1. ENHANCEMENT OF DIVERSITY GAIN IN
MIMO SYSTEM
SUNJEEV KUMAR GUPTA
Telecommunication Department of Nepal Telecom (NTC),
URL: www.ntc.net.np, Kathmandu, Nepal
E-mail: sk.gupta@ntc.net.np /4u.gupta@gmail.com, Tel: +977-9855068555
Abstract- In wireless Environment the signal is Antenna separation: With wider separations between
propagating from transmitter to receiver along number of transmit antennas and between receive antennas, there is a
different paths collectively called multipath causing three greater time difference among the various signal receiver can
effects: path loses, microscopic and macroscopic fading which
more easily distinguish between those paths and recover the
can be mitigated by different diversity techniques. Multiple-
Input-Multiple-Output (MIMO) on the front exploits spatial
data with fewer errors than with closed spaced antennas.
diversity by having several transmit and receive antenna, each Signal path knowledge: To coordinate the decoding of
receive antenna sees different versions of transmitted signal and transmitted signals, and to adjust the transmitted signal for
when this versions are combined in a proper manner, the
impairment in the signal path, additional information must be
outcome has better quality (lower bit-error-rate, BER) or higher
date rate than a single version of signal. Specifically, if the communicated between transmitter and receiver. For this,
number of multi path components exceeds certain value, the transmitter sends a “training signal” in addition to the normal
increment of channel capacity can be proportional to the data content, to enable synchronization of the receiver with
number of transmit and receive antennas and no additional all transmitted channels. But these signals can consume a
power or bandwidth is required. In this paper, I strongly focus significant portion of total data stream when operation is in a
on spatial receiving antenna diversity concept accomplishing difficult propagation environment with deep, rapid
Diversity processing technique called Maximum Ratio propagation changes.
combining (MRC), in which output signals from diversity
antennas are weighted by their respective SNR, Co-phased and Equipment complexity: The enhance performance of
added to optimize the received signal power or Signal-to Noise MIMO comes at the cost of complexity. Each channel
Ratio (SNR) which is one of the key features that constitute the requires most of a transmitter’s and receiver’s circuitry-
performance improvement of MIMO system. modulator through power amplifier in a transmitter, LNA
through demodulator in a receiver.
1. INTRODUCTION
MIMO is the single frequency system uses space –time 2. RECEIVING ANTENNA DIVERSITY
diversity, transmitting different portions of data via separate CONCEPT
antennas. These multiple signals are summed at the receiver The multiple propagation paths of the mobile signal to the
to recover the entire data stream. Because transmitted data is radio base station antenna results in short term or fast fading
divided among two or more channels, the net data rate can be of the signal. This multiple path propagation channel often
higher than a single channel, single antenna system. The referred to as a Rayleigh fading channels experiences large
difficulty is that the channels use same frequency-the drops in received signal strength. So one technique to
separation is accomplished by the different time delays as the mitigate these short-term fades is receiving antenna diversity
signal travels between transmit antenna and each receive in which the signals received over different antenna/channels
antenna [1]. are combined properly to increase the probability that the
There is some functional similarity to Orthogonal received signal is of adequate strength. The basic principle of
Frequency Domain Multiplexing (OFDM) which also divides antenna diversity is that multiple antenna outputs experience
the data into multiple channels. However, in OFDM, different signals due to the different channel conditions and
channels are separated in frequency and phase but are these signals are only partially correlated. Thus, it is highly
transmitted by a single transmitter and antenna. The biggest likely that if one antenna is of deep fade then the other one is
differences are that OFDM requires more bandwidth for its not and provides sufficient signal, because in multipath
total signal, while MIMO requires more antennas, with a propagation conditions, as encountered with a blocked or
separate transmitter and receiver for each antenna. The key shadowed direct line-of-sight(LOS) path, each receive
factors that influence a MIMO system are: antenna experiences different fading environments. Diversity
antennas provide three major benefits [2] as: Reliability is
improved in multipath channels where interference from

