Performance Analysis Of Mimo Systems For Different Data Traffics.

PERFORMANCE ANALYSIS OF MIMO SYSTEMS FOR DIFFERENT DATA TRAFFICS. Vidya Gogate

Shikha Nema

R.P.Singh

Aditya Goyal

S.A.K.E.C., Chembur,

V.E.S.I.T., Chembur,

MANIT, Bhopal

MANIT, Bhopal

Mumbai University,

Mumbai University,

+91-9223279454

+91-9820589303

[email protected]

ABSTRACT:The uses of multiple transmit and receive antennas (MIMO) have received much attention due to its potential to support large capacity in wireless communication systems [1]. Recently, the MIMO technology has been under investigation for integrating it with the OFDMA and the MCCDMA systems. In this paper, the performance of multi-cell MIMO-MCCDMA and MIMOOFDMA systems are evaluated for three different types of users/traffic. This includes (i) high data rate delay-insensitive users, (ii) high data rate delay-sensitive users, and (iii) low data rate voice users [6]. We have made an attempt to evaluate the performance of the two systems based on system Ergodic capacity at various path loss exponents. As path loss is related to the resource allocation, we propose an idea of adaptive resource allocation for different users in two 4G systems. Ideal situation is considered as Zero path loss exponent. In this situation all the users will get resources allocated. The capacity at this path loss is the maximum. Then path loss exponent is varied and capacity is calculated in each case. The ratio of two capacities gives cell loading factor [9] which is simulated and presented here which can be useful to select the best operating parameters for a particular cell in the system.

Categories and Subject Descriptors C.2.1 Network Architecture and Design Wireless communication

General Terms Algorithms, Performance, Economics, Theory

Keywords MIMO, OFDM, MCCDMA, CELL LOADING FACTOR

1. INTRODUCTION To study the performance of MIMO-OFDMA and MIMO-MCCDMA in multi-cell multiuser downlink scenario, three types of users, each inducing a particular pattern of interference power spectral density (PSD), are selected for evaluation [6]. In OFDMA systems subchannels and in MC-CDMA systems code channels, tend to be occupied by the few strongest users Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ICWET’10,February 26-27,2010,Mumbai, Maharashtra, India.

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depending upon the path loss exponent. The aim is to achieve maximum system capacity to optimize overall performance gain. Therefore study of the performance of TYPE-I users does not consider delay constraint whereas fairness is crucial in TYPE-II users. This type of users can tolerate large delays and high data rate service is assumed. Therefore, the system is optimized without taking any delay constraint into consideration. Fairness is not crucial here and hence most of the subchannels tend to be occupied by the few strongest users. In case of TYPE-II users, one possible way is to impose upper limits on the number of channels assigned to every user [5]. Activity factor of each user in each occupied subband plays a key role in all types of users. Voice users normally refer to those with low-data rate with a regular delay constraint. Since voice users cannot afford large overhead to dynamically allocate the subcarriers and are delay sensitive, they have no CSIT. i.e. channel state information at the transmitter. The subchannel allocation is fixed and the power allocation is uniform. Hence at some instants, some subchannels may have no transmission due to the bursty voice activity of the users. The activity factor (AF) is used to model such phenomenon. 4G systems in discussion here are OFDMA and MCCDMA. MCCDMA is based on multicarrier or OFDM CDMA technology. OFDM converts a frequency selective channel into a parallel collection of frequency flat sub-channels. The subcarriers have the minimum frequency separation required to maintain orthogonality of their corresponding time domain waveforms, yet the signal spectra corresponding to the different subcarriers overlap in frequency. Hence, the available bandwidth is used very efficiently. In MCCDMA, many users with distinct signature code sequence can transmit on same or closely spaced orthogonal subcarriers, further increasing bandwidth efficiency. Multiple antennas can be used at the transmitter and receiver, an arrangement called a multiple-input multiple-output (MIMO) system. A MIMO system takes advantage of the spatial diversity that is obtained by spatially separated antennas in a dense multipath scattering environment. MIMO systems may be implemented in a number of different ways to obtain either a diversity gain to combat signal fading, or to obtain a capacity gain. Main purpose of using MIMO here is to increase capacity [2] depending directly on spatial paths provided which is given by minimum of number of transmit or receive antennas.

