Unit-3

Diversity Techniques
(1)Repetition coding and time diversity:
(i)Repetition coding:

In modern broadband wireless access systems such as mobile worldwide

interoperability for microwave access (WiMAX) and others, repetition coding is
recommended for the lowest modulation level repetition coding as a time-
diversity technique using maximum ratio combining (MRC) and proposes
techniques to define and to calculate the repetition coding gain G r and its effect
on bit error rate (BER) under the two fading conditions.
In modern wireless communication networks such as 3G long-term
evolution and WiMAX, modulation and coding are adapted to the fading
condition of the channel, typically to the received signal-to-noise ratio (SNR)
fed back to the base station by the subscriber station. This adaptive modulation
and coding (AMC) scheme is usually designed to maximize the system average
spectral efficiency over the whole fading range while maintaining a fixed given
target bit error rate (BER). In order to maintain a constant ratio of bit energy-to-
additive white Gaussian noise (Eb/N0). For a given target BER, the system can
achieve high average spectral efficiency by transmitting at high rates for high
channel SNR and at lower rates for poorer channel SNR.
Repetition coding (RC) with the number of repetition times x = {2, 4, 6}
is also applied to QPSK for diversity gain in order to protect vital control
information during deep fading. Thus, the scheme forms a discrete set of
combined modulation and coding specified by the corresponding standard.
Diversity channel model for repetition coding in OFDMA systems In the AMC
zone of an OFDMA frame in IEEE802.16e sub channels are formed from
grouping of adjacent subcarriers.
Adjacent subcarrier allocation results in sub channels which are suitable
for frequency non-selective and slowly fading channels, e.g., lognormal
shadowing. In an OFDMA system, the basic unit of resource allocation in the 2-
D frequency-time grid is the slot being 1 sub channel in frequency by 1, two or
three OFDM symbols in time. More slots can be concatenated to accommodate
larger forward error correction (FEC) encoded data blocks. Since repetition
coding repeats the same encoded data block in different contiguous slots in the
AMC zone, it can be assumed that the MRC gain from combining repeating
signals is predominantly via micro diversity reception in which all repetition
sub channels experience the same shadowing having N(μZ, σZ2) distribution.
 Effect of repetition coding on BER and effective repetition coding gain
Repetition coding for QPSK in WiMAX
An improvement in BER is equivalent to a saving in signaling power required
to combat deep fades in order to maintain the given target BER. Since in the
AMC scheme in mobile WiMAX, and repetition coding of 6, 4, and 2 times is
recommended only for rate ½ QPSK modulation and coding . it is important
that we first derive accurate closed-form formulas for BER of QPSK signals
from an MRC combiner and the corresponding RC gain when the wireless
system operates in lognormal shadowing and in composite Rayleigh-lognormal
fading environments.
(ii)Time diversity:

Another approach to achieve diversity is to transmit the desired signal in M

different periods of time, i.e., each symbol is transmitted M times. The intervals
between transmissions of the same symbol should be at least the coherence time
so that different copies of the same symbol undergo independent fading.
Optimal combining can also be obtained with the maximum ratio combiner. We
notice that sending the same symbol M times is applying the (M,1) repetition
code. Actually, non-trivial coding can also be used. Error control coding,
together with interleaving, can be an effective way to combat time selective
(fast) fading.

Figure 1. Time Diversity

Advantages of time diversity:

 Not require increased transmit power.
Disadvantage of time diversity:
 Decrease the data rate.
(2)Frequency and space diversity:

To combat fading, there are two commonly used approaches:

(i) frequency diversity

(ii)space diversity.

(i)Frequency diversity:

Frequency diversity relies on the fact that the fading is different at different
frequencies. It is sometime said that it is not correlated. Hence when there is a
fade at one frequency, there may not be a fade at another. To make use of this,
you simply transmit your signal on two frequencies, perhaps 100KHz apart. At
the receiving end, a circuit measures the signal-to-noise ratio in two receivers
and automatically selects which is best at any instant in time. This works well
but... it is rather inefficient to have the same information transmitted on two
frequencies.

One approach to achieve diversity is to modulate the information signal through

M different carriers. Each carrier should be separated from the others by at least
the coherence bandwidth so that different copies of the signal undergo
independent fading. At the receiver, the L independently faded copies are
“optimally” combined to give a statistic for decision. The optimal combiner is
the maximum ratio combiner, which will be introduced later. Frequency
diversity can be used to combat frequency selective fading.

