In this section, a description of how the parameters obtained for an OFDM radar wave- form directly influence the performance of the OFDM radar system [182], is given. This section covers concepts such as the radar’s bandwidth and resolution properties, from a practical point of view, in accordance with the requirements described at the beginning of this chapter.
5.3.1 Signal Bandwidth and Range
The total signal bandwidth plays a significant role in determining the number of subcar- riers N and the subcarrier spacing ∆f . Usually, when considering an implementation of an OFDM radar system [183], the bandwidth is a fixed parameter, since it is most likely limited by the performance of the analogue to digital converters. This is true for the cases where the OFDM signal is generated from a digital board and, obviously, not for the cases where the signal is generated from an expensive, big and hardly portable lab- oratory signal generator, which is out of the scope of the targeted low cost and compact radar applications of this thesis. As an example, the ADCs which have been used in the MIMO radar demonstrator presented in Chapter 4, have 14 bit conversion at up to 125 MSPS. Therefore, the achievable bandwidth, in this case, would fall in the range of 50 MHz. Therefore, this is the bandwidth that is considered, from now on, for the system concepts presented in this chapter, but also for the following chapters, where models, simulations and a complete 3D OFDM MIMO radar demonstrator, based on the digital board and ADCs of the radar in Chapter4, are shown.
Having said this, it is important to remember from Chapter2, that the achievable range resolution of a radar system depends purely on the total bandwidth occupied by the transmitted radar signal and it is expressed as ∆R = c0
2B, according to equation2.14.
Higher bandwidth means higher resolution (decreasing ∆r). For the previous mentioned example, considering a bandwidth of 50 MHz, the range resolution would translate to ∆R = 3 m.
5.3.2 Doppler Shift
The motion of an antenna positioned on an airborne radar produces Doppler shifts of incoming received waves over a multi-path channel, as well as moving targets do, for a
Chapter 5. OFDM Radars Concepts and Parametrization 147 static mounted radar. The Doppler effect, connected to the speed of the moving targets and the direction in which they are moving, is a critical factor in the parametrization of the OFDM radar’s waveform. As a matter of fact, it represents the starting point for the characterization of the other parameters. Before defining the number of subcar- riers and symbols in the OFDM frame, a consideration must be given on what is the maximum speed of the targets that need to be acquired. After a limit is set, defined as vmax, according to the equation previously defined in 5.8, the maximum associated
Doppler shift which is intended to be captured by the radar, is calculated and defined as fD. Considering the maximum relative velocity of 23 m/s or 83.8 km/h as per system
specification [56], the maximum capturable Doppler shift is calculated as fDmax =
2vmaxfC
c0
(5.10) For the considered system, therefore, it means that targets can be captured, in an environment where the Doppler shift value is maximum fDmax = 2.6 kHz.
5.3.3 Subcarrier Spacing and Number of Subcarriers
The subcarrier spacing must be kept at a level so that synchronization is achievable and the Doppler shift does not cause a significant disturbance to the orthogonality between the subcarrier. According to [184], a good OFDM system design rule, that ensures orthogonality, is to assume a spacing 10 times larger than the previously defined max- imum Doppler shift frequency, meaning ∆f >10fDmax. Which means that it must be
that ∆f >26 kHz. The exact value for the subcarrier spacing is decided upon considera- tions on the number of subcarriers, which should be the product of the smallest possible prime numbers, preferably an integer power of 2, to use the highly efficient FFT but- terfly algorithm. With the already fixed parameters, a number of subcarriers N = 1024 could be chosen. Therefore, the redefined minimum spacing that is tolerable due to the Doppler constraint and chosen for the system concept is ∆f = B/N , which translates to 48.8 kHz. The total OFDM period, being the inverse of the subcarriers spacing, is easily deducted and it’s Ts = 20.48 µs.
5.3.4 Radar Range Ambiguity
The maximum range at which a target can be located, so as to guarantee that the leading edge of the received backscatter from that target is received before transmission begins for the next symbol, is called maximum unambiguous range. Considering the OFDM symbol duration and periodic structure, it can be calculated, recalling from Chapter2, that the maximum unambiguous measurement distance is rumax = c0Ts/2 = 3.07 km.
5.3.5 Multipath Propagation and Maximum Detectable Range
Transmission over a multi-path channel causes the received signals to be affected by inter-symbol interference (ISI) which is a type of distortion caused when consecutive
Chapter 5. OFDM Radars Concepts and Parametrization 148 transmitted symbols interfere with each other at the receiver. ISI is only completely eliminated in OFDM by the use of a cyclic prefix. The duration of the CP must encom- pass the longest delay that is expected to be present in the channel [185]. The longest delay in the so called radar channel corresponds to the round trip radio path for the maximum range of interest, considering that there is a factor of 2 involved, since the signals travel twice the distance between radar device and scattering object.
Based on the maximum detectable distance that the OFDM radar is intended for, the 250 m of the detectable target as per requirements [56], in order to keep the symbols isolated, the CP has to satisfy the relation
TCP =
2dmax
c0
(5.11)
with dmax the maximum detectable distance. For the considered system concept, (5.11)
becomes TCP >1.66 µs. It is common practice in OFDM system to the choose TCP =
Ts/8 [184], which translate into TCP = 2.56 µs and so, dmax= 768 m.
5.3.6 Total OFDM Symbol Duration
Therefore, the total OFDM period is Tof dm = Ts+ TCP = 23.04 µs, according to the
equation previously anticipated in (5.3).
5.3.7 Doppler Resolution
The Doppler resolution is related to the total OFDM period and the number of symbols transmitted according to
∆vmax=
λ 2Tof dm
(5.12)
which, considering the OFDM period previously defined, and the carrier’s frequency of 17 GHz, translates to ∆vmax = 383 m/s. Additionally, considering the fact that the
Doppler can be both positive and negative, it is better expressed as ∆vmax = ±191, 5
m/s. Consequently, this corresponds to around ±689, 32 km/h which is more than the given requirements. Taking into account that twice the Doppler of the relative velocity occurs for a reflected wave, the Doppler resolution in terms of velocity resolution is dependent on the number evaluated symbols M , and amounts to
∆v = λ
2M Tof dm
(5.13) Therefore, by considering 512 symbols, a value of ∆v = 0.74 m/s is obtained. Theo- retically, an evaluation of an even greater number of OFDM symbols would result in a finer velocity resolution. However, this becomes in the long run impractical, as moving
Chapter 5. OFDM Radars Concepts and Parametrization 149
Table 5.1: Model Parameters Summary
Symbol Parameter Value
fc Carrier Frequency 17 GHz
N Number of subcarriers 1024
∆f Subcarrier spacing 48,82 kHz
T Elementary OFDM symbol duration 20,48 us TCP Cyclic prefix duration 2,56 us
TOF DM Transmit OFDM symbol duration 23,04 us
B Total signal bandwidth 50 MHz
∆r Range resolution 3 m
rmax Maximum unambiguous range 3072 m
vmax Maximum unambiguous velocity ± 191,48 m/s
M Number of evaluated symbols 512
∆v Velocity resolution 0,74 m/s
objects must remain within one range resolution cell during the evaluation. On the other hand, by evaluating over M = 512 symbol, with a total duration of 11.79 ms, an object traveling at the maximum unambiguous velocity would have travelled only 2,25 m, which is still within the resolution cell size of 3 m. Therefore, an appropriate performance for practical flying platform’s applications is guaranteed and 2,69 km/h is perfectly in line with requirements.
5.3.8 Summary
The OFDM system parameters of the previous subchapters and summarized in Table5.1, are an example set that fit the real-time OFDM radar system requirements [56]. It has to be noticed, that the above parameters are obtained considering, as a starting point, a bandwidth of 50 MHz, limited by the ADCs inside the digital board presented in Chapter
4. Obviously, it would be better if the ADCs could be upgraded to devices with higher MSPS, giving higher achievable bandwidths and so, increasing the range resolution of the radar. However, a trade-off would now arise concerning the cost efficiency of the OFDM radar system.