2. SPECTRAL EFFICIENCY Spectral efficiency has its origins in Shannon’s theorem that expresses the information carrying capacity of a channel [1] as

C ∧ = BC * 1n(1 + S N )

equation p = min( N t , N r )

(1)

where

Nt

is number of

transmit antennas and Nr is number of receive antennas.

Where Cˆ is the capacity in units of bits per second, Bc is the channel bandwidth in hertz, and S and N are signal and noise powers so S/N is the signal-to-noise ratio (SNR). N is assumed to be Gaussian noise so interference that can be approximated as Gaussian can be incorporated by adding the noise and interference powers and then it is more appropriate to use SIR. Then Shannon’s capacity theorem becomes

With all this information, the actual mutual information of user k, Ck can be expressed as

C = BC 1n[1 + S ( N + I ) ] = BC 1n(1 + SIR )

Where

∧

(2)

Shannon’s theorem cannot be proved [2] but is widely accepted as the upper limit on the information carrying capacity of a channel. So the stronger the signal, or the lower the interfering signal, the greater a channel’s information carrying capacity. Shannon’s second capacity formula tells us that increasing the interference level, and hence resulting in a lower SIR, has a weakened effect on the decrease in capacity than may initially be expected. That is, doubling the interference level does not halve Cˆ. This is the conceptual insight that supports the use of closely packed cells and frequency reuse as the resulting increase in interference and its moderated effect on capacity is offset by having more cells.

3. SPECTRAL EFFICIENCY AND ERGODIC CAPACITY Shannon’s capacity limit for a MIMO system becomes

 γ ( p ) P( p ) / a  Ck = a ∑∑ log 2 1 + k ,b2 k , b ( p )  σ + I k ,b  b p 

(5)

I k( ,pb) is the instantaneous interference power of the

particular subchannel seen by user k,

Pk(,pb ) is the total power

allocated to user k in spatial channel p on subband b in stage 1. The parameter is equal to N S for OFDMA and is equal to the number of codes assigned to user k for MC-CDMA [6].

a

3.1

Activity

Factors

for

K

∑ρ( k , b ) = 1 ; ∀b ∈{1,......, k =1

TYPE-I

N B },

users.

---OFDMA

(6)

K

∑ρ(k , c) =1 ∀c ∈{1,.......

N S },

k =1

C ∧ = Bc 1n(1 + SIR × H ) (3)

MCCDMA (7)

Where H is a MIMO capacity factor that depends on min(M, N) and effectively multiples the SIR. The capacity of a MIMO system [2] with high SIR scales approximately linearly with the minimum of M and N, min (M, N), where M is the number of transmit antennas and N is the number of receive antennas (provided that there is a rich set of paths). Signal to interference ratio is calculated as

of time that user k uses subband b. ρ(k,b) {0,1} means ρ(k,b)=1 if user k uses subband b and 0 otherwise. By using the concept of time-sharing, the range of the indicator functions ρ(k,b) {0,1} and ρ(k, c) {0,1} is relaxed to real numbers within the interval [0, 1] and can be interpreted as time-sharing factors [7].

