**6. Results**

The results obtained due to the implementation of the proposed IWFA algorithm under Perfect CSIT and uniform power allocation algorithm for No CSIT conditions. The concepts detailed in Section 5, along with Eqs. (18)–(35), were computed for the optimal power allocation and calculation of ergodic capacity. The random channel matrix for computation of ergodic and outage capacity are considered to be following the Rayleigh distribution. The ergodic capacity and outage capacity are calculated from the mean value of instantaneous capacity obtained by Monte-Carlo simulations. All simulations are done in MATLAB.

The spectral efficiencies of SISO, SIMO, MISO and MIMO systems under ICSIT and ICSIR conditions for different SNR value (0 to 20 dB) are illustrated in the **Figure 3**.

The capacities for different multi antenna systems under ICSIT and ICSIR conditions as discussed in section 5 are computed and tabulated in **Table 1**. The results indicate that for a Rayleigh fading channel, the spectral efficiency of MISO is lower than that of SIMO system. Due to spatial diversity antennas, MIMO system provides better spectral efficiency compared to other system. It is observed that for a given SNR value of 20 dB, in case of 4 � 4 MIMO performance (20.25 bit/s/Hz) is tetrad the Shannon limit of a SISO system performance (5.04 bit/s/Hz).

The cumulative distribution functions (CDFs) of the maximal achievable rate for different multi antenna systems are illustrated in **Figure 4**.

The CDFs are one of the ways to illustrate the benefits of MIMO system capacity and the capacity with 10% outage can easily be determined from the CDF.

The 10% outage capacity (Cout, 10) represents the information rate that is guaranteed for 90% of the channel realizations with probability

#### **Figure 3.**

*Spectral efficiency of SISO, SIMO, MISO, and MIMO systems under ICSIT and ICSIR conditions.*


### **Table 1.**

*Different multi antenna systems spectral efficiencies under ICSIT and ICSIR.*

Prout(Ctargeted ≤ Cout,10) = 10%. From the above figure it is observed that the 19.6, 14.1, and 8.71 bit/s/Hz obtained is the 10% outage capacity value for 4 4, 3 3, 2 2 MIMO systems respectively, whereas 6.8, 4.78 and 3.55 bit/s/Hz obtained is the 10% outage capacity value SIMO, MISO and SISO systems respectively. So it means that, 90% of time the MIMO system has achieved more capacity values than the capacity of SIMO, MISO and SISO systems. It is also observed that the outage probability decreases as the as antenna size of MIMO channel increases.

The capacity with outage as a function of SNR can also be determined as shown in **Figure 5**, where a fixed outage probability of 10% is considered.

The outage capacities for different multi antenna systems as discussed under Section 5 are computed and tabulated in **Table 2**.

*Performance Analysis of Multiple Antenna Systems with New Capacity Improvement Algorithm… DOI: http://dx.doi.org/10.5772/intechopen.98883*

**Figure 4.**

*10% outage capacity for different multi antenna systems.*

**Figure 5.** *Comparison graph of Outage capacities for different multi antenna systems.*


*The capacity with 10% outage observed is 9.30, 1.87, and 3.58 bit/s/Hz at 10 dB of SNR for the 4 4 MIMO system, 2 1 MISO system, and 1 3 SIMO system.*

#### **Table 2.**

*Outage capacities for different multi antenna systems.*

Similarly the ergodic capacities computed for different multi antenna systems are shown in **Figure 6**. The ergodic capacity values observed for SISO, SIMO and MISO are less than the values obtained for MIMO systems. From simulated results, the change in ergodic capacity due to SISO, SIMO and MISO systems to MIMO systems are


In **Table 3** ergodic capacities for different SNR in dB and different antennas as discussed in Section 5 are computed.

**Figure 6.** *Comparison graph of Ergodic capacities for different multi antenna systems.*


#### **Table 3.**

*Ergodic capacities for different multi antenna systems.*

*Performance Analysis of Multiple Antenna Systems with New Capacity Improvement Algorithm… DOI: http://dx.doi.org/10.5772/intechopen.98883*

In **Figure 7** ergodic capacities plotted for different configurations of MIMO systems under UPA and IWFA are shown. It indicates that the proposed algorithms is having better ergodic capacity than the UPA. The percentage of improvement in ergodic capacity is given below.


so it can infer that, at different SNR values an percentage improvement in ergodic capacity is obtained.

In **Figure 8**, different Eigenmode capacities are illustrated. It is observed that the maximum eigenmode is having more capacity for proposed IWFA algorithm then

**Figure 7.** *Ergodic capacity of different configurations of MIMO systems under UPA and IWFA.*

**Figure 8.** *Capacities for Eigenmodes for 4 4 MIMO system under perfect CSIT and No CSIT.*

UPA algorithm i.e. at high SNR IWFA tends to be like UPA and at low SNR the stronger streams are assigned more power with IWFA algorithm to increase the MIMO system capacity.
