF, the spurs power decreases. Thus, it can be proved that the radar receiver generates spurs. To solve this problem, we add two isolators at the input and output of LNA. The comparison between IF frequency without isolators and IF frequency with isolators is shown in figure 4.8.
The red curve is power spectrum after adding isolators, we can find that the quality of spectrum improves because of isolators. Besides, we also need to consider LO phase noise, [37]. The noise source of LO and RF signals are correlated and as a result, the phase noise partially cancels out due to range correlation effects. (3) Reflection: the reflection from the environment can also generate spurs. The radar system is tested in an empty aisle for weak reflection. But multireflection still generates spurs, particularly when the object is close to radar system. Multireflection can generate more than one RF signal and result in mixer inter modulation: when more than one RF signals, and , go into mixer RF port, spurs ] ) [( will be generated periodically.  recorded after the result is stable. After that, we use cables with the same distance to measure it again, the IF spectrum in the "pure environment" is recorded again. The two data can be compared to check the accuracy of the radar. All data can be checked in appendix. After range is larger than 10 m, the effective IF signal is inundated in spurs and noise. After calculation, we can find that there is difference between calculation and real range information. With the increase of range, such error increases and positioning accuracy decreases.

Analysis and Future Work
It's necessary for us to discuss about ideal maximum detection range: the radar range equation represents the physical dependences of the transmit power, that is the wave propagation up to the receiving of the echo-signals.   T  T  T  T  P   P  T   T  T   T  T   B  T  T  k   B  T  T  The input attenuator also affects the location of a true input signal on the display.
Signals present at the analyzer input remain stationary on the display as we change the input attenuator, while the displayed noise moves up and down. Thus, we get the best sensitivity by selecting minimum input attenuation.
The video filter can be used to reduce the amplitude fluctuations of noisy signals while at the same time having no effect on constant signals. It should be noted that the video filter does not affect the average noise level and so does not, by this definition, affect the sensitivity of an analyzer. In the measurement, the maximum range is 10 m. The difference between calculation and measurement is resulted by assumed noise temperature and spectrum analyzer. Large RBW will increase the noise floor of the spectrum analyzer. Table 4.4 makes a summary of some problems and components which affect maximum detection range. Since we cannot get the precise value of ideal maximum detectable range, it is still necessary to analyze these parameters.

Receiver Noise
It includes noise from antenna, devices in receiver and spectrum analyzer.
Decrease noise in receiver in future work, including loss of filters and noise of LNA.

Gain
In this radar system, receiver gain is 9.2 dB Increase receiver gain in future work, including gain of LNA and antenna efficiency.

Transmitter LO Leakage
It results from finite isolation between RF and LO ports of the mixer.
In this radar receiver, isolation of the mixer is good.

LO Phase Noise
Phase noise from LO may affect weak RF signals.
The phase noise of LO and RF signals are correlated and the phase noise partially cancels out. This paper proposes a FMCW radar system at 2.4 GHz for intelligent housing system. In the part of frequency source, the thesis uses ADF4158 PLL chip to generate the 2.4 GHz continuous wave signal. It is the only PLL chip which can implement triangle frequency modulation at 2.4 GHz band from ADI. And in the thesis, a DDS chip is used as the reference frequency of PLL. Such DDS-based PLL frequency synthesizer provides an economic and efficient method to generate frequency modulated continuous wave at ISM band in small period with high linearity. Although the thesis has some discussion about phase noise and spurs, we still need do more research on decreasing phase noise and spurs. Table 4.5 shows some problems and components which affect maximum detection range. [2] This noise figure only includes NF of receiver, doesn't include NF of power spectrum analyzer.
The comparison between the FMCW radar in this thesis and radars in other papers in shown in table 4.4. From the comparison, it can be seen that our advantages are economic and portable frequency source, and detection range is far enough for indoor position. Although we choose 2.4 GHz ISM band for less loss in FR4 PCB, we need higher frequency has less interference, for example, bluetooth and WiFi. Paper [31] adopts 65 nm CMOS technology and the transmitter and receiver To implement human tracking and positioning for intelligent housing system, the FMCW radar system needs to have three abilities: 1) the ability to determine whether people comes in or goes out; 2) the ability of positioning and tracking; 3) the ability of velocity detection.
When the object moves, the power spectrum analyzer shows a fluctuation, which proves that the radar system can detect the movement of objects. According to the test shown above, the system shows the ability to detect the distance between radar and the object. As discussed in chapter 2, the velocity resolution depends on resolution bandwidth of spectrum and FMCW radar is not the best choice for velocity detection.
In conclusion, we need to make some improvements in future: 1) Improvements in device performance: I need to increase performance of LNA and BPF, decrease the noise of LNA and use material with less loss to replace FR-4. And we need to use antennas with high gain. We also need a new design of LNA for better input and output return loss.
2) Improvements in receiver architecture: I need to build a homodyne receiver with two orthogonal I/Q signals in order to make the results more precise.
3) Research on indoor position algorithms: Since FMCW radar can only get the distance information between radar and object, we need range-based indoor position algorithms for human positioning, for example, triangulation method.
Besides, the IF signal is small because the distance between radar and object is small. Thus, the power at 0 Hz caused by DC will influence our observation and calculation. As it has been discussed in section 2.1, FMCW radar can detect velocity information. But the Doppler frequency shift for human walking is too small, which means that it's hard to distinguish and from power spectrum. In order to get better range and velocity information, we can use two radars with different frequency range, which is shown in figure 4.11: