这是一篇来自瑞典的关于多天线系统项目4的**作业代写**

**1 Purpose **

The purpose of this project is to study and implement difffferent types of MIMO receivers to achieve spatial multiplexing scheme (Lecture 9). The advantage of antenna selection will be also discussed (Lecture 11).

**2 Tasks **

- Implement a 3
*×*3 MIMO eigenmode transmission scheme in order to achieve spatial multiplexing gain,*i.e.*, to transmit 3 independent data streams simultaneously. The i.i.d. Rayleigh channel**H**=**H***w*is used. With full channel knowledge at the transmitter, the signal model is given as= r*y**E**s**M*T**HV**+*s**n**,*

and

** z **=

**U**

*H*

*y**,*

is performed at the receiver, in which

**H **= **UΣV***H *

denotes the singular value decomposition of **H**.

Transmit 3 data streams using BPSK modulation, *i.e.*, a data sequence of *{*-1, 1*} *is to be transmitted from each transmitting antenna, and AWGN is assumed at the receiver. No encoding scheme is considered at the transmitter, and each data steam is detected independently at the receiver. Generate several channel realizations and enough number of bits in order to get good statistics. Channels are properly normalized so that SNR reflflects the actual signal to noise ratio in the system.

Plot the overall BER as a function of SNR (*e.g.*, 0-12 dB), *i.e.*, the average BER of the 3 data streams.

Also plot BER of 3 difffferent data streams (*i.e.*, eigen-channels) separately. What determines the BER performance of each eigen-channel fundamentally? Perform the same simulation with the channel matrix of **H **= **I**3 instead of **H***w*. Do you expect any difffferent results? Compare all these BER curves with the SISO system (the performance of SISO systems has been discussed in Project 3). Is your MIMO system performing better or worse comparing to the SISO system? Why or why not?

- Assume that BPSK is used as modulation. Use the fifirst 2 transmit and fifirst 2 receive elements from the MIMO measurement “LOS 8 8.mat”. Assuming uncoded Spatial Multiplexing operation, implement the ZF receiver, the MMSE receiver, and the ML receiver, respectively. Simulate the BER for difffferent SNRs (
*e.g.*, 0-40 dB) and comment on the performances. What is the main drawback of the receiver with better performance?

- (This task is OPTIONAL)

The cost of a RF (radio frequency) chain typically exceeds the cost of the radiating element by several orders of magnitude. This motivates the problem of antenna subset selection where we use fewer RF chains than transmit/receive antennas and switch the RF chains into the appropriate antennas (depending on the channel conditions and level of channel knowledge) to optimize a certain performance criterion. In the following we assume a MIMO channel with *M*T = 2 and *M*R = 4 employing the Alamouti scheme. However, the transmitter and receiver are each equipped with only 2 RF chains.

**H**formulate an appropriate switching rule at the receiver so as to minimize symbol error rate.

**H***w*and BPSK transmission with the Alamouti scheme plot the symbol error rate (SER) as a function of SNR for a MIMO channel with*M*T =*M*R = 2. On the same graph plot the SER for the*M*T = 2 and*M*R = 4 channel assuming antenna selection for 2 receive RF chains, with the optimal selection rule formulated in above. For the sake of comparison, plot the SER for the*M*T = 2 and*M*R = 4 channel with all 4 receive RF chains.

Also plot for a SIMO channel with maximum ratio combining (MRC) for *M*R = 4 and *M*R = 8 respectively. Comment on your results. Specififically, comment on the diversity realized by the antenna selection scheme. In this task, no implementation or simulation is required. One can simply calculate the theoretical approximate SER using the Q-function (*e.g.*, (5.4) in textbook) with appropriate arguments (post-processing SNRs) and average over a large number of channel realizations.

**3 Report **

Write a short report. In order to pass, you should (1) describe the methods you apply to solve the problem,(2) present the results, *e.g.*, in readable fifigures, and (3) comment on the results (important!). Computer code can be included as an attachment.