Modelling of Multi-antenna Wireless Channels and Relay Based

This is to confirm that the thesis entitled "Modelling of Wireless Multi-Antenna Channel and Relay Based Communication Systems", submitted by Babu Sena Paul, a research student at the Department of Electronics and Communication Engineering, Indian Institute of Technology Guwahati, for the award of the Doctor of Philosophy, is a record of an original research work done by him under my supervision and guidance. Ratnajit Bhattacharjee for his suggestions, constant encouragement and support during the thesis work.

List of Tables

Nomenclature

Mathematical Notations

List of Publications

Introduction

Outline of the Thesis and Contributions
OUTLINE OF THE THESIS AND CONTRIBUTIONS 5 mobile stations are assumed to be surrounded by uniformly distributed local scatterers. As either

Wireless systems are also witnessing major changes in the nature of the traffic they must deal with. The models were used in obtaining the analytical expressions for the AOA and TOA in terms of the model parameters.

Multi-antenna Channel Modelling

Introduction

Site-specific physical models help with network deployment and planning, while site-independent models are mostly used for system design and testing. The stochastic models are based on the fact that although wireless propagation channels are unpredictable and vary with time, some of its parameters such as angle of arrival (AOA), angle of departure (AOD), time delay profiles, etc. are modeled by statistical means.

Figure 2.1: Channel model classification.

Review of MIMO Channel Models

But in practice the elements of the channel matrix have finite correlations due to the limited spacing between the antennas. The coherence distance gives a measure of the separation between the antennas below which the correlation between the channel elements is significant.

REVIEW OF MIMO CHANNEL MODELS 11

Deterministic models
Geometrically based channel models

In geometry-based single bounce modeling, a wave from the BS(MS) is assumed to reach the MS(BS) after being scattered by a single scatterer. OVERVIEW OF MIMO CHANNEL MODELS 13where N is the total number of scatterers present around the MS.

Figure 2.3: Geometry based one ring model.

REVIEW OF MIMO CHANNEL MODELS 13 where, N denotes the total number of scatterers present around the MS. f n denotes the doppler

Non-geometrical physical models
Independent and identically distributed (iid) model
Kronecker model

Thus, for the iid channel, the correlation matrix is a diagonal matrix, with each element equal to ρ2. Thus, the channel correlation matrix RH can be written as the Kronecker product of the transmitter correlation matrix (RTx) and the receiver correlation matrix (RRx).

Array effects on macrocellular MIMO system capacity

It is assumed that the BS is placed in the origin of the XY coordinate system and the M on the X axis at a distance of 200λ. The minimum distance between two adjacent antennas (d in Fig. 2.4) in the array is kept at λ, the working wavelength.

ARRAY EFFECTS ON MACROCELLULAR MIMO SYSTEM CAPACITY 17

However, when there is misorientation between arrays due to mobility, a combination of other array geometries has been found to perform better than a combination of linear arrays at BS and MS. Performance changes were simulated for all sixteen array combinations, but only four were plotted for better readability.

Table 2.1: Mean and standard deviation of the channel capacity for different antenna configurations at the base station and the mobile station.

MIMO channel modelling from microwave perspective

Geometry based MIMO channel modelling from microwave perspec- tive using scattering matrixtive using scattering matrix

If there are NT transmit, NR receive and N scattering antennas, then the scattering matrix S is a (NT +NR +N)X(NT +NR + N) matrix and the same is first determined. NT +NR + N)X(NT +NR+N)scattering matrix thus obtained is then reduced to (NT +NR)X(NT +NR) matrix by applying appropriate load condition to the N dipoles acting as scatterers. Once the S-matrix is thus obtained, the terminating condition for the scattering dipoles is applied to reduce the scattering matrix to a (NT +NR)X(NT +NR)matrix.

MIMO CHANNEL MODELLING FROM MICROWAVE PERSPECTIVE 21 Table 2.2: Model parameters for Case I

Case I: Two-ring model of MIMO system
Case II: Macrocellular scenario with dual polarised transmitting and receiving antennasreceiving antennas

A macrocellular scenario modeled by the one-ring distribution model is shown in Fig. To study the performance of the dual polarized antenna system, the BS and M ones are assumed to include two co-located half-wavelengths.

Figure 2.7: Two ring model with half wave length dipole antenna as scatterers.

