Dongxu Yang, Meng Cao Supervisor: Prabin

 Review of the Beamformer  Realization of the Beamforming Data Independent Beamforming Statistically Optimum Beamforming

 A Beamformer is a processor used with an array of sensors to provide a universal form of spatial filtering  The sensor array collects spatial samples of propagating wave fields  The objective is to obtain the signal arriving from a desired direction in the presence of noise and interfering signals

The Beamformer performs spatial filtering to separate signals that have overlapping frequency content but from different directions

More universal and complicated one

 Review of the Beamformer  Realization of the Beamforming Data Independent Beamforming Statistically Optimum Beamforming

 We know the direction as well as the frequency band of the signal which we want to obtain  But we don’t have any knowledge about the statistics of the array data  So we just have a desired response

 Least-squares(LS) criterion Minimizing the squared error between the actual and desired response at P points (θ i, ω i ), 1 ≤ i ≤ P. If P > N, then we obtain the overdetermined least squares problem where Provided AA H is invertible, then the solution is given as where A + =(AA H ) -1 A is the pseudo inverse of A.

 Simulation: ◦ J=6, K=8 ◦ For θ=10⁰ and f=6kHz~10kHz r(10⁰,6kHz~10kHz)=1 ◦ For other θ and f, r(θ,f)=0

 Review of the Beamformer  Realization of the Beamforming Data Independent Beamforming Statistically Optimum Beamforming Multiple Sidelobe Canceller Use of Reference Signal Maximization of Signal to Noise Ratio Linearly Constrained Minimum Variance

 We know some statistics of the data received at the array, so we can make use of this.  Weights are based on the statistics of the data.  Data independent v.s. statistically optimum  Different approaches: ◦ Multiple Sidelobes Canceller ◦ Use of Reference Signal ◦ Maximization of Signal to Noise Ratio ◦ Linearly Constrained Minimum Variance

◦ We want to cancel the interference signal in the main channel with the help of the auxiliary channels. ◦ Get minimized output power when desired signal is absence. ◦ The weights:

◦ Sensor Array :  N_primary=1,  N_auxiliary=5,  K=6,  fs =4e4 Hz, ◦ Main channel is a 5 th order LPF ◦ Signal:  Desired ⁰,  Interference ⁰,  White Gaussian ⁰, with the power of -10dBW,

At 4000Hz Main channel auxiliary channel subtract

 Review of the Beamformer  Realization of the Beamforming Data Independent Beamforming Statistically Optimum Beamforming Multiple Sidelobe Canceller Use of Reference Signal Maximization of Signal to Noise Ratio Linearly Constrained Minimum Variance

◦ We know what the desired signal looks like ◦ We want to pick up the desired signal ◦ We should minimize the difference between the reference signal and the output. ◦ We can get the weights :

◦ Sensor Array :  J=6,  K=6,  fs =4e4 Hz, ◦ Signal:  Desired ⁰,  Interference ⁰,  Another ⁰,  White Gaussian with the power of -10dBW,

Reference signal

◦ Sensor Array :  J=6,  K=1,  fs =4e4 Hz, ◦ Signal:  Desired ⁰,  Interference ⁰,

Reference signal

 Problem: ◦ The signal in the same frequency band can not be filtered. ◦ The desired signal may be all cancelled  ◦ The figure on the right shows the direction response at f=4000Hz

 Review of the Beamformer  Realization of the Beamforming Data Independent Beamforming Statistically Optimum Beamforming Multiple Sidelobe Canceller Use of Reference Signal Maximization of Signal to Noise Ratio Linearly Constrained Minimum Variance

◦ We know the statistical characteristic of the desired signal and the interference signal ◦ We want the maximum SNR ◦ So the weights:

◦ Sensor Array :  J=6,  K=6,  fs =4e4 Hz, ◦ Signal:  Desired ⁰,  Interference ⁰,  White Gaussian -10dBW

SNR=141.6

At 4000Hz

 Review of the Beamformer  Realization of the Beamforming Data Independent Beamforming Statistically Optimum Beamforming Multiple Sidelobe Canceller Use of Reference Signal Maximization of Signal to Noise Ratio Linearly Constrained Minimum Variance

◦ We want the signals from the direction of interest are passed with specified gain and phrase ◦ We want minimum output signal power so that least interference signal is added. ◦ The weights:

◦ Sensor Array :  J=6,  K=6,  fs =4e4 Hz, ◦ Signal:  Desired ⁰,  Interference ⁰,  Another interference  White Gaussian -10dBW

Desierd signal sourecs Power: 0.75W Total output Power: W

At 4000Hz

TypeMSCReference Signal Max SNRLCMV Criterion Optimum Weights AdvantagesSimpleDirection of desired signal can be unknown True maximizatio n of SNR Flexible and general constraints DisadvantagesRequires absence of desired signal for weight determinati on Must generate reference signal Must know Rs and Rn, Solve eigenproble m for weights Computation of constrained weight vector