Article Directory
Diversity technology is used to compensate fading channel loss, which is usually realized by two or more receiving antennas. Like an equalizer, it improves the transmission quality of a wireless communication channel without increasing transmission power and bandwidth. In mobile communication, receivers of both base station and mobile station can adopt diversity technology.
Diversity refers to distributed transmission and centralized reception. The so-called distributed transmission enables the receiving end to obtain multiple statistically independent fading signals carrying the same information. Concentrated reception means that the receiver combines (selects and combines) multiple received statistically independent fading signals to reduce the influence of fading.Baidu Encyclopedia
Diversity techniques include
- Diversity transmission technology: how to obtain multiple statistically independent signals on different attenuation channels
- Diversity combining techniques: How to combine multiple received signals for optimal detection performance
Diversity can be divided into
- Macro diversity: reduce large-scale fading, that is, slow fading ( large-scale fading is slow fading, but slow fading is not necessarily large-scale fading ). Multiple base stations are set up in different geographical locations and in different directions, and communicate with a mobile station in the cell at the same time. This approach ensures uninterrupted communication as long as signal propagation in all directions is not simultaneously subject to severe slow fading due to shadowing effects or terrain.
- Micro diversity: Reduce fast fading.
Micro diversity
Microdiversity techniques include:
- time diversity
- space diversity
- frequency diversity
- polarization diversity
- angle diversity
Time Diversity
The signal is retransmitted multiple times in an independent time interval, and the retransmission time interval must satisfy
Δ T ≫ 1 2 fm = 1 2 ( v / λ ) \Delta T \gg \frac{1}{2f_m}=\frac{1 }{2(v/\lambda)}ΔT≫2 fm1=2 ( v / l )1
A modern implementation of time diversity is spread-spectrum CDMA using a RAKE receiver, where multipath channels provide redundancy of transmitted information. In addition to RAKE, interleaving (interleaving) is used in digital communication systems to achieve time diversity without adding any overhead.
Since speech coders attempt to represent a wide range of sounds in a uniform and efficient digital format, the encoded data bits (source bits) carry a large amount of information, some source bits are more important than others, and errors must be guarded against. It is typical for many speech coders to generate several "important" bits in succession, and the function of the interleaver is to disperse these bits in time so that if a deep fade or burst of noise occurs, the important bits of the source data block are will not be destroyed at the same time. By spreading the source bits over time, it is possible to use error control coding to protect the source data from channel corruption. Since error control coding is designed to prevent possible random (random) or burst (bursty) channel errors , the interleaver scrambles the time order of the source bits before channel coding, making a series of errors into a single random or bursty Burst errors can be detected by error control coding. The image below is an example of interleaving:
If we transmit as before AAAA, then if the channel happens to be wrong when transmitting this series of bits, we will not be able to recover the correct codeword at the receiving end. But if you use interleaving, you can resist such errors. The following picture may be more intuitive:BBBBCCCCCCCC
On the receiving side, the de-interleaver (de-interleaver) stores the received data by sequentially increasing the number of rows of each consecutive bit, and then clocks out the data row by row, one word (row) at a time, as shown in the following figure:
Frequency Diversity
Frequency diversity is achieved by transmitting information on multiple carrier frequencies . The principle behind this technique is that the attenuation of two signals separated by more than the channel's correlation bandwidth is uncorrelated . In theory, if the channels are uncorrelated, then the probability of simultaneous fading will be the product of the individual fading probabilities. The formula for the correlation bandwidth is
B c = 1 2 π Δ B_c=\frac{1}{2\pi \Delta}Bc=2 p D1
where Δ \DeltaΔ is the delay spread (the difference between the maximum transmission delay and the minimum transmission delay).
Spatial Diversity
When receiving the same signal at any two different locations, as long as the distance between the two locations is large enough, the fading of the received signals at the two locations is irrelevant. In other words, we need at least two distances of ddAntenna of d :
- d d d must be large enough to ensure independence;
- d dd is related to wavelength, ground objects and antenna height
in urban areas, ddd usually takes0.5 λ 0.5\lambda0 . 5 λ , while in the suburbs,ddd usually takes0.8 λ 0.8\lambda0 . 8 l .
Combination of signals
We introduce 3 merge techniques:
- Selection Combining (SC)
- Maximal Ratio Combining (MRC)
- Equal Gain Combining (EGC)
Selection Combining
Selective merging is the simplest merging technique. The block diagram for this approach looks like the one shown below:
Among them, m demodulators are used to provide m diversity branches, whose gain is adjusted to provide the same average SNR for each branch. The branch with the highest instantaneous signal-to-noise ratio is connected to the demodulator. In practice, use with max ( S + N ) / N (S+N)/N(S+N ) / N branch, because it is difficult to measure the signal-to-noise ratio alone.
