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This matrix is also known as the pseudo inverse for a general m x n matrix. Ber with zf equalizer with 22 mimo note that the off diagonal terms in the matrix are not zero (Recall: The off diagonal terms where zero in Alamouti 21 stbc case). Because the off diagonal terms are not zero, the zero forcing equalizer tries to null out the interfering terms when performing the equalization,. E when solving for the interference from is tried to be nulled and vice versa. While doing so, there can be amplification of noise. Hence zero forcing equalizer is not the best possible equalizer to do the job. However, it is simple and reasonably easy to implement. Further, it can be seen that, following zero forcing equalization, the channel for symbol transmitted from each spatial dimension (space is antenna) is a like a 11 rayleigh fading channel (Refer Section.3 of wireless-tse, viswanath ).
The received signal on the second receive antenna. Where, are the received symbol on the first and second antenna best respectively, is the channel from transmit antenna to receive antenna, is the channel from transmit antenna to receive antenna, is the channel from transmit antenna to receive antenna, is the channel from transmit antenna. We assume that the receiver knows, and. The receiver also knows and. The unknown s are and.
Two equations and two unknowns. Can we solve it? For lijnen convenience, the above equation can be represented in matrix notation as follows. Equivalently, to solve for, we know that we need to find a matrix which satisfies. The zero forcing (ZF) linear detector for meeting this constraint is given.
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The channel experience by each transmit antenna is independent from the channel experienced by other transmit antennas. For the transmit antenna to receive antenna, each transmitted symbol gets multiplied by a randomly varying complex number. As the channel under consideration is a rayleigh channel, the real and imaginary parts of are gaussian distributed having mean and variance. The channel experienced between each transmit to the receive antenna is independent and randomly varying in time. On the receive antenna, the noise has the gaussian probability density function with with and. The channel is known at the receiver. Zero forcing (ZF) equalizer for 22 mimo channel Let us now try to understand the math for extracting the two symbols which interfered with each other. In the first bepaalde time slot, the received signal on the first receive antenna.
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This forms the simple explanation of a probable mimo transmission scheme with 2 transmit antennas and 2 receive antennas. Having said this, some of you will wonder the two adapter transmitted symbols interfered with each other. Can we ever separate the two out? The rest of the post attempts to answer this question. Figure: 2 Transmit 2 Receive (22) mimo channel. The channel is flat fading In simple terms, it means that the multipath channel has only one tap. So, the convolution operation reduces to a simple multiplication. For a more rigorous discussion on flat fading and frequency selective fading, may i urge you to review Chapter.3 Signal Time-Spreading from. Digital communications: sklar.
22 mimo channel, in a 22 mimo channel, probable usage of the available 2 transmit antennas can be as follows:. Consider that we have a transmission sequence, for example. In normal transmission, we will be sending in the first time slot, in the second time slot, and. However, as we now have 2 transmit antennas, we may group the symbols into groups of two. In the first time slot, send and systems from the first and second antenna. In second time slot, send and from the first and second antenna, send and in the third time slot and. Notice that as we are grouping two symbols and sending them in one time slot, we need only time slots to complete the transmission data rate is doubled!
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We had discussed three, single Input Multiple output simo also known as receive diversity) schemes. Selection combining, equal gain Combining, maximal Ratio combining and a, multiple Input Single output miso, also known as transmit diversity) scheme. Let us now discuss the case where there a multiple transmit antennas and multiple receive antennas resulting in the formation. Multiple Input Multiple output (mimo) channel. In this post, we will restrict our discussion to a 2 transmit 2 receive antenna case (resulting in a 22 mimo telproblemen channel). We will assume that the channel is a flat fading. Rayleigh multipath channel and the modulation is bpsk.