Figure 2.1. Frequency diversity

(ii)space diversity:

Another approach to achieve diversity is to use M antennas to receive M

copies of the transmitted signal. The antennae should be spaced far enough
apart so that different received copies of the signal undergo independent fading.
Different from frequency diversity and temporal diversity, no additional work is
required on the transmission end, and no additional bandwidth or transmission
time is required.

However, physical constraints may limit its applications. Sometimes, several

transmission antennae are also employed to send out several copies of the
transmitted signal. Spatial diversity can be employed to combat both frequency
selective fading and time selective fading.

Figure 2.2. Space Diversity

(3)Receiver Diversity:
System Model
In receiver diversity the independent fading paths associated with multiple
receive antennas are combined to obtain a resultant signal that is then passed
through a standard demodulator. The combining can be done in several ways
Which vary in complexity and overall performance. Most combining techniques
are linear: the output of the combiner is just a weighted sum of the different
fading paths or branches, as shown in Figure for M-branch diversity.
 Figure 3: Linear equal combiner
Specifically, when all but one of the complex α is are zero, only one path is
passed to the combiner output. When more than one of the αi’s is nonzero, the
combiner adds together multiple paths, where each path may be weighted by
different value. Combining more than one branch signal requires co-phasing,
where the phase θi of the ith branch is removed through the multiplication by αi
= aie−jθi for some real-valued ai. This phase removal requires coherent detection
of each branch to determine its phase θi. Without co-phasing, the branch signals
would not add up coherently in the combiner, so the resulting output could still
exhibit significant fading due to constructive and destructive addition of the
signals in all the branches. The multiplication by αi can be performed either
before detection (predetection) or after detection (post detection) with
essentially no difference in performance. Combining is typically performed
post-detection, since the branch signal power and/or phase is required to
determine the appropriate αi value. Post-detection combining of multiple
branches requires a dedicated receiver for each branch to determine the branch
phase, which increases the hardware complexity and power consumption,
particularly for a large number of branches. There are two types of performance
gain associated with receiver space diversity: array gain and diversity gain.
For example, suppose there is no fading so that ri = √Es for Es the energy per
symbol of the transmitted signal. Assume identical noise PSD N0 on each
branch and pulse shaping such that BTs = 1. Then each branch has the same
SNR γi = Es/N0. Let us set ai = ri/√N0: we will see later that these weights are
optimal for maximal-ratio combining in fading. Then the received SNR is

MEs
γΣ =(¿ ¿ =¿ ¿ = N 0
This SNR increase in the absence of fading is referred to as the array gain. More
precisely, array gain Ag is defined as the increase in averaged combined SNR
γΣ over the average branch SNR γ:
γΣ
Ag= γ
In fading the combining of multiple independent fading paths leads to a more
favorable distribution for γΣ than would be the case with just a single path. In
particular, the performance of a diversity system, whether it uses space diversity
or another form of diversity, in terms of P s and Pout is as defined as
∞

Ps=∫ ps(γ)p γΣ(γ)d γ

0

Where Ps(γ) is the probability of symbol error for demodulation of s(t) in

AWGN with SNR γΣ, and
γ0

Pout=p(γΣ<=γ0)=∫ p γΣ(γ)d γ,
0

The maximum diversity order of a system with M antennas is M, and when the
diversity order equals M the system is said to achieve full diversity order.

(4) Concept of diversity branches and signal paths:

(i) Diversity branches:

1. When the noise in the diversity branches is not identically distributed, we can
still perform MRC, as long the relative noise levels (also known as the noise
power profile) are known.
2. When the diversity branches are not identical and the noise power profile is
not known, the receiver can simply use equal gain combining (EGC). The
received signals in different branches will only be co-phased but not amplitude
scaled.
3.A pilot-tone (or tones) can be inserted into the transmitted spectrum to assist
the MRC and EGC receivers to coherently combined the IF signals in the
different branches the BEP in fading channels with infinite number of
time/frequency diversity branches equals the BEP in AWGN channel.
4. In some diversity systems, the decision variable D after combining has a
characteristic function.
∅ D(s) = [p1p2/(s-p1)(s-p2)]N
Which is the N-th power of QsΦ? This occurs when all the diversity branches
are independent and have identical statistics. The fading gains in the different
diversity branches are independent Increasing the number of diversity branches
from two to three will give much less gain than going from one to two, and in
general increasing M yields diminishing returns in terms of the SNR gain. The
average combiner SNR increases linearly with the number of diversity branches
additional diversity branches can significantly reduce average BER, even when
the SNR on these branches is somewhat low.