MIMO CHANNEL MODELLING FROM MICROWAVE PERSPECTIVE 23 dipole antennas perpendicular to each other. The antennas BS 1 and MS 1 lie in the same plane and

Mutual coupling and its effect on MIMO system capacity

MUTUAL COUPLING AND ITS EFFECT ON MIMO SYSTEM CAPACITY 25

Coupling matrix for two dipole antennas
Performance of macrocellular MIMO system with the inclusion of mu- tual couplingtual coupling

Dipole antennas have an omnidirectional radiation pattern in the azimuth plane and such antennas are used in many practical communication systems. Therefore, evaluating the mutual impedance effect for a MIMO system composed of dipole antennas would provide some insight into the performance of actual systems.

MUTUAL COUPLING AND ITS EFFECT ON MIMO SYSTEM CAPACITY 27

MUTUAL COUPLING AND ITS EFFECT ON MIMO SYSTEM CAPACITY 29

The space-time cross-correlation function between the main diagonal elements (h11 and h22) of the channel matrix is defined as. Knowing the correlation between different channel paths for different inter-element separations helps in designing MIMO systems with spatial multiplexing or beamforming capabilities.

Fig. 2.11 and Fig. 2.12 gives the plot of the correlation between different paths. It may be observed from Fig

Conclusion

Modelling of Channel Characteristics for Mobile-to-Mobile Communication

Introduction

Model Description

It is also assumed that all scattered rays reaching the receiver have the same power. It is assumed that the distance between transmitter and receiver is large compared to the rays of the scattering regions.

Derivation of Time of Arrival Probability Density Function

An alternative approach to obtain an analytical expression for the TOA pdf for a macrocell scenario by computing the cumulative distribution function (CDF) of the TOA using a geometric basis was presented in [ER99]. pdf TOA is obtained from CDF TOA,Fτ(τ) when differentiated with respect to time delayτ.

Figure 3.2: Shaded regions of scatterers for evaluating TOA CDF.

DERIVATION OF TIME OF ARRIVAL PROBABILITY DENSITY FUNCTION 37

Expressions for TOA pdf for a circular scattering model with uniform distribution of scatterers representing the macrocellular environment can be found in [ER99], which has been reproduced for the sake of equation 3.3.16.

Figure 3.4: Area contributing to the TOA pdf, with M 2 as the transmitter and M 1 as the receiver.

DERIVATION OF TIME OF ARRIVAL PROBABILITY DENSITY FUNCTION 39 of completeness,

Radial distances are obtained by the product of the square root of numbers uniformly distributed between 0 and 1, multiplied by the radius of the distribution circles (R1 for distributions around mobile station M1 and R2 for distributions around mobile station M2). In Fig.

Figure 3.5: Theoretical and simulated density function of TOA for D = 2000m, R 1 = 100m, R 2 = 100m, N N 12 = 1.

DERIVATION OF AOA PROBABILITY DENSITY FUNCTION FOR M2M CHANNEL 41

Derivation of AOA Probability Density Function for M2M channel

Since there is symmetry in the system model about the x-axis, the AOA pdf is symmetric about θ= 0. The AOA CDF is given by the ratio of the number of scatterers that lie within the shaded regions.

DERIVATION OF AOA PROBABILITY DENSITY FUNCTION FOR M2M CHANNEL 45 Combining equation 2 to equation 7 gives,

The above formulation for the AOA pdf has been verified by computer simulation.

Figure 3.10: Theoretical and simulated density function of AOA for D = 500m, R 1 = 100m, R 2 = 100m, N N 12 = 1.

Dual Annular Strip Model (DASM) for M2M communica- tiontion

DUAL ANNULAR STRIP MODEL (DASM) FOR M2M COMMUNICATION 49

DUAL ANNULAR STRIP MODEL (DASM) FOR M2M COMMUNICATION 51

The AOA analysis for the double ring ring model for the M2M channel was performed according to Section 3.4.

DUAL ANNULAR STRIP MODEL (DASM) FOR M2M COMMUNICATION 53

The width of the dome is determined by the outer radius of the annular ring around the receiver and the distance between the transmitter and the receiver. The flat part of the AOA pdf is contributed by scatterers around the emitter, which do not contribute to the domed part.

Figure 3.18: Plots of the theoretical and simulated probability density function of AOA having annular ring of scatterers of equal width around the transmitter and the receiver.

DUAL ANNULAR STRIP MODEL (DASM) FOR M2M COMMUNICATION 55

Conclusion

Relay Based Virtual MIMO System

Introduction

The Nakagami fading model has been considered because of the flexibility it offers in changing the fading statistics of the individual links by changing the parameterm, which is known as the Nakagami parameter [Nak60]. The remainder of the chapter is organized as follows: Section 4.2 discusses the two-hop relay system.

