RADAR Chirp Configuration

One of the key aspects of RADAR based application design is configuration of chirp parameters? . Before ?diving deep into ?this topic let’s take ?a quick look at ?the chip which is as shown in picture below .

?A chirp is a signal in which the frequency increases (up-chirp) or decreases (down-chirp) ?with time , in the time domain it looks like the one below

Chirp in frequency domain looks like the one shown below

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It is characterized using following key parameters

1.?????? Chirp Start Frequency ?- Base Parameter

2.?????? Chirp End Frequency- Base Parameter

3.?????? Chirp Bandwidth – Derived Parameter ?- B

4.?????? Chirp Duration - ?Base Parameter

5.?????? Chirp Slope? - Derived Parameter ?- S

?Some of the key points to consider with respect to basic parameters of chirp are as follows

The Range Resolution (dres) depends only on the Bandwidth swept by the chirp ???????? = c / 2*B , where c is the velocity of light and B is the bandwidth

From this formula we can easily formulate below table for range resolution for various bandwidths

Before we proceed further with ?further ?details on configuration of chirp parameters ?let’s have a look at ?reflected chirp ?processing ?at ?RADAR ?as shown in picture below

It is characterized using following key parameters :

1.?????? Idle Time : The time between two consecutive transmit chirps which is nothing but ?transmitter off ?time ( cooling period) ?+ transmitter start time – Base Parameter

2.?????? ADC start time : The time it takes for ADC to start sampling the beat frequency ( IF) – Base Parameter

3.?????? Ramp End Time : Which is a summation of ADC start time and ADC sampling time – Base Parameter

4.?????? Chirp Cycle Time : Total time of chirp including idle time

Parameter Setting Guidelines : ?In order to understand how to optimally set the parameters like ?idle time , ?ramp end time ?etc. let’s first understand how it affects the maximum velocity through another derived parameter named chirp repetition time which is calculated using below formula

?Chirp Repetition period ?(CRP) = Number of Tx Antennas *( Idle time + Ramp end time)

The relation between maximum velocity and chirp repition time is provided using following formula

Vmax = c / (4*CRP*Carrier Frequency)

It is clearly evident from above formula that Maximum velocity reduces when the chirp Repetition period ?increases and that means maximum velocity is inversely proportional to both idle time as well as ramp end time . The lower the value of idle time and ramp end time the higher is maximum detectable velocity .

Another important point to be noted is for increasing maximum velocity we have to reduce number of Tx antenna , unfortunately ?this becomes a trade of between angle resolution and maximum velocity

Another constraint to note is Ramp End time must be more than ADC start time + chirp time for obvious reasons and hence there is a limit up to which it can be reduced .

The chirp time is defined as number of ADC samples / sampling rate of ADC and is responsible for determining the range resolution as B = Frequency Slope * chirp time.

To summarize lower values of ?Ramp End time will increase maximum detectable velocity but reduce range resolution and is a tradeoff between two

Another point to be noted is Vmax ?can be increased by reducing carrier frequency , carrier frequency is defined as carrier frequency = Start Frequency +( Frequency Slope * ADC Valid Start Time) + ( sweep bandwidth /2) ?, this means the lower the start frequency the higher is Vmax?

Unfortunately choosing lower start frequency slightly affects velocity resolution , but is not a big concern as it is very slight change

Once we configure the chirp parameters for desired value of maximum velocity we can then configure parameter for velocity resolution

Velocity Resolution is defined as Vres = maximum velocity / number of chirps per ?frame

The more the number of chirps in the frame , better will be velocity resolution , however point to be noted is if we increase number of chirps per frame , the RADAR cube memory requirement will increase also it will reduce the frame rate and hence this parameter has to be set to achieve optimal performance in terms of resolution ,frame rate and RADAR cube size

Following picture depicts reception of reflected signals from single object in front of RADAR

Tou represents round trip delay between object and RADAR

As it can be clearly seen from above picture , IF = S*2*d / c ( where d is the distance to object and S is slope of chirp)

Maximum value of IF (Intermediate frequency) depends upon the desired maximum distance and is governed by formula

fIF_max = S*2*dmax / c .?

IF signal is typically digitized (LPF+ADC) for further processing on a DSP. IF Bandwidth is thus limited by the ADC sampling rate (Fs). ?

Fs ≥ S*2*dmax/ c , this in turn? means? dmax = Fs c / 2S

For increasing maximum distance we need to increase the sampling frequency ?/ rate of ADC in Mega Samples / Sec . ?

Please make a note that it is inversely proportional to Slope of chirp , if we increase slope maximum range will decrease and vice versa . To summarise to increase the max range of RADAR either we have to increase the sampling frequency of RADAR or decrease the slope of chirp

As far as ADC mode ?goes it shall be set as complex base band for higher maximum range . ?

One last point to note is chirp configuration do not affect angle resolution and max angle ( FOV) , stay tuned to read ?my next article on this topic

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