2. reflected signals causes fading of the received signal. The 4. MAXIMUM RATIO COMBINING
fade level experienced on average for a given outage (MRC)
probability is decreased through diversity. The overall
Maximum ratio combining is a method of diversity
received signal power is increased and it allows us to use
combining in which the signals from each channel are added
lower transmit power for a given level or reliability. This
together, the gain if each channel is made proportional to the
decreases interference, increase battery life and reduces the
rms level and inversely proportionally to mean square noise
probability that a hostile party will intercept the signals.The
level in that channel and the different proportionality
diversity technique in this case I prefer is spatial diversity
constants are used for each channel, so as to call it as ratio-
where main goal is to obtain uncorrelated signals.
squared combining and predetection combining as a optimum
combiner for independent Additive White Gaussian Noise
3. MATHEMATICAL DERIVATION
(AWGN) channels [3].
OF RECEIVING DIVERSITY
I assumed x(1) and x(2) are the received signal voltages r1
from a two antennas diversity scheme and these signal at the a1
receiver are passed to a combining or processing system to
reduce channel distortion such as fading and co-channel
interference creating a signal x(t). The amount of reduction in r2 a2
signal fading or diversity gain on x(t) depends on two
properties: the cross correlation and the relative signal
strength levels between the received signals x1(t) and x2(t).
The average received signal strength at each of the antenna Receiver
branches can be expressed as: Adder Detector
P1 = E {[x1(t)] ^2} and P2 = E {[X2 (t)] ^2}
Where E is the expectation and I can also define the
complex cross correction between the signals as follow:
rL aL
It is also further related to envelope cross correlation Phase Attenuators
between the signals with the complex cross correlation: Shifters
Fig. 1 L- Branch antenna diversity receiver (L=5). With MRC, the
attenuation/amplification factor is proportional to the signal amplitude ai=ri
for each channel i.
By assuming that the received signals have a Rayleigh- It obtains the weight that maximizes the output SNR that is
distributed envelope and randomly distributed phase. Under it is optimal in terms of SNR. Writing the received signal at
those definitions, typically good diversity gain is said to be the arra9ty elements as a vector x (t) and the output signal as
possible when the received signals satisfied the following two r (t):
conditions, power imbalance and low correlation: X (t) = h (t) u (t) + n (t)
h = [h0, h1………..h N-1] T
n = [n0, n1……….n N-1] T
As further, we can also obtain a close form expression for r (t) = WHX = WHhu(t) + WHn.
the envelope correlation as the function of power correlation
Since the signal u (t) has unit average power, the
for the correlated Rayleigh channel:
instantaneous power SNR is:
Where E () is the complete elliptical integral of second
kind.

3. The noise power in the demodulator is given by: Rayleigh channel, the real and imaginary part of hi are
H 2 H H 2 H 2 2 Gaussian distributed having mean µhi = 0 and variance σ2hi =
Pn = E {|W n| } = W E{nn } W = σ W INW = σ ||W||
1/2. The channel experienced by each receive antenna is
Where IN represents an N*N identity matrix. Since independent from the channel experienced by the other
constant do not matter, one should always scale W such that receive antennas. On each receive antenna, the noise n has
||W|| = 1. The SNR is therefore given by: the Gaussian probability density function with
By the Cauchy-Schwarz inequality, this has a maximum
when W is linearly proportional to h i.e. W = h The noise on each receive antenna is independent from the
noise on the other receive antennas. In the presence of
channel hi, the instantaneous bit energy to noise ratio at ith
receive antenna is |hi|2 Eb / N0 that is:
γi = |hi|2 Eb / N0
6. A MRC EQUATION PATTERN
WITH AWGN
On the ith receive antenna, the received signal is,
The output SNR is therefore the sum of the SNR of yi = hi x + ni
each element. The best a diversity combiner can do is to Where yi is the received symbol on the ith receive antenna,
choose the weights to be the fading to each element. Since
matched filter is effectively used, from above equations, the hi is the channel on the ith receive antenna, x is the
expected value of output SNR is therefore N times the transmitted symbol and ni is the noise on ith receive antenna.
average SNR at each element, i.e. Expressing it in matrix form, the received signal is,
E {γ} = N γ y = hx +n where
Which indicates that on average, the SNR improves by a T
y= [y1, y2……..yN] is the received symbol from all the
factor of N, this is significantly remarkable improvement at receive antenna, h= [h1, h2……..hN] T is the channel on all the
total SNR at the receiver side having N multiple antennas [4]. receive antenna, x is the transmitted symbol and n = [n1,
n2…….nN] T is the noise on all the received antenna [5].
5. ASSUMPTION MADE FOR MRC
CALCULATION The equalized symbol is:
Channel is a flat fading Rayleigh Multipath channel, the
modulation is BPSK and noise added is purely Additive
White Gaussian Noise (AWGN). In Rayleigh fading model,
the phase of each path can change by 2π radian when the
delay τn (t) changes by 1/fc. If is fc is large, relative small
It is intuitive to note that the term,
motions in the medium can cause changes of 2π radians.
Since the distance between the devices are much larger than
the wavelength of the carrier frequency, it is reasonable to
assume that the phase is uniformly distributed between 0 and
2π radians and the phases of each path are independent. Here
I assumed large number of paths, applying central limit This is the sum of the channels powers across all the
theorem, each path can be modeled as circularly symmetric received antennas.
complex Gaussian random variable with time as variable
which is inferred as Rayleigh fading channel model. 6. B EFFECTIVE Eb/No WITH MRC
Some constraints assumed as: In the presence of channel hi, the instantaneous bit energy
to noise ratio at ith receive antenna is:
I have assumed N received antennas, channel is flat
fading, the channel experienced by each receive antenna is γi = |hi|2 Eb / N0
randomly varying in time. For ith receive antenna, each Given that I am equalizing the channel with hH with the N
transmitted symbol gets multiplied by a randomly varying receive antenna case, the effective bit energy to noise ratio is:
complex number hi. As channel under consideration is a

