Small numbers of pulses - BEAM SHAPE LOSS

Antennas

5.8 BEAM SHAPE LOSS

5.8.3 Small numbers of pulses

Both the estimations for coherent and noncoherent integration use integrals that assume many pulses between the half- power points of the beam pattern. The estimations assume that the noncoherent integration gain is proportional to the square root of the number of pulses integrated and are valid down to about four integrated pulses. Further, the distributions of the sums of small numbers of noise samples are gamma distributions instead of Gaussian distributions.

For less than two pulses, the value will be greater than 1.23 dB for high detection probability.

Incoherent scan loss '

I

^1/2

&1/2

exp(&4ax²)dx

I

^1/2

&1/2

exp &2a x % "

exp &2a x & "

power ratio

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1 -0.5 0.5 1

Transmitted beam one-way

Received beam one-way Two-way transmit and receive

without movement Two-way transmit and receive

with movement of 0.2 beamwidth

Angle, beamwidths

Coherent scan loss '

I

^1/2

&1/2

exp(&2ax²)dx

I

^1/2

&1/2

exp &a x % "

exp &a x & "

2 power ratio

(5.103)

Figure 5.75 The effective one-way and two-way patterns when the antenna has rotated two tenths of a beamwidth between transmission and reception.

(5.104) 5.9 SCANNING LOSS

The beam shape loss does not account for the movement of the antenna between the moments of transmission and reception. Figure 5.75 shows a reference two-way Gaussian beam, the positions of the transmitting and reception beams each offset a tenth of a beamwidth from the center, and the resulting two-way pattern.

The resulting transmission and reception beam with movement gives an effective loss of gain. When the combined beam is integrated over a beamwidth, we obtain with incoherent integration

and for coherent integration

0 1 2 3 4 5 6

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Angle moved between transmission and reception, beamwidths Scanning

loss, dB

Noncoherent and coherent integration with Gaussian beams Sin x/x beam with

noncoherent integration Sin x/x

beam with coherent integration

Figure 5.76 Scanning loss when the antenna rotates between transmission and reception.

Figure 5.76 shows the scanning loss in decibels for from zero to half a beamwidth between transmission and reception.

Scanning loss, in practice, applies only to scanning antennas with narrow beams at long ranges. For example, if a surveillance radar rotates at six revolutions per minute and has a beamwidth of half a degree, then the angle between transmission and reception depends on range.

• Antenna rotation speed: 6 × 360/60 36 degrees/second 36/0.5 72 beamwidths/second

Each kilometer in range needs 6.67 µs for the pulse to travel out and the echo to return which gives an angle difference that increases with range.

• Converting to range: beamwidths/second 1 000/150 = 0.00048 beamwidths/km

The result is shown in Figure 5.77 which is an extreme case. Commonly, beamwidths of 1 degree to 1.5 degrees are used which reduce the scanning loss to an almost negligible value.

0 0.1 0.2

100 200 300 400

Range, km

Output signal to noise ratio ' n S_in k T B

A_rf A_rf

Figure 5.77 Two-way scanning loss for a surveillance radar with a beamwidth of 0.5 degrees rotating at 6 rpm.

(5.105) 5.10 THE EQUIVALENCE OF DIFFERENT SIGNAL COMBINING SYSTEMS

With a planar array with a radio frequency combiner (or beam former) or a parabolic reflector reflecting the signals into a horn there is a single output feeding the radio frequency amplifier. Neglecting the cosmic noise and antenna loss noise, the signal-to-noise ratio at the output of the radio frequency amplifier, gain A , fed by the radio frequency combiner, is_rf

where n is the number of antenna elements;

S is the signal power delivered by each element;_in k is Boltzmann’s constant;

T is the receiver noise temperature in K;

B is the receiver bandwidth.

There are a number of applications where it is a great advantage in having a radio frequency amplifier behind each antenna element:

• A number of receiving beams are to be formed by dividing the output of the amplifiers between a number of beam forming networks. Without the amplifiers there would be a loss.

• A complete transmitter-receiver is mounted behind each element or a group of elements in an active array.

The combination of the signals from each element or group of elements may take place at radio frequency or intermediate frequency using combining networks using phase shifters to steer the beam and attenuators to shape the beam. At baseband, polyphase combination must be used and digital techniques are mostly used to achieve this, called digital beam forming. These three types of combinations are shown in Figure 5.78.

Radio frequency beam forming

using a corporate

feed Antenna

elements

RF Amp.

IF Amp.

A to D conv.

Intermediate frequency (IF) beam forming

Local oscillator

(LO) Local

oscillator (LO)

Coherent oscillator (COHO) Radio

frequency

amplifiers Mixers Mixers Synchronous

detectors Digital beam forming

Combined radio frequency (RF)

output

Combined intermediate frequency (IF) output

Combined digital output

2 2

2 2 2

2 2

RF Amp.

Output signal to noise ratio, each amplifier ' S_in k T B

A_rf A_rf

Output signal to noise ratio, all amplifiers ' n² n

S_in k T B

A_rf

A_rf ' n S_in k T B

S_in n S_in nkTB

Figure 5.78 Radio frequency, intermediate frequency, and digital beam forming systems.

(5.106)

(5.107) When each element feeds a radio frequency amplifier, the signal-to-noise ratio at the output of each amplifier is

Each of the wanted signals ( volts) adds coherently and the sum is volts. The noise adds incoherently to give in voltage.

This is the same as (5.106) above so that there is no difference in performance between passive and active radio frequency combination. The signal-to-noise ratio is not changed by shaping the beam as noise is attenuated at the tips of the aperture function as well as the signal.

Distributing the transmitter and receiver components among many parallel elements in an antenna gives a characteristic known as graceful degradation. That is, if one transmitter-receiver element fails, the radar can continue in operation with slightly reduced, but acceptable, performance. Low sidelobe antennas depend on very accurate illumination functions so that the sidelobe performance will be affected to a much greater degree.

Dalam dokumen Modern Radar Systems, 2nd Edition.pdf (Halaman 180-184)