![]() A gap in Doppler between the first and last transmit element's target returns exists because of the virtual transmit antennas used to compute the DDMA Doppler offsets. There are ten returns modulated in Doppler at the same range for each target corresponding to the ten Doppler offsets applied across each of the ten transmit elements. The returns from the target vehicle merging into the lane in front of the ego vehicle appear at a range of 40 meters from the radar and returns corresponding to the highway overpass are located at approximately 80 meters. ![]() These unused Doppler offsets will enable Doppler ambiguities to be unwrapped, preventing a reduction in the maximum ambiguous velocity of the MIMO radar.Ī range and Doppler map for one of the receive elements is shown in the previous figure. This will assign two Doppler offsets to unused virtual transmit elements. Generate the Doppler offsets uniformly across the Doppler space for the 10 transmit antennas and 2 virtual antennas. , Ĭreate a DDMA waveform for the MIMO radar that assigns a unique Doppler offset to each of the transmit elements so that each element will transmit the same FMCW waveform, but with a unique offset in Doppler. This enables the maximum ambiguous velocity of the radar's waveform to be maintained. An adaptation of the conventional DDMA MIMO which introduces an unused region of Doppler without regularly spaced peaks by adding virtual transmit elements to the array is used here. A drawback of this technique is that the maximum ambiguous velocity is still reduced by the number of transmit antennas due to the Ntx peaks from the transmitted signals spread across the Doppler space. This is realized by DDMA MIMO weights which modulate each transmit antenna's signal into its own Doppler frequency subband. The motivation of this conventional DDMA scheme is to separate transmit signals from the Ntx transmit antennas into Ntx Doppler frequency subbands at the receiver. One such technique, Doppler Division Multiple Access (DDMA) MIMO maintains orthogonality in the frequency domain by shifting the waveforms transmitted by each antenna in Doppler. Instead of maintaining orthogonality in the time domain, new techniques using the frequency and code domains have been proposed. For more information on TDMA MIMO radar, see the Increasing Angular Resolution with Virtual Arrays example. Only using one transmit element at a time maintains the needed orthogonality but at the cost of reducing the total transmit power and decreasing the maximum unambiguous velocity of the radar. TDMA only transmits from one antenna element at any given time. Time Division Multiple Access (TDMA) is a common technique used to maintain orthogonality in the time domain. Maintaining this orthogonality across the transmit antennas is essential in order to assemble the virtual array used by the MIMO radar as will be demonstrated later in the Signal Processing section of this example. This orthogonality is often realized by encoding the transmitted waveforms in time, frequency, or code domains. = db2pow(10) Define MIMO DDMA WaveformĪn essential characteristic of any MIMO radar implementation is a waveform that maintains orthogonality along all the transmit antennas. Be specific! (b) Compute E-1 and ET (recall that ET is computed in MATLAB with the command E') and observe that they are also permutation = txArray ![]() How are the two matrices related? Describe the effect on A of right multiplication by the permutation matrix E. Be specific! Compute the product AE and compare the answer with the matrix A. How are the two matrices related? Describe the effect on A of left multiplication by the permutation matrix E. ![]() Generate a 5 x 5 matrix A with integer entries using the command Afloor(10*rand (5)) (a) Compute the product EA and compare the answer with the matrix A. If you haven't already done so, enter the commands in the example above to generate the permutation matrix E defined in (2) (you can suppress this matrix). For example, we can construct 0 01 0 01 E1 00 0 0 by using the MATLAB commands p- % permutation vector that defines E -eye (length (p) E E(p, :) % permute the rows of E according to the % the new order of the rows % define E as the identity matrix % permutation vector p The second command creates the 5x 5 identity matrix, and the third command uses the vector p to permute its rows, so row p(1)- 3 becomes row 1, row p (2) 5 becomes row 2, row p(3) 1 becomes row 3 and so on (compare these row permutations with the vector p defined above
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