4. The above expression shows effective bit energy to noise
ratio in a N receive antenna case is N times the bit energy to
noise ratio for single antenna case.
7. A SIMULATIONS RESULTS FOR
SNR IMPROVEMENT WITH MRC
Computing SNR improvement considering following
parameters as input to the Mat lab script [6]:
Fig. 2 Parameters
Symbol (n) = 10^4
Modulaiton: BPSK
Receiving antennas (N) = 10
Channel: Rayleigh fading channel
Noise: AWGN
Diversity combining: MRC
Fig. 3 Parameters Fig. 2 Effective SNR improvement with MRC using N =10 in Rayleigh
fading channel.
Symbol (n) = 10^4
Modulaiton: BPSK
Receiving antennas (N) = 30
Channel: Rayleigh fading channel
Noise: AWGN
Diversity combining: MRC
7. B SIMULATION INTERPRETATION
As seen to the simulations figures, it is concluded that
for the BPSK modulation along with increasing number of
receiving antenna, the performance of optimized signals (or
SNR) is enhanced. Considering other parameters constraints,
as increasing the receiving antennas, the signal to noise ratio
(SNR) is drastically increased, as shown in Figure 2. But the
ratio of increasing SNR when receiving antennas are
increasing from 10 to 30 is not same proportional to the
initial increments N = 10 as shown in figure 2 and 3. In figure
3. The increments when N increases from 10 to 20 results
only 3dB increment of SNR, Like wise 3dB more when N
increases from 20 to 30 as shown in figure 3. This strongly
signifying that large increase of receiving antennas do not
results same proportional increment of SNR because of
circuit complexity.
Fig. 3 Effective SNR improvement with MRC using N =30 in Rayleigh
fading channel.

5. 8. A EFFECTIVE BIT ENERGY TO
NOISE RATION WITH MRC
From above 6. A, I have calculated effective bit energy
to noise ratio in a N receive antenna case is N times the bit
energy to noise ratio for single antenna case:
Computing Eb / N0 improvement considering following
parameters as input to the Mat lab script:
Fig. 4 Parameters
Symbol (n) = 10^6
Modulaiton: BPSK
Receiving antennas (N) = 1
Channel: Rayleigh fading channel
Noise: AWGN
Diversity combining: MRC Fig. 4 Eb / N0 measurement with MRC using N =1 in Rayleigh fading
channel.
Fig. 5 Parameters
Symbol (n) = 10^6
Modulaiton: BPSK
Receiving antennas (N) = 3
Channel: Rayleigh fading channel
Noise: AWGN
Diversity combining: MRC
8. B SIMULATION INTERPRETAITON
As seen in the simulations results, it is concluded that
for BPSK modulation with MRC in Rayleigh fading channel,
effective bit energy to noise ratio is enormously increased
approximately to the N times to the increasing number of
receiving antennas without significant increasing Bit Error
Rate. As shown if figure 3. It is found that for receiving
antenna N = 1, effective bit energy to noise ratio is 16 dB
with Bit Error Rate 10^ -1.2 but when number of receiving
antennas is increased upto N = 3, effective bit energy to noise
ratio is enormously increased upto the level 34 dB. Thus, this
value of bit energy to noise ratio is (N-0.87) times the bit
energy to noise ratio for single antenna case which is
approximately supporting theoretical calculation of bit energy
to noise ratio as calculated above. On other side, The Bit
Error Rate is 0.2 which shows its significance on increasing
receiving antennas is tolerable and can be comprised in
MIMO system when Diversity Gain is prime factor to Fig. 5 Eb / N0 improvement with MRC using N =3 in Rayleigh fading
increase. channel.

6. 9. CONCLUSIONS
In this paper, I have proposed Maximum Ratio combining
(MRC) as a spatial diversity which is one of the promise techniques
of Diversity Gain that constitute the performance improvement of
MIMO system. Considering both theoretical and practical research
data, it is concluded that outcome of signal at receiving side has
better quality, tolerable Bit Error Rate or higher data rate than a
single receiving antenna that signify that increment of channel
capacity is proportional to the number of receiving antennas without
additional power or bandwidth requirement. From the simulation
results, it is said that both signal to noise ratio and effective bit
energy to noise ratio are enormously increased with the increment of
number of receiving antennas under BPSK modulation, Rayleigh
fading channel, Additive White Gaussian Noise (AWGN)
considered to be constraints parameters for simulation
computation.
10. REFERENCES
[1] Technical Report on MIMO and Related Diversity techniques
improves wireless range and reliability, from June 2007 high
frequency electronics, LLC.
[2] Alfred Grau Besoli, “Influence of Reconfigurable antenna
Parameters on the Diversity gain in fading MIMO parameters
on the Diversity gain in fading MIMO environments”,
university of California, Iravine, 2005.
[3] Analog and Digital Transmission, Diversity, from Wireless
Communication.NL URL.
[4] R. Janaswamy, Radiowave Propagation and Smart Antennas for
Wireless Communications, Kluwer Academic Publishers, 2000.
[5] Google Search on www.dsplog.com .
[6] Use of Language of Technical Computation “MATLAB” for
simulation results.