We consider M independent Rayleigh fading channels on a receiver. Each channel is called a diversity branch. Furthermore, assuming each branch has the same average SNR,
SNR = Γ = E b N 0 α 2 ‾ SNR=\Gamma=\frac{E_b}{N_0}\overline{\alpha^2}SNR=C=N0ANDba2
We assume α 2 ‾ = 1 \overline{\alpha^2}=1a2=1 . If the instantaneous SNR of each branch isγ i \gamma_ici, n γ i \gamma_icipdf sing
p ( γ i ) = 1 Γ e − γ i / Γ p(\gamma_i)=\frac{1}{\Gamma}e^{-\gamma_i/\Gamma}p ( ci)=C1and− ci/ C
The instantaneous SNR of a branch is less than the threshold γ \gammaγ dispersion ratio
P r [ γ i ≤ γ ] = ∫ 0 γ p ( γ i ) d γ i = 1 − e − γ / Γ Pr[\gamma_i\le\gamma] = \int_0^\gamma p(\ . gamma_i)d\happiness_i=1-e^{-\happiness/\Happiness}P r [ gi≤c ]=∫0cp ( ci)dγi=1−and− c / C
All M independent branches receive simultaneously less than a certain SNR threshold γ \gammaγ dispersion equation:
P r [ γ 1 , ... , γ M ≤ γ ] = ( 1 − e − γ / Γ ) M = PM ( γ ) Pr[\gamma_1,\dots,\gamma_M \le \gamma ]=\left(1-e^{-\gamma/\Gamma}\right)^M=P_M(\gamma)P r [ g1,…,cM≤c ]=( 1−and− c / C )M=PM( c )
Therefore, the probability that the instantaneous SNR of one or more branches is greater than the threshold is
P r [ γ i > γ ] = 1 − ( 1 − e − γ / Γ ) M Pr[\gamma_i>\gamma]=1-\left(1 -e^{-\gamma/\Gamma}\right)^MP r [ gi>c ]=1−( 1−and− c / C )M
Suppose we use four branches, each receiving an independent Rayleigh fading signal. If the average SNR is 20 dB (100), then the probability that the SNR drops below 10 dB (10) is
( 1 − e − γ / Γ ) M = ( 1 − e 0.1 ) 4 = 0.000082 \left (1-e^{-\gamma/\Gamma}\right)^M=\left(1-e^{0.1}\right)^4=0.000082( 1−and− c / C )M=( 1−and0 . 1 )4=0 . 0 0 0 0 8 2
And if diversity is not used, that is, M=1, then the probability that the signal-to-noise ratio drops below 10 dB is
( 1 − e − γ / Γ ) M = ( 1 − e 0.1 ) 1 = 0.095 \left(1-e ^{-\gamma/\Gamma}\right)^M=\left(1-e^{0.1}\right)^1=0.095( 1−and− c / C )M=( 1−and0 . 1 )1=0 . 0 9 5
Here we directly give the combined gain of SC as
GSC = γ ˉ Γ = ∑ k = 1 M 1 k G_{SC}=\frac{\bar{\gamma}}{\Gamma}=\sum_{k=1} ^M\frac{1}{k}GSC=Ccˉ=k=1∑Mk1
Selective merging is easy to implement because only one side monitoring station and one receiver antenna switch are required. However, it's not the best merge technique because it doesn't use all possible branches at the same time. MRC utilizes all branches in a co-phased and weighted manner, so that the receiver has the highest achievable signal-to-noise ratio at any time.
Maximal Ratio Combining
The signals from all M branches are weighted according to their respective signal voltage-to-noise power ratios and then summed. The following figure is the block diagram of MRC:
Here, the individual signals must be co-phased (unlike selective combining) before being summed, which typically requires separate receiver and phasing circuits for each antenna element. Maximum ratio combining produces an output SNR equal to the sum of the SNRs of the individual branches. Thus, it has the advantage of producing an output with an acceptable SNR, even if each branch has a poor SNR.
In MRC, the voltage signal ri r_i from each branchriAfter phase adjustment, according to the appropriate gain coefficient, add in phase. If the gain of each branch is G i G_iGi, then the signal sent to the detector is
r M = ∑ i = 1 MG iri r_M=\sum_{i=1}^MG_ir_irM=i=1∑MGiri
Assume that each branch has the same noise power NNN , so the total noise power is also the weighted sum corresponding to each branch:
NT = N ∑ i = 1 MG i 2 N_T=N\sum_{i=1}^MG_i^2NT=Ni=1∑MGi2
So the SNR is
γ M = r M 2 2 NT \gamma_M=\frac{r_M^2}{2N_T}cM=2N _TrM2
By means of Chebyshev's inequality, γ M \gamma_McMAt G i = ri / N G_i =r_i/NGi=ri/ N to obtain the maximum value, at this time
γ M = ∑ i = 1 M γ i \gamma_M=\sum_{i=1}^M\gamma_icM=i=1∑Mci
That is, the SNR of the signal before the detector is the sum of the SNRs of each branch.
Here we directly give the SNR of MRC less than a certain SNR threshold γ \gammaγ displacement function1
− e − γ / Γ ∑ k = 1 M ( γ / Γ ) k − 1 ( k − 1 ) ! 1-e^{-\gamma/\Gamma}\sum_{k=1}^M\frac{(\gamma/\Gamma)^{k-1}}{(k-1)!}1−and− c / Ck=1∑M(k−1 ) !( c / C )k−1
因为 γ M = ∑ i = 1 M γ i \gamma_M=\sum_{i=1}^M\gamma_i cM=∑i=1Mci, so the average SNR is also the sum of the average SNR of each branch, that is,
γ M ‾ = ∑ i = 1 M γ i ‾ = M Γ \overline{\gamma_M}=\sum_{i=1}^M\overline{\ gamma_i}=M\GammacM=i=1∑Mci=MΓ
So the combined gain of MRC is
GMRC = γ M ‾ Γ = M G_{MRC}=\frac{\overline{\gamma_M}}{\Gamma}=MGMRC=CcM=M
Equal Gain Combining
In some cases, it is not convenient to provide the required variable weighting capability for maximum ratio combining. In this case, the branch weights are all set uniformly, but the signals from each branch are co-phased to provide equal gain combining. This enables the receiver to take advantage of the simultaneously received signal on each branch.
We directly give the combined gain of EGC:
GEGC = 1 + ( M − 1 ) π / 4 G_{EGC}=1+(M-1)\pi/4GEGC=1+(M−1 ) p / 4
It can be seen that when M increases, EGC is almost the same as MRC, and the experiment proves that the difference is only about 1 dB.
References
Wireless Communications: Principles and Practices, 2nd Edition, Theodore S. Rappaport.