Space-Time Adaptive Processing: Fundamentals
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20-09-2009, 04:01 PM


Space-Time Adaptive Processing: Fundamentals


ABSTRACT


Space-time Adaptive Processing (STAP) is a signal processing technique most commonly used in radar systems. It involves adaptive array processing algorithms to aid in target detection. Radar signal processing benefits from STAP in areas where interference is a problem (i.e. ground clutter, jamming, etc.). Through careful application of STAP, it is possible to achieve order-of-magnitude sensitivity improvements in target detection.STAP involves a twodimensional filtering technique using a phased-array antenna with multiple spatial channels. Coupling multiple spatial channels with pulse-Doppler waveforms lends to the name space-time. Applying the statistics of the interference environment, an adaptive STAP weight vector is formed. This weight vector is applied to the coherent samples received by the radar.In this lecture, we present the principles of spacetime adaptive processing (STAP) for radar, applied to moving target indication. We discuss the properties of optimum STAP, as well as problems associated with estimating the adaptive weights not encountered with spatialonly processing (i.e. beam forming) .


1 INTRODUCTION What is Space-Time Adaptive Processing (STAP)? Space-Time Adaptive Processing (STAP) is a signal processing technique used to suppress the effects of cochannel interference, ISI, and jammers in wireless communications systems. From the implementation of STAP algorithms, greater capacity gains and communication quality can be realized . The fundamental principle in all STAP algorithms involves the usage of multiple receive antennas on the receiving platform. Spacing the antennas apart by at least half the wavelength of the desired signal provides space diversity, which helps mitigate the effects of fading. Furthermore, the incoming signals on each antenna element are adaptively weighted using a variety of algorithms in order to steer the antenna gain towards the desired signals while nulling the signals from unwanted noise and interference.
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26-03-2011, 12:51 PM


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Space-Time Adaptive Processing (STAP) in Wireless Communications
Abstract

Space-Time Adaptive Processing (STAP) algorithms have been proven to be a very effective way to mitigate the effects of multipath and interference in wireless communication systems. However, when implementing the STAP algorithm several design issues arise. This paper will examine two proposed implementations of STAP algorithms. These implementations will include covariance matrix estimation (a statistical method) and Direct Data Domain (D3) processing approach (a non-statistical method). These two STAP methods will be compared and contrasted and the implications of STAP on wireless networks will be examined.
Background: What is Space-Time Adaptive Processing (STAP)?
Space-Time Adaptive Processing (STAP) is a signal processing technique used to suppress the effects of co-channel interference, ISI, and jammers in wireless communications systems. From the implementation of STAP algorithms, greater capacity gains and communication quality can be realized
The fundamental principle in all STAP algorithms involves the usage of multiple receive antennas on the receiving platform. Spacing the antennas apart by at least half the wavelength of the desired signal provides space diversity, which helps mitigate the effects of fading. Furthermore, the incoming signals on each antenna element are adaptively weighted using a variety of algorithms in order to steer the antenna gain towards the desired signals while nulling the signals from unwanted noise and interference. Figure 1 below shows the baseline setup for most STAP implementations.
Figure 1. Baseline STAP receiver configuration.
STAP algorithms will typically begin with the configuration above in Figure 1 and add extensions such as tapped delay lines behind each antenna receiver or different antenna array topologies.
Two algorithm approaches to STAP will be analyzed in this paper. They are interference covariance matrix estimation and direct data domain (D3) processing.
Interference Covariance Matrix Estimation Approach
Interference covariance matrix estimation is the well-known classical approach to STAP implementation. Research using this approach has been around since the 70’s. The approach begins by utilizing the initial antenna structure in Figure 1 and adding tapped delay lines after each receiver. Figure 2 illustrates this new configuration.
As observed in the above figure, each of the taped delay signals is adaptively weighted as before according to the designer’s processing algorithm that minimizes interference and noise while preserving or enhancing the desired signal. The final output signal is the sum of all the weighted taps.
For a system of N antenna elements and M taps per element, a total of NxM signals are received and weighted. Thus, the input signal has the form:
XT(k) = [x1(k), x2(k), … xNM(k)]
where (T) denotes transpose and k is the multiple of the time the sample is taken. The received voltages on the taps are the sum of the desired signal in the direction of interest plus noise. Hence,
X(k) = L(k) + N(k)
where L(k) is the contribution on each tap from the desired signal in the “look direction” and N(k) is the noise contribution on each tap[6].
Again, because of the NxM signal taps, L(k) & N(k) have the form:
L(k) = [l11(k, l12(k), …l1M(k) …
l21(k -  l22(k - ), …l2M(k - ) …


lN1(k -(M-1) ), lN2(k -(M-1)), …lNM(k -(M-1))]
and
N(k) = [n1(k), n2(k), …nNM(k)].
The weight vector containing the weights after each tap has a similar form:
WT = [w11,…w1M, …, wN1,…wNM].
It is shown in [2] and [6] that noise and interference power not in the “look direction” of the desired signal can be minimized by minimizing the power of the system output. The system output is given by:
y(k) = n=1 m=1 wnmxn(k+M-m)
and the expected power is
P = E{|y(k)|2} = E{(n=1 m=1 wnmxn(k+M-m))(i=1 j=1 wijxi(k+M-j))
= E{n=1 m=1 i=1 j=1 wnmxn(k+M-m) xi(k+M-j) wij}
However, since the weights and tap voltages can be expressed as vectors, the output signal simplifies to:
y(k) = WTX(k)
and the expected output power becomes
P = E[y2(k)]
= E[WTX(k)XT(k)W]
= WTRXXW.
The covariance structure (RXX) of the tap voltages is easily recognizable in this solution.
Now adapting the weights to minimize the expected output power would yield the trivial result of zeros. This would also completely cancel the desired signal. Thus, an additional constraint must be placed on the weight calculation.
Both [2] and [6] show that a linear constraint must also be placed on the weights using this STAP algorithm. This linear constraint has the form
cHw = 1
where c is the NMx1 constraint vector (designed to maintain the response of the filter to the desired target), (H) is the conjugate transpose, and w is the vector of weights containing the NM filter weights [2].
Minimizing the output power now according to the linear constraint yields the following solution:
w = (R-1c)/(cHR-1c)
with R representing the covariance structure (RXX) as before.
This methodology for STAP has proven to be very effective at reducing the effects of noise and interference in wireless communication systems and is especially useful in Pseudo-randomly coded systems with signals below the noise floor.
Direct Data Domain (D3) Approach
The direct data domain (D3) STAP approach begins with the baseline STAP receiver setup as shown previously in Figure 1. The are no tapped delay lines following the weight on each receiver element; therefore, the voltages are then summed and the output y(t) is given
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11-02-2012, 09:58 AM

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