 γ k( ,pb) • Pk(,bp )  SIR =  2 ( p )  (4)  σ + I k ,b  ( p) ( p) Where γk , b and Pk , b are the channel gain and the power, respectively, of user k in spatial channel p on subband b, σ 2 is the noise power and

_

Ik

is the average PSD of the intercell

ρ( k , b ) ∈[0,1] is the sharing factor indicating the fraction

∈

∈

∈

3.2 Activity Factors for TYPE-II users. For Type II: Delay-Sensitive Users, an additional constraint expressed in terms of the maximum number of channels occupied per user is added to the problem for Type I users. The constraints for the two systems are as follows: NB

OFDMA : ∑ ρ (k , b) ≤ ρ k ,max

∀ k

b =1

interference to user k. This equation is placed in Shannon’s capacity theorem. In case user k occupies more than one subband, its capacity will be sum of the capacities in each subband. This is indicated by

∑ b

. If the system is MIMO, number of

spatial paths available is more than one. Then capacity of each path is to be added for every user. This can be achieved by incorporating

∑ p

where p gives number of spatial paths by

NS

MC − CDMA : ∑ ρ (k , c) ≤ ρ k ,max

∀ k

C =1

Where b indicates subband in OFDMA system and c indicates code channels in MC-CDMA system respectively [7]. N B And N S are the total numbers of subbands of OFDMA and

code channels of MC-CDMA, respectively [3]. Therefore a matrix is generated with sum of rows equal to one as well as sum of columns also as equal to maxlim.

3.3 The path loss model.

orthogonal code in the frequency domain [4]. In this system, a user who is assigned a code channel occupies the whole spectrum. The mutual information of user k is therefore defined as

The path loss model is summarized by

 dk = PB , c  d  0

PB , k , c

−α

   

C

for dk ≥ d0, (8)

where PB,k,c is the average received power from base station B by user k in subcarrier c at a distance dk from B, PB,c is the average received power in subcarrier c at distance d0 from B and depends on the transmit power spectrum of B, and α is the path loss exponent. For dk < d0, Pb,k,c is upper bounded by PB,c in order to avoid unreasonably huge received power for users who are too near to the base station [7].

3.4 The Average Intercell Interference PSD of user k The average inter-cell interference PSD for user k is given by

 dk , j I k = ∑PB j   d j =1  0 _

NI

est MC −CDMA

   γ k( ,pb) ( p)  = ∑∑ ρ (k , c)∑∑ log 2 1 + Pk ,b ,c  _ 2 k =1 c =1 b =1 p =1  σ +  Ik   K

NS

NB N p

(11) Hence, the spreading factor is equal to the number of subcarriers Ns within a subband leading to a total number of Ns codes.

3.5.3 Type III Users They are Voice, or Low Data Rate users. In all simulations for Type III users, the performance is to be evaluated based on different levels of user activity that is characterized by the user activity factor. So equation of Ergodic capacity for these users would be same as that of equation (5).

3.5.4 MIMO CAPACITY

−α

   

indicate different levels of cell overlapping and d 0 is set to 100m.

Each cell is loaded with K mobile users and is interfered by NI external cells. NT transmit antennas and NR receive antennas, where NT ≥ NR, are deployed respectively at each base station and mobile, forming together an NR ×NT MIMO channel, characterizing the effects of path loss, shadowing and smallscale fading, for every subcarrier within subband b. The number of available spatial channels NP for every subcarrier in subband b of user k is almost sure to be min{NT, NR} in a rich scattering environment, i.e. NP = min {NT, NR} for all k = 1. . . K and b = 1…… NB. Number of spatial paths available for particular MIMO is denoted by variable ‘p’ [5].

3.5 Ergodic capacity

4. Cell loading factor.

(9)

Where B j the j-th interfering base station and

PB j is the

average received power per subcarrier from B j at distance

d0 . d

k, j

is the distance of user k from j-th interfering base

station B j [7]. In the numerical results, SNR is used to

We decided to find out cell loading factor [9] for TYPE-I as well as TYPE-II users for all path loss exponents 2, 3 and 4. In order to determine effect of path loss exponent (alpha) on the ratio of It is of practical interest to investigate the performance of both practical and ideal case situation, we obtained Ergodic capacities systems in a multi-cell scenario for different types of traffic and at alpha=0. All users are (ideally) selected for zero path loss evaluate the degree of importance of the individual advantages with 100% resource utilization. Then dividing Ergodic of both systems. capacities at required alpha, we obtained cell loading factor. Then if number of channels allocated per user is varied from one ( p) Np NB K  γ Pk(,bp )  number of allowable channels (that can be to maximum k , b  COestFDMA = NS ρ( k , b). log 2  1 + 2 allocated per user), we observed variation in cell loading factor  σ + I N   b = 1 k = 1 p = 1 k S   loss exponent.   at required path ρ( k ,b )∈[ 0 ,1] 

