63

CHAPTER 3

MIMO-OFDM DETECTION

3.1 INTRODUCTION

This chapter discusses various MIMO detection methods and their

performance with CE errors. Based on the fact that the IEEE 802.11n channel

models have high SFCF, a low complexity method of implementing the MIMO-

OFDM detectors is proposed with no significant performance degradation. The

performance analysis is based on simulation which was done for the TGn sync

proposal and with various MIMO detection algorithms. The effect of CE on the

system performance is also studied.

The chapter is organized as follows, the first section discusses the

simple MIMO system model with a flat fading channel between the transmitter

and receiver antenna pair. In section 3.3.2 various MIMO detection methods are

employed for the system model established and the performance of the schemes

are discussed with simulations. Section 3.4 discusses the system model of the

MIMO-OFDM system and a low complexity method of implementing the MIMO

detectors with representative results. In section 3.5, the performance of the TGn

sync system with various CE schemes discussed in chapter 2 is discussed with

various MIMO detectors. Finally the performance of the TGn system in terms of

packet error rate (PER) is obtained by simulations for the low complexity method.

64

3.2 MIMO SYSTEM MODEL

A simple MIMO system model shown in Figure-3.1 is established for

discussing the MIMO detection algorithms and to extend the idea to the MIMO-

OFDM system. In Figure-3.1 a system with Nt transmit and Nr receive antennas is

shown. Let us assume that Nt=Nr=2 as it is the mandatory mode of operation in the

802.11n proposals.

The two streams of incoming bits are modulated to symbols and

transmitted simultaneously from the two antennas. According to the flat fading

channel assumption, there is a single tap between every transmit-receive antenna

pair. The channel taps are Rayleigh distributed and independent of each other. The

AWGN is added at the front end of the receiver. The received signal on the two

antennas are passed into the MIMO detector block, whose function is to separate

out the spatially combined signal transmitted from the multiple antennas, with the

knowledge of the channel coefficients. The output of the MIMO detector block is

passed through the demodulator for obtaining the bits. In these spatial

multiplexing systems, no explicit orgthogonalization or coding is necessary at the

transmitter for signal decorrelation; instead the propagation medium with rich

multipath scattering can be used at the receiver for separating out the spatially

combined transmitted streams (Arogyaswami Paulraj et al, 2003).

MOD

MOD

b1(n)

b2(n)

Demod

MIMO

Detector

Demod

w1

w2

h11

h22

h21

h12

Figure 3.1: A simple 2x2 spatial multiplexing MIMO system

x1(n)

x2(n)

x’1(n)

x’2(n)

b’1(n)

b’2(n)

65

The received signal in the matrix form is written as,

1 11 12 1 1

2 21 22 2 2

( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )

y n h n h n x n w ny n h n h n x n w n⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤

= +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

(3.1)

1

( ) ( ) ( ) ( )tN

i ii

y n h n x n w n=

= +∑ (3.2)

Where ( )y n is the Nrx1 vector of received signal, ( )ih n is the ith

column of the MIMO channel matrix whose elements are Rayleigh distributed,

( )ix n is the symbol transmitted from the ith transmit antenna in the nth symbol

time and ( )iw n denotes the Nrx1 AWGN vector. The channel information is

needed at the receiver for the MIMO detector to decode the streams.

3.3 MIMO DETECTORS

The MIMO detectors which are popular in the literature (David Tse,

2005) and used in practice are decorrelator, MMSE, successive interference

cancellation (SIC), VBLAST, ML method. The decorrelator and the MMSE are

linear MIMO detectors, whereas the rest of the methods mentioned are non linear

methods.

3.3.1 Decorrelator

The received signal vector in equation (3.2) can be written as given

below, where kx is the desired data stream and it faces interferences from the

remaining k-1 streams. The index for symbol period is dropped for simplicity.

k ik ii k

y h x h x w≠

= + +∑ (3.3)

The interference faced by the kth data stream from the remaining

streams can be perfectly cancelled by projecting the received signal onto the

subspace orthogonal to the one spanned by 1 2 1 1, ... , ... tk k Nh h h h h− + . Let kV be the

basis of the new subspace. The signal vector after projection is given by

66

' 'kk k ky y h x w= = +V V (3.4)

The demodulation of the kth stream can be performed by match filtering

on the signal to get the unquantized estimate of the data symbol on the kth stream,

,k uqx and quantization is finally applied to obtain data symbol on the kth stream,

kx , which is given below,

( ) ( )

( ),

,

'H H

k uq k k kk k k k

k k uq

x h h x h w

x Q x

= +

=

V V V (3.5)

The combination of projection operation followed by the matched filter

is called the decorrelator or zero forcing (ZF) detector. A simple formula for

demodulating all the streams at once, is given by

† †uqx x w= +H H H (3.6)

where ( ) 1† H H−=H H H H , is the pseudo inverse of H. The ZF detector suffers from

noise enhancement especially in the lower SNR range as it tries to completely null

out the interference without regard to the loss in energy of the desired stream.

3.3.2 Linear MMSE

As we have already discussed, since the decorrelator completely

cancels out the interference, it performs better in higher SNR range. On the other

hand, the matched filtering or maximal ratio combining receiver tries to maximize

the output SNR of the desired stream. The matched filtering receiver performs

well in the lower SNR case where the AWGN is dominant and in the higher SNR

range it suffers from heavy inter-stream interference. Thus, there exists a tradeoff

between completely eliminating the inter-stream interference and preserving as

much energy content of the stream of interest. The linear detector which optimally

combines the decorrelator and the matched filter is the MMSE detector, which is

shown in the Figure-3.2.

67

The objective function of the MMSE MIMO detector is given by,

{ }2 2arg min arg minuqE x x E x w x⎧ ⎫

= − = + −⎨ ⎬⎩ ⎭V V

V VH V (3.7)

Using Wiener-Hopf equation and solving for the optimal solution leads to the

MMSE solution matrix given by

12

2H n

opt mmses

σσ

−⎛ ⎞

= = +⎜ ⎟⎝ ⎠

V V H H H I (3.8)

The data symbols transmitted on all the streams, x is obtained as follows,

( )

12

2

( )

H H Hnuq mmse

s

uq

x y y

x Q x

σσ

−⎛ ⎞

= = +⎜ ⎟⎝ ⎠

=

V H H I H (3.9)

From the MMSE solution matrix given in equation (3.8) it can be

observed that at higher SNR values it is very close to the pseudo inverse of H

matrix, which is the decorrelator. On the other hand, for lower SNR values, the

solution is close to the HH, which is the MRC or matched filtering. Thus, the

MMSE detector performs better compared to the ZF detector; however, the SNR

of operation is required for obtaining the solution matrix.

3.3.3 Successive interference cancellation (SIC)

The SIC is a non linear MIMO detection scheme in which a linear

detector is used to decode a stream and subtract it off from the received vector and

detect the next stream and this process continues till all the data streams are

detected. Thus, at each stage the number of interfering streams decreases. The SIC

Vmmse y x w= +H

x

uqx

- + mine

Figure 3.2: A simplified MMSE detector

( ).Q x

68

scheme is explained in the flow chart shown in Figure-3.3. The post detection

SNR of the ith data stream is defined as,

{ }2

22

i

iin

E x

Wρ

σ= (3.10)

For the linear detection schemes, the post detection SNR remains the

same for all the streams. However, for the SIC method, the post detection SNR of

the stream increases in each stage and it is lower bounded by their corresponding

post detection SNR obtained without interference cancellation. Thus, the

performance of the SIC scheme is better compared to its corresponding linear

detection scheme. It is assumed that the stream detected at each stage is perfect,

however, the wrong decisions may lead to error propagation. The SIC scheme

Input , yH

( )

( )( )

†

†

r

is the ith row of matrixwith dimension N x1

i i i

i i

i i i

W

W

x Q W y

=

=

H

H

STOP

[ ][ ]

1

i+1

where is the ith column of matrix

is obtained by makingzeroing columns 1,2,...i+1 of H

ii i i

i

y y x+ = − H

H H

H

Figure 3.3: Flow chart of the SIC – Decorrelator

i=1; H1=H

Is i = Nt Yes

No

i=i+1

69

described here follows an arbitrary ordering; for instance, order can be from

stream 1 to Nt.