(ii)Signal paths:

One of the most powerful techniques to mitigate the effects of fading is to use
diversity-combining of independently fading signal paths. Diversity-combining
uses the fact that independent signal paths have a low probability of
experiencing deep fades simultaneously. Thus, the idea behind diversity is to
send the same data over independent fading paths. These independent paths are
combined in some way such that the fading of the resultant signal is reduced.
For example, consider a system with two antennas at either the transmitter or
receiver that experience independent fading. If the antennas are spaced
sufficiently far apart, it is unlikely that they both experience deep fades at the
same time. By selecting the antenna with the strongest signal, called selection
combining, we obtain a much better signal than if we just had one antenna.
This chapter focuses on common techniques at the transmitter and receiver to
achieve diversity. Multiplexing is obtained by exploiting the structure of the
channel gain matrix to obtain independent signaling paths that can
be used to send independent data.

(5)Combining methods:

(i)Selection combining:

In selection combining (SC), the combiner outputs the signal on the branch with
the highest SNR r2i /Ni. This is equivalent to choosing the branch with the
highest r2 i + Ni if the noise power Ni = N is the same on all branches Since
only one branch is used at a time, SC often requires just one receiver that is
switched into the active antenna branch. However, a dedicated receiver on each
antenna branch may be needed for systems that transmit continuously in order
to simultaneously and continuously monitor SNR on each branch. With SC the
path output from the combiner has an SNR equal to the maximum SNR of all
the branches. Moreover, since only one branch output is used, co-phasing of
multiple branches is not required, so this technique can be used with either
coherent or differential modulation.
The combiner output is given by
Y(t)= Ae jθs(t)+z(t),with A=max{A0,A1,……AM-1}
The received SNR can be written as follows:
Γ=A2Eb/N0 =max{ Γ0, Γ1, ….., ΓM-1}
With uncorrelated branches, the CDF of is
M−1

PΓ(γ )= PΓ{ Γ<γ }= ∏ P Γi(γ )

i=0

For i.i.d branches, we have

PΓ(γ )=[ PΓ0(γ )]M , and PΓ(γ )=M PΓ0(γ )[ PΓ0(γ )]M-1

Fig: selection combining

Fig: selection combining in Rayleigh fading channel

(ii)Threshold combining:

SC for systems that transmit continuously may require a dedicated receiver on

each branch to continuously monitor branch SNR. A simpler type of combining,
called threshold combining, avoids the need for a dedicated receiver on each
branch by scanning each of the branches in sequential order and outputting the
first signal with SNR above a given threshold γT . As in SC, since only one
branch output is used at a time, co-phasing is not required. Thus, this technique
can be used with either coherent or differential modulation. Once a branch is
chosen, as long as the SNR on that branch remains above the desired threshold,
the combiner outputs that signal. If the SNR on the selected branch falls below
the threshold, the combiner switches to another branch. There are several
criteria the combiner can use to decide which branch to switch to [5]. The
simplest criterion is to switch randomly to another branch. With only two-
branch diversity this is equivalent to switching to the other branch when the
SNR on the active branch falls below γT . This method is called switch and
stay combining (SSC). The switching process and SNR associated with SSC is
illustrated in Figure. Since the SSC does not select the branch with the highest
SNR, its performance is between that of no diversity and ideal SC.

(iii)Maximal ratio combining:

In SC and SSC, the output of the combiner equals the signal on one of the
branches. In maximal ratio combining (MRC) the output is a weighted sum of
all branches, so the αis in Figure are all nonzero. Since the signals are
co phased, αi = aie−jθi , where θi is the phase of the incoming signal on the ith
branch. Thus, the envelope of the combiner output will be

Fig: maximal ratio combining

The combiner output is given by

M−1

Y(t)= ∑ w iri(t)
i=0
Choose the weights to be the channel gain conjugate [must be estimated]
M−1 M−1
-jθ
y(t)= ∑ A ie i ri(t) = ∑ A ie -jθi[Aie -jθis(t)+zi(t)]
i=0 i=0

M−1 M−1

=( ∑ A i2)s(t)+ ∑ A ie -jθ iz i(t)

i=0 i=0

The SNR of the combined signal is

γ
PΓ(γ )=1- ie - −γ M

∑
( γ 0)
i−1

γ0 i=1 ( i−1)

(6)Equal gain combining:

Equal-Gain Combining Diversity Various techniques are known to combine the
signals from multiple diversity branches. In Equal Gain Combining, each signal
branch weighted with the same factor, irrespective of the signal amplitude.
However, co-phasing of all signal is needed to avoid signal cancellation.

Figure:L-branch antenna diversity receiver (L= 5).

