The phased.ReceiverPreamp object lets you model the effects of gain and component-based noise on the signal-to-noise ratio (SNR) of received signals. phased.ReceiverPreamp operates on baseband signals. The object is not intended to model system effects at RF or intermediate frequency (IF) stages.

The phased.ReceiverPreamp object has the following modifiable properties:

• EnableInputPort — A logical property that enables you to specify when the receiver is on or off. Input the actual status of the receiver as a vector to step. This property is useful when modeling a monostatic radar system. In a monostatic radar, it is important to ensure the transmitter and receiver are not operating simultaneously. See phased.Transmitter and Transmitter.

• Gain — Gain in dB (GdB)

• LossFactor — Loss factor in dB (LdB)

• NoiseMethod — Specify noise input as noise power or noise temperature

• NoiseFigure — Receiver noise figure in dB (FdB)

• ReferenceTemperature — Receiver reference temperature in kelvin (T)

• SampleRate — Sample rate (fs)

• NoisePower — Noise power specified in Watts (σ2)

• NoiseComplexity — Specify noise as real-valued or complex-valued

• EnableInputPort — Add input to specify when the receiver is active

• SeedSource — Lets you specify random number generator seed

• Seed — Random number generator seed

The output signal, y[n], of the phased.ReceiverPreamp System object™ equals the input signal scaled by the ratio of receiver amplitude gain to amplitude loss plus additive noise

$y\left[n\right]=\frac{G}{L}x\left[n\right]+\frac{\sigma }{\sqrt{2}}w\left[n\right]$

where x[n] is the complex-valued input signal and w[n] is unit-variance noise complex-valued noise.

When the input signal is real-valued, the output signal, y[n], equals the real-valued input signal scaled by the ratio of receiver amplitude gain to amplitude loss plus real-valued additive noise

$y\left[n\right]=\frac{G}{L}x\left[n\right]+\sigma w\left[n\right]$

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The amplitude gain, G, and loss, L, can be express in terms of the input dB parameters by

$\begin{array}{l}G={10}^{{G}_{dB}/20}\\ L={10}^{{L}_{dB}/20}\end{array}$

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respectively.

The additive noise for the receiver is modeled as a zero-mean complex white Gaussian noise vector with variance, σ2, equal to the noise power. The real and imaginary parts of the noise vector each have variance equal to 1/2 the noise power.

You can set the noise power directly by choosing the NoiseMethod property to be 'Noise power' and then setting the NoisePower property to a real positive number. Alternatively, you can set the noise power using the system temperature by choosing the NoiseMethod property to be 'Noise temperature'. Then

${\sigma }^{2}={k}_{B}BTF$

where kB is Boltzmann’s constant, B is the noise bandwidth which is equal to the sample rate, fs, T is the system temperature, and F is the noise figure in power units.

The noise figure, F, is a dimensionless quantity that indicates how much a receiver deviates from an ideal receiver in terms of internal noise. An ideal receiver produces thermal noise power defined by noise bandwidth and temperature. In terms of power units, the noise figure F = 10FdB/10. A noise figure of 0 dB indicates that the noise power of a receiver equals the noise power of an ideal receiver. Because an actual receiver cannot exhibit a noise power value less than an ideal receiver, the noise figure is always greater than or equal to one. In decibels, the noise figure must be greater than or equal to zero.

To model the effect of the receiver preamp on the signal, phased.ReceiverPreamp computes the effective system noise temperature by taking the product of the reference temperature, T, and the noise figure F in power units. See systemp for details.

### Model Receiver Effects on Sinusoidal Input

Specify a phased.ReceiverPreamp System object™ with a gain of 20 dB, a noise figure of 5 dB, and a reference temperature of 290 degrees kelvin.

Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent step syntax. For example, replace myObject(x) with step(myObject,x).

'NoiseFigure',5,'ReferenceTemperature',290,...
'SampleRate',1e6,'SeedSource','Property','Seed',1e3);

Assume a 100-Hz sine wave input with an amplitude of 1 microvolt. Because the Phased Array System Toolbox assumes that all modeling is done at baseband, use a complex exponential as the input when executing the System object.

t = unigrid(0,0.001,0.1,'[)');
x = 1e-6*exp(1i*2*pi*100*t).';

The output of the phased.ReceiverPreamp.step method is complex-valued as expected.

Now show how the same output can be produced from the multiplicative amplitude gain and additive noise. First assume that the noise bandwidth equals the sample rate of the receiver preamp (1 MHz). Then, the noise power is equal to:

noisepow = physconst('Boltzmann')*...

The noise power is the variance of the additive white noise. To determine the correct amplitude scaling of the input signal, note that the gain is 20 dB. Because the loss factor in this case is 0 dB, the scaling factor for the input signal is found by solving the following equation for the multiplicative gain G from the gain in dB, ${G}_{dB}$:

$G=1{0}^{\left({G}_{dB}/20\right)}$

G = 10

The gain is 10. By scaling the input signal by a factor of ten and adding complex white Gaussian noise with the appropriate variance, you produce an output equivalent to the preceding call to phased.ReceiverPreamp.step (use the same seed for the random number generation).

rng(1e3);
y1 = G*x + sqrt(noisepow/2)*(randn(size(x))+1j*randn(size(x)));

Compare a few values of y to y1.

disp(y1(1:10) - y(1:10))
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