the interferences among users. Diversity technique is another way to increase the spectrum usage efficiency. If a single antenna is used at the transmitting end and multiple antennas are used at the receiving end, this diversity is often called diversity reception which is also known as the single-input multiple-output (SIMO) system. The use of optimal combined diversity reception techniques generally improves the SNR at the receiving end, thereby increasing the channel capacity and the spectrum usage efficiency. If multiple antennas are used at the transmitting end and a single antenna is used at the receiving end, this diversity is often called the transmit diversity, which is also known as the multiple-input single-output (MISO) system. However, if the state information of the channel is not known at the transmitting end, beamforming technology and adaptive allocation cannot be used in the multi-transmitting antenna for transmitting power, and thus, the channel capacity cannot be improved much. The development and integration of SIMO and MISO technologies have evolved into MIMO technology, which is an effective method to break through the SISO channel capacity bottleneck. The core idea of the system is to synthesize the signals at both ends of the spatial sampling by way of generating effective multi-parallel spatial data channels (increasing the data traffic), so as to greatly improve the channel capacity, or by way of increasing the diversity to improve communication (reduce bit error rate).
2.3.1Diversity technique
The particularity of a wireless link is that it is affected by random fluctuations in signal levels across time, space, and frequency. This characteristic is fading and affects the system performance (symbol or bit error rate). Take the SISO Rayleigh fading channel transmitted by binary phase shift keying (BPSK) as an example.
When there is no fading (h = 1), in the additive white Gaussian noise (AWGN) channel, the bit error rate (SER) is
When considering the fading, the level of the received signal fluctuates with
where ps(s) is the distribution function of the fading. For Rayleigh fading, the integration of the above equation yields
When the SNR is large, the bit error rate in Eq. (2.91) becomes
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 MR ≥ 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 MR 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 MR 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 sn(n = 1, . . . , MR) and selects the branch having the largest amplitude smax = max(s1, . . . , sMn}. The probability that smax is below a certain threshold S2 is given by
The distribution corresponding to smax can be obtained by the differentiation of Eq. (2.93).
The average SNR of the combiner output is3
when MR 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 MR-branch selection diversity scheme is equal to MR, 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 Wn denotes the combined weight and W = [W1, . . . , WMR]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 MR antennas. Each antenna is described by the channel hn = |hn|ejϕn (n = 1, . . . , MR). Suppose they obey the unit variance Rayleigh distribution and all
