Spatial Multidimensional Cooperative Transmission Theories And Key Technologies. Lin Bai

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      In order to overcome the negative impact of fading on the bit error rate, diversity techniques are often employed. The principle of diversity is to provide the receiver with multiple copies of the same transmitted signal, and each replica acts as a diversity branch. If this replication is affected by independent fading conditions, the probability that all branches will be in a fading state at the same time can be greatly reduced. Therefore, diversity stabilizes the link by channel enhancement, which improves the bit error rate performance of the system.

      As fading can occur in time, frequency, and space domains, diversity techniques can be used in these domains. For example, time diversity can be obtained by coding and interleaving, and frequency diversity can exploit the time spread of the channel (in the τ domain) by equalization techniques or multi-carrier modulation. Obviously, time and frequency diversity techniques can result in a loss of time or bandwidth due to the introduction of redundancy. Conversely, because multiple antennas are used at one or both ends of the link, space or polarization diversity does not sacrifice time and bandwidth.

2.3.2SIMO system

      The SIMO system relies on the number of antennas at the receiving end M_R ≥ 2 to realize diversity. If these antennas are sufficiently spaced (such as a wavelength), then when the physical channel exhibits good characteristics, the system will fade independent of the diversity of each branch. Reception diversity can be achieved in two different ways: selective combining and gain combining.

      2.3.2.1Reception diversity through selective combining

      Among M_R received signals, the combiner selects a branch having the largest SNR (or the highest absolute power, bit error rate, etc.) for signal detection. Suppose that M_R channels are subject to unit Rayleigh energy independent and identical distribution and the noise level is equal on each antenna. At this time, the selection algorithm compares the instantaneous amplitude of each channel s_n(n = 1, . . . , M_R) and selects the branch having the largest amplitude s_max = max(s₁, . . . , s_Mn}. The probability that s_max is below a certain threshold S² is given by

      The distribution corresponding to s_max can be obtained by the differentiation of Eq. (2.93).

      The average SNR of the combiner output is³

      when M_R is large, the array gain is approximately

      where γ ≈ 0.577 215 66 is the Euler constant.

      The diversity obtained by the selective combining can be estimated by calculating the bit error rate using the fading distribution given by Eq. (2.94). For the system using BPSK modulation and owning a two-branch diversity, the bit error rate as a function of the average SNR can be expressed corresponding to each channel ρ⁴ as follows:

      when the SNR is high,

      The slope of the bit error rate curve is 2. In general, the diversity gain of the M_R-branch selection diversity scheme is equal to M_R, which indicates that the selection diversity collects all possible diversity from the channel.

      2.3.2.2Reception diversity based on gain combining

      In gain combining, the signal z used for detection is a linear combination of all branches.

      where W_n denotes the combined weight and W = [W₁, . . . , W_MR]^T. According to the selection of these weights, there are different gain combining methods. It is assumed that the data symbol c is transmitted by the channel and received by M_R antennas. Each antenna is described by the channel h_n = |h_n|e^jϕn (n = 1, . . . , M_R). Suppose they obey the unit variance Rayleigh distribution and all СКАЧАТЬ