Two hop relay based system

However, in a non-regenerative transmission system, due to the presence of intermediate relay nodes, the statistics of the received signal at the destination depend on the channel conditions of all individual links. In this thesis two-hop relay links are considered where individual links are assumed to be independent but not necessarily identical to distributed Nakagami.

TWO HOP RELAY BASED SYSTEM 59

In a typical two-hop cooperative relay environment, the source transmits the information in a time window T2 and the relay amplifies and retransmits the same information to the destination node in the next time window T2 as shown in Fig.

Figure 4.3: The plot of Nakagami-m distribution for different values of m.

TWO HOP RELAY BASED SYSTEM 61 can be written as,

For the purpose of simulating S-D channel statistics, Nakagami-m channels of individual links were generated using techniques reported in the literature [BC05]. Ω for the Nakagami distributed random numbers generated in this way is 2mσx2, where σx2 gives the variance of the Gaussian distributed RVs.

Figure 4.4: The S-D channel statistics of a two hop relay system.

DIVERSITY COMBINING OF RELAY PATHS 63

Diversity combining of relay paths

4.6 source node S sends a message to both relay nodes R1 and R2 in the first time slot T1. In the second time slot T2, the relay node R1 forwards the message (received in the first time slot T1) to the destination node D, where it is stored in a buffer for later processing.

Figure 4.5: Two branch dual hop relay diversity links.

DIVERSITY COMBINING OF RELAY PATHS 65

Selection combining

SNRVsel|N=1 = max (z1, z2) (4.3.6) The pdf of voltage signal to noise ratio or power signal to noise ratio at the output of the selection combiner is required to evaluate the system performance. In this regard, the pdf of the voltage signal-to-noise ratio is first evaluated by setting the noise power to unity.

Figure 4.8: The block diagram of a selection combiner.

DIVERSITY COMBINING OF RELAY PATHS 67

Maximal ratio combining

But the pdf of the power signal to noise ratio for any arbitrary noise power is of theoretical interest and can be derived from equation 4.3.15. It must be integrated to find the probability density function at the output of the maximum.

Figure 4.11: Block diagram of a two-branch maximal ratio combiner having equal noise power in both the branches.

DIVERSITY COMBINING OF RELAY PATHS 73

Bit error rate performances

The density function at the output of the MRC given by equation 4.3.29 needs to be evaluated numerically for specific values of mi andΩi, where=1,2,.,4. The above integral is numerically calculated to obtain the final density function at the output of the maximum ratio combiner and is shown in Fig.

Figure 4.14: Comparison of bit error rate obtained analytically and through simulation at the output of the selection combiner.

DIVERSITY COMBINING OF RELAY PATHS 75

The target SNR range was taken as 0 - 30 dB and the same range was used for relay SNR as well. From knowing the BER values at different target SNRs for a given SNR at the relay and comparing the same with the BER values for these target SNRs for an ideal relay; the root mean square (rms) error in BER at a given relay SNR was calculated.

Conclusion

CONCLUSION 77 rameter, m. The bit error rates for the two combining schemes (selection combining and maximal

Conclusions

Summary of Contributions
SUMMARY OF CONTRIBUTIONS 79
Tracks for Future Work
TRACKS FOR FUTURE WORK 81 For the relay based system, the analysis has been kept limited to dual-hop two diversity path

It has been found that the average capacity for the said series combination is maximum with minimum standard deviation. The channel statistics of the individual hops of a relay diversity branch are assumed to be Nakagami-mfaded.

Appendix A

S-Parameter

S-PARAMETER 83

If gate 2 is terminated with a load such that V2+ = 0, meaning no reflected signal ie. unity property: for any lossless network, the product of any column of the scattering matrix with the conjugate of that column is unity.

S-PARAMETER 85 Zero Property : The product of any column of the scattering matrix with the complex conjugate

Appendix B

Channel Capacity

Since the channel power is limited, the information capacity of the channel can be defined as C = max. CHANNEL PERFORMANCE 89 where h(n) gives the complex channel gain and is assumed to be stationary and ergodic.

CHANNEL CAPACITY 89 where, h(n) gives the complex gain of the channel and is assumed to be stationary and ergodic

Bibliography

In Proceedings of IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications, volume 1, pages 573–578, September 2005. In Proceedings of IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications, vol. - ume 1, pages 562–567, September 2005.