3.3.4 VBLAST The order in which the streams are detected in the SIC impacts the

performance as it might lead to error propagation. The VBLAST detection scheme

is same as the SIC method except that it follows an order for detection of the

streams at each stage. It is also called as ordered SIC (OSIC). It is proved in

(Wolniansky et al, 1998) that by simply choosing the best iρ at each stage in the

detection process leads to the globally optimum ordering.

The ZF-VBLAST scheme is shown in the flow chart in Figure-3.4, in

which the ZF scheme is used for detection. The MMSE-VBLAST is also an

ordered SIC, in which the MMSE filter is used for detecting the streams and the

ordering is based on the maximum post detection SINR (Hufei zhu, 2004). The

stream which corresponds to the minimum value in the main diagonal of the

matrix, 12

2H n

s

σσ

−⎛ ⎞

+⎜ ⎟⎝ ⎠

H H I is detected first and the effect of that stream is removed

from the received signal and process is iterated to get all streams. The MMSE-

VBLAST has the advantage of both MMSE detection and optimal ordering in the

SIC maximizing the output SINR at each stage and hence it performs better than

the ZF-VBLAST.

3.3.5 Maximum likelihood detection

The objective function of the maximum likelihood detection is given as

2

argminMLx

x y x= −H (3.11)

Where x takes all possible combinations of all symbols from all

streams. The ML method is the optimal and it chooses the transmit symbol vector

70

which minimizes the Euclidean norm between the received signal and all possible

combinations of constellations from multiple transmit antennas. The number of

possible combinations is given by MtN , where M is the constellation size. The

search space increases exponentially with number of antennas and the

constellation size. Though the ML method is the optimal, it is computationally

complex.

Input: H, r

Intialization i=1

( )

†1

2

1 1arg minj

jk

=

=

G H

G

( )ii

k i kW = G

Where ( )i

i kG correspond to

the ki th column of Gi

ii

Tikky W r=

( )i ik ka Q y=

( )1

†1

ii

i

i i k k

i k

r r a+

+

= −

=

H

G H

Where †

ikH is the matrix obtained

by zeroing columns k1,k2..ki of H

{ }( )

1 2

2

1 1, ..

arg minj

i i jj k k k

k + +∉

= G

Is i = Nt

STOP

i=i+1

Figure 3.4: Flow chart of the VBLAST scheme

Yes

No

71

3.4 MIMO-OFDM SYSTEM

The simplified MIMO-OFDM system is shown in Figure-3.5 with

Nt=Nr=2. The incoming symbols are made into a block of size N, where N is the

number of subcarriers and OFDM symbols are constructed and transmitted from

the 2 antennas. The received signal is obtained by passing the transmitted signals

through the multipath channels and AWGN is added at the receivers.

At the receiver, the typical OFDM receiver operations are done in the

two antennas separately to obtain the frequency domain signals. The MIMO

detector is applied at each subcarrier to detect the data transmitted on that

subcarrier. Thus, the MIMO-OFDM system can be viewed as N parallel MIMO

systems with flat fading channel coefficients and the detection has to be

performed on each subcarrier independently (Allert Van Zelst, 2004). The system

forms the basis for the IEEE 802.11n standard proposals.

3.4.1 Mean square error of detection

The mean square error (MSE) between the transmitted data symbols

and the output of the detection algorithm is a good measure for the performance of

MIMO detection algorithms though there is no simple relation with BER or PER.