3.5.1 OFDMA

∑∑

 

) P (k p ,b ≥0

∑

 

(10) The terms in the bracket i.e. product of channel gain and channel power upon noise and intercell interference indicate signal to noise ratio, SNR. For OFDMA it is averaged over number of subcarriers Ns.

3.5.2 MCCDMA In MC-CDMA system, every user transmits a symbol in every subband and each symbol is spread by an Ns-chip long

5. Result and Analysis The effects of path loss, number of antennas and different user types are studied and insightful results are obtained [8]. It is found that OFDMA has a higher system Capacity and goodput for both Type I and Type II high data rate users, while MCCDMA has a higher goodput for Type III users. Compared to MC-CDMA, the goodput of an OFDMA system is more sensitive to the activity factor of the voice users and suffers from noticeable loss. This demonstrates the superiority of the two systems in different practical situations. SNR is taken in decibels. Capacity and Goodput are in bits/s/Hz

5.1- Ergodic capacity for TYPE-I and TYPE-II USERS. In general, multiple antennas increase the actual capacity per channel per user

35

spectral efficiency (bits/s/Hz)

30

TYP E-I US ERS alpha= 3,(Das hed:Ergodic c apac ity ,S olid:Goodput) OF DM A(Nt= Nr=1) Ntx Nr= 1x 1 M C-CDM A (Nt=Nr=1)Ntx Nr= 2x 2 Ntx Nr= 4x 4 OF DM A(Nt= Nr=2) M C-CDM A (Nt=Nr=2) OF DM A(Nt= Nr=4) M C-CDM A (Nt=Nr=4)

While Capacity increases linearly with the number of antennas, in MC-CDMA systems, the increase appear less than linear in OFDMA systems, unlike Type-I users. This is due to the inherent conflict between the spatial diversity and the multiuser diversity. Increasing the number of antennas effectively reduces the effect of fading for every subcarrier and therefore fluctuation of channel gain in the frequency domain. When the numbers of antennas are large, due to the fairness constraint, multiuser diversity can not be exploited by subcarrier allocation and the growth of capacity tends to be linear.

25 20 15 10 5 0 10

12

14

16

18

20 22 s nr(db)

24

26

28

30

FIG 1- Ergodic capacity of Type I users with path loss exponent =3, Nt x Nr=1x1, 2x2, 4x4 but at the same time reduces the fluctuation of small-scale fading among users.

9 8

Due to the fairness constraint for Type II users, the resources of OFDMA and MC-CDMA will be allocated to more number of users, than Type I users. In this scenario, the intrinsic difference between OFDMA and MC-CDMA on system performance in the multicell environment is more noticeable.

On the other hand every MC-CDMA user occupies the whole band and multiuser diversity can not be exploited in this way. For all number of antennas, OFDMA exhibits better performance than MC-CDMA. Performance gap seems fairly constant with respect to number of antennas and depends upon SNR only.

5.2 Ergodic Capacity for TYPE-III users It is plotted Vs activity factors instead of SNR as in TYPE-I and TYPE-II users. In this case, all the six neighboring cells and the home cell are assumed to have the same value of activity factor. The performance will be evaluated based on different levels of user activity.