Thus, EGC is simpler to implement than Maximum Ratio Combining(MRC).

The adaptively controller amplifiers / attenuators are not needed. Moreover, no
channel amplitude estimation is needed.
 Figure:L-branch Equal Gain Combining antenna diversity receiver (L= 5).

BER performance

When wireless signals travel from a single transmit antenna to multiple receive
antennas they experience different fading conditions. While signal from one
path may experience a deep fade the signal from another path may be stronger.
Therefore selecting the stronger of the two signals (selection combining,
threshold combining) or adding the signals (equal gain combining, maximal
ratio combining) would always yield much better results (lower bit error rate).
However, there must be sufficient spacing between the different receive
antennas for the received signals to be dissimilar (uncorrelated). In the
simulation below we consider a 1-Tx, 2-Rx scenario. The signals arriving at the
two receive antennas are added together before detection

(7)Performance analysis for Rayleigh fading channels:

Rayleigh fading is a statistical model for the strong influence of a propagation
environment on a radio signal, used by wireless communication devices
Rayleigh fading models consider that the magnitude of a signal that has passed
through a transmission channel or medium will vary often and in a random
manner, or fade, according to a Rayleigh distribution- the radial component of
the addition of two uncorrelated Gaussian random variables. For wireless
communications, the envelope of the received carrier signal is Rayleigh
distributed; such a type of fading is called Rayleigh fading. This can be caused
by multipath with or without the Doppler Effect.
Rayleigh fading is most applied in situations when there is less or no dominant
propagation along a line of sight between the transmitter and receiver.
According to the central limit theorem, if there is sufficiently too much
scattering, the impulse response of the channel can be modeled well as a
Gaussian process, not bothering about the distribution of the individual
components Absence of a dominant component to scatter clearly indicates that
the process will have zero mean and phase evenly distributed between 0 and 2π
radians. The envelope of the channel response will therefore be known as a
Rayleigh distributed one. Calling this random variable R, it will have a
probability density function
𝑃𝑅𝑟 =2𝑟Ω𝑒−𝑟2Ω, ≥0 where Ω= 𝑅2
In the multipath case, when the dominant signal becomes weaker, such as in the
non LOS case, the received signal is the sum of many components that are
reflected from the surroundings.

BPSK And QPSK Modulation Schemes

Phase shift keying technique is a process that conveys information or data by

modulating the phase of a reference signal which is also called as the carrier
wave. PSK has an envelope which is constant, and thus the requirements of the
transmitter power amplifier are made simple. The bandwidth efficiency of PSK
is much more than FSK and more power efficient than ASK and FSK. In BPSK,
the carrier signal has constant amplitude but its phase is switched between two
values, which are separated by π, to represent 0 and 1, respectively BPSK (also
sometimes called PRK, Phase Reversal Keying, or 2PSK) is the simplest form
of phase shift keying (PSK). Two phases are made use here which are separated
by 180 degrees and so can also be termed as 2-PSK. BPSK is functionally
equivalent to 2-QAM modulation.

QPSK is also known as quaternary PSK, quadriphase PSK, 4-PSK, or 4-QAM.

QPSK uses four points on the constellation diagram, equispaced around a circle.
With four phases, QPSK helps to encode two bits per symbol; with gray coding
so that the bit error rate (BER) can be minimized-sometimes it is misperceived
as twice the BER of BPSK. The mathematical analysis shows that QPSK can be
used either for doubling the data rate compared with a standard BPSK system
while maintaining the same bandwidth of the signal, or to maintain the data rate
of BPSK but halving the requirement of bandwidth needed. In the latter case,
the BER of QPSK is exactly the same as the BER of BPSK and deciding
differently is a common chaos when QPSK is considered or described. the
advantage of QPSK over BPSK becomes very clear and evident: QPSK
transmits twice the data range in a given bandwidth when compared to BPSK at
the same BER and QPSK transmitters and receivers are very much complicated
than the ones for BPSK.

The BER performance of MIMO OFDM systems in Rayleigh fading channels

has been analyzed with two basic different modulation schemes (BPSK and
QPSK). After comparing the simulation result obtained by plotting the Bit Error
Rate against the Signal to Noise Ratio (SNR), we get the following two results.

Fig: – SNR Vs BER Plot for BPSK Modulation in Rayleigh Fading Channel
Fig – SNR Vs BER Plot under BPSK Modulation in a Rayleigh Fading Channel
for a MIMO-OFDM System

Fig – SNR Vs BER Plot under QPSK Modulation in a Rayleigh Fading Channel
for a MIMO-OFDM System