It should be noted that if MT virtual data channels are established, all of these channels will be fully decoupled. Therefore, the mutual information of the MIMO channel is the sum of the SISO channel capacities.
where {p1, . . . , pMT} is the eigenmode power allocation for each channel, satisfying the normalization condition
2.3.4.2MIMO system without transmit channel information
When the transmitter has no channel information, multiple antennas can be used at the transmitter and receiver ends to achieve diversity and increase the system capacity. This can be realized by spreading the symbols over the antenna (space) and time using the so-called space–time coding. In the following, the space–time block code will be briefly introduced.
Similar to MISO system, two symbols c1 and c2 are simultaneously transmitted from antenna 1 and antenna 2 in the first symbol period, and the symbols –
Assuming that the flat fading channel remains unchanged in the two consecutive symbol periods, the 2 × 2 channel matrix can be expressed as
It is worth noting that the subscripts here represent the receive and transmit antenna labels instead of the symbol periods. The signal vector received by the receiving array in the first symbol period is
The signal vector received in the second symbol period is
where n1 and n2 are additive noise components per symbol period of the receive antenna array (the subscripts represent symbol periods instead of antenna labels). Therefore, the receiver produces a mixed signal vector
Similar to the MISO system, two symbols c1 and c2 are transmitted during two symbol periods of two transmit antennas. Therefore, matrix Heff is orthogonal to all channel information, namely
If
where n′ satisfies E{n′} = 02×1 and
The average output SNR is
The Alamouti algorithm of the 2 × 2 structure obtains the receive array gain (ga = MR = 2) but does not get the transmit array gain (because there is no channel information). The above method can get the full diversity
The diversity gain of both the Alamouti algorithm and the dominant eigenmode transmission is 4, but the array gain of the dominant eigenmode transmission is 3 dB larger than the Alamouti algorithm. Alamouti algorithm can also be used for any number of receive antennas
2.3.4.3MIMO system with partial transmit channel information
If the transmitter has only partial channel information, it is also possible to exploit the gain of the array. The complete channel information at the transmitter requires high-speed feedback links at both ends of the receiver and transmitter to ensure that the latter can continuously obtain channel state information. On the converse, exploiting the statistical property of the channel at the transmitter or the quantitative description of the channel requires only a lower rate feedback link.
Precoding techniques usually combine a multi-mode beamformer that can spread codewords in orthogonal directions of the channel distribution-related direction with a constellation shaper, or more simply, with a power allocation algorithm. There are many similarities with various eigenmode transmissions, while the difference is that the eigenbeam is based on the statistical property of matrix H rather than its instantaneous value.
Similarly, the antenna selection technique may also only depend on partial channel information, namely the first- and second-order statistics of the matrix H to select the transmitting or receiving antenna. Intuitively, they are selected from the antenna pair with the lowest selective correlation ratio. Such techniques do not minimize transient error performance metrics, but minimize the average error probability.
By quantization precoding, the generalization of antenna selection is to derive limited feedback from the transmitter. This technique depends on the selection of codebooks in the precoding matrix, which is a finite set of precoders. It can be designed offline and is known to both the transmitter and the receiver. The receiver estimates the best precoder as a function of the current channel and then feeds the index of the best precoder back into the codebook.
2.4MIMO Traditional Detection Technology
In Section 2.3.4, we introduced the basic concepts and principles of the MIMO systems. In the following, we will discuss the signal detection problem at the receiving end of the MIMO system from the perspective of the MIMO receiver.