T Y P E -II U S E R S a lp h a = 3 , (D a s h e d : E rg o d ic c a p a c it y , S o lid : G o o d p u t ) O F D M A (N t = N r= 1 N) t x N r= 1 x 1 N t x N r= 2 x 2 M C -C D M A (N t = N r= 1 ) N t x N r= 4 x 4 O F D M A (N t = N r= 2 ) M C -C D M A (N t = N r= 2 ) O F D M A (N t = N r= 4 ) M C -C D M A (N t = N r= 4 )

TY P E -III U S E R S a lp h a = 2 N t x N r= 1 x 1 1.4

1.2 1.1 spectral efficiency (bits/s/Hz)

spectral efficiency (bits/s/Hz)

7 6 5 4 3 2

1 0.9 0.8 0.7 0.6

1 0 10

c a p -o fd m a g o o d p u t-o fd m a c a p -m c -c d m a g o o d p u t-m c -c d m a

1.3

0.5

12

14

16

18

20 22 s n r(d b )

24

26

28

30

FIG 2- Ergodic capacity of Type II users with path loss exponent =3, Nt x Nr=1x1, 2X2, 4X4 Without the fairness constraint, multiple antennas not only reduce the effectiveness of multiuser diversity in user selection for users having the same path loss, but at the same time magnify the effect of path loss on user selection. Those users with severe path loss will be excluded due to their increased chance of not being selected.

0.4 0 .2

0.3

0.4

0 .5 0 .6 0 .7 0.8 A c t ivity F a c t o r (A F )

0.9

1

FIG 3- Type III users with path loss Exponent =2, Nt x Nr=1x1. Performance of both the systems drops when the AF is small. As the number of active users is small, despite the fixed total power constraint, under fixed subchannel allocation, it leads to fewer subchannels to allocate the power. Hence a decrease in capacity and goodput is observed.

T Y P E -I U S E R S a lp h a = 4 N t x N r= 1 x 1 C E L L L O A D IN G F A C T O R

TY P E -III U S E R S a lp h a = 3 N tx N r= 4 x 4

1

8

o fd m a m c -c d m a

0.8 0.7 0.6

6 cell loading

spectral efficiency (bits/s/Hz)

7

0.9

c a p -o fd m a g o o d p u t -o fd m a c a p -m c -c d m a g o o d p u t -m c -c d m a

5

0.5 0.4 0.3

4

0.2 0.1

3 0 2 0.2

0 .3

0 .4

0.5 0.6 0 .7 0 .8 A c t ivit y F a c t o r (A F )

0 .9

0

2

4

6 8 10 12 N u m b e r O f C h a n n e ls

14

16

1

FIG 4- Ergodic capacity of Type III users with path loss exponent =3, Nt x Nr=4X4. The capacities increase about linearly with the number of antennas, but the goodput of MC-CDMA increases more rapidly than that of OFDMA as the number of antennas increase.

5.3 Cell loading factor

FIG 5- Cell loading factor of Type I users with path loss exponent =4, NB= NC=1…16 Cell loading factor for TYPE-I as well as TYPE-II users for all path loss exponents 2, 3 and 4 is obtained and shown in the results. As the number of subbands and number of code channels increase, cell loading factor increases and never exceeds value 1. T Y P E -II U S E R S a lp h a = 4 N t x N r= 1 x 1 C E L L L O A D IN G F A C T O R

Resource allocation i.e. number of channels allocated per user will play important role in deciding the cell loading factor. Numbers of subbands (OFDMA) and number of code channels (MC-CDMA) allocated per user are varied from minimum to maximum depending upon the path loss exponent. Also note that number of subbands or code channels allocated per user differs from one type of user to another as per the change in activity factor.

1 0.9

o fd m a m c -c d m a

0.8

cell loading

0.7

The cell loading factor (f) is the convenient way to express the amount of potential capacity being used. As path loss is related to the resource allocation, we propose an idea of adaptive resource allocation for different users in two 4G systems. Ideal situation is considered as Zero path loss exponent. In this situation all the users will get resources allocated. The capacity at this path loss is the maximum. Then path loss exponent is varied and capacity is calculated in each case. The ratio of two capacities gives cell loading factor [9] which is simulated and presented here which can be useful to select the best operating parameters for a particular cell in the system.

0.6 0.5 0.4 0.3 0.2 0.1 1

2

3

4 5 6 N u m b e r O f C h a n n e ls

7

8

FIG 6- Cell loading factor of Type II users with path loss exponent =4, NB= NC=1…8 If f is equal to 0.5, interference in the system is equal to the thermal noise level. Its value less than 0.5 implies that the system is noise limited, whereas f greater than 0.5 indicates that the system is interference limited. With optimum resource allocation, for maximum users for that path loss exponent, a value of ‘f’ is observed to be closer to 1.

6. Conclusion

[3] Syed Ali, Ki-dong Lee, Victor Leung , “Dynamic Resource

In this paper, the MIMO technique is studied for the fourth generation wireless communication system. OFDM is a multicarrier-based technique for mitigating ISI i.e. inter-symbol interference; originated from multipath propagation and the inherent delay spread, to improve capacity in the wireless system with spectral efficiency. MIMO systems promise to increase capacity and performance proportionally with the number of antennas .By simulation we get the results of the performance due to different factors.

Allocation in OFDMA Wireless Metropolitan Area Networks.”, IEEE Wireless Communications , February 2007.

The study showed that 1. The performance difference depends heavily on the path loss exponent and the number of antennas, as well as the intercell interference. 2. Resource allocation i.e. number of channels allocated per user will play important role in deciding the cell loading factor. 3. As Path loss exponent increases, maximum number of subbands allocated per user, which is nothing but the resources, reduces. This is because as user goes away from BS, path loss increases, reducing path gain which in turn decreases Ergodic capacity at that path loss exponent. 4. When number of subbands allocated per user goes down it results in small cell loading factor. When all the selected users get allocated maximum number of subbands for that path loss exponent, cell loading factor approaches one. These graphs can be useful to select the best operating parameters for a particular cell in the system.

7. References [1] Michael Steer,” Beyond 3G”, IEEE Microwave magazine, February-2007.[5] W.C.Y. Lee, “Spectrum efficiency in cellular [radio],” IEEE Trans. Vehicular Technol., vol. 38, no. 2, May 1989. [2] A. Goldsmith, S.A. Jafar, N. Jindal, and S. Vishwanath, “Capacity limits of MIMO channels,” IEEE J. Select. Areas Commun., vol. 21, no. 5, pp. 684–702, June 2003. .

[4]Mathias Bohge, James Gross, Adam Wolisz, Dynamic Resource Allocation in OFDM Systems.”, IEEE Network, JANUARY/FEBRUARY, 2007. [5]L.Badia, Andrea Baiocchi, Alfredo Todini, “On the Impact of Physical layer Awareness on scheduling and Resource Allocation in Broadband Multicellular IEEE802.16 SYSTEMS.”, IEEE Wireless Communications, February 2007 [6] Adaptive Resource Allocation and Capacity Comparison of Downlink Multiuser MIMO-MC-CDMA and MIMO-OFDMA Ernest S. Lo, Student Member, IEEE, Peter W. C. Chan, Vincent K. N. Lau, Senior Member, IEEE, Roger S. Cheng, Member, IEEE, K. B. Letaief, Fellow, IEEE, Ross D. Murch, Senior Member, IEEE, and Wai Ho Mow, Senior Member, IEEE, IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 3, MARCH 2007 [7] Performance Comparison of Downlink Multiuser MIMOOFDMA and MIMO-MC-CDMA with Transmit Side Information - Multi-Cell Analysis Peter W. C. Chan, Ernest S. Lo, Student Member, IEEE, Vincent K. N. Lau, Senior Member, IEEE, Roger S. Cheng, Member, IEEE, K. B. Letaief, Fellow, IEEE, Ross D. Murch, Senior Member, IEEE, and Wai Ho Mow, Senior Member, IEEE IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 6, JUNE 2007 8] Book- Contempary communication systems using MATLAB by John Proakis, M asoud Salehi, Gerhard Bauch; Thomson publications. [9] Book-“ Evolution of …2G to 3G “ by Vijay P. Garg ,TMH Publications And many more …………..