Since the MSE can be derived for the MIMO detection algorithms, we use the

MSE as performance metric for comparing the various MIMO detection

Figure 3.5: MIMO-OFDM system

h11(n)

w1(n)

w2(n)

h22(n)

h21(n)

h12(n)

s/p

I F F T

p/s

s/p

I F F T

p/s

Multipath channel

CP

CP

CP

s/p

F F T

p/s

s/p

F F T

p/s

MIMO Detector

1 ( )X k

2 ( )Y k

1( )Y k

CP 2 ( )X k

2 ( )X k

1( )X k

72

processes. However, the entire system performance result including the effects of

the encoder etc., can be obtained in terms of the BER and PER and we also show

these simulation results in section 3.4.4. It has been seen in simulations and in

other studies that a reduction in MSE leads to a reduction in the BER. The system

model is shown in Figure-3.5. The MSE is given as follows,

{ }2( ) ( )MSE E x n x n= − (3.12)

The closed form MSE for the decorrelator and the MMSE detector is

derived in Appendix 2 and is given as follows,

{ }H HdecorrMSE E w w= V V (3.13)

( ){ } ( ){ } ( ){ }2 2 2 21 2 32 Remmse t u t u t n t uMSE N N E trace G N E trace G N E trace Gσ σ σ σ ⎡ ⎤= + + − ⎣ ⎦

(3.14)

3.4.2 Low complexity MIMO detection

In a MIMO-OFDM system with N subcarriers typically, we need to

employ N independent MIMO detectors. The system complexity increases with

the increasing number of antennas and particularly in OFDM systems, the

complexity is still more as we might need to employ N parallel MIMO detectors.

In this work, a low complexity solution for a certain type of MIMO

detectors is proposed. The idea is to reduce the number of MIMO detectors

applied for detecting the data in all the subcarriers. As previously discussed, the

IEEE 802.11n channel models have significant amount of correlation across

subcarriers. This frequency correlation among the adjacent subcarrier can be used

to reduce the complexity of the MIMO-OFDM system. Since the channel matrices

for adjacent subcarriers are similar, instead of independently employing MIMO

detectors in all the subcarriers, only the solution for the MIMO detector on

alternate subcarrier positions are found. The solution for the other subcarriers is

73

found by interpolating the solutions obtained for the neighboring subcarriers.

Linear interpolation using weights which are simple to implement can be used.

Let k-1 and k+1 be the subcarrier positions where the direct solution for

MIMO detection is obtained and let k be the subcarrier position in which the

solution is obtained by linear interpolation as given by,

1 1

2k k

k− ++

=V VV (3.15)

Where Vk is the matrix solution for MIMO detection. If the number of complex

multiplications is L for a single MIMO detector, the number of complex

multiplications for applying the MIMO detector independently on each subcarrier

is NxL and with this low complexity method, it becomes (NxL)/2. Thus, there is a

50% reduction in the complexity when compared to the normal MIMO-OFDM

detection methods. Another notable advantage of this method is that there is no

need for the channel estimates on alternate subcarriers. This idea can be used for

ZF, MMSE, MMSE-SIC, ZF-SIC detection method. It cannot be directly applied

to the VBLAST based detection schemes, since the order in which the detection is

performed varies for each subcarrier.

3.4.3 Complexity comparison

The computational effort needed for the MIMO detectors so far

discussed is shown in the Table-3.1. The number of complex multiplications

tabulated here is calculated by considering detection on all the streams and on all

the N subcarrier (Mohammed Alamgir, 2003). The computations required for

various MIMO detection methods is plotted for 2,3,4 transmit and receive

antennas is plotted in Figure-3.6. The value of N assumed is 56.

The decorrelator/ZF solution is the pseudoinverse of the channel

matrix. The MMSE solution requires matrix multiplications and a normal matrix

inverse. The number of complex operations of the MMSE method is less than that

74

of the ZF since the pseudoinverse requires more computations. The non-linear

methods such as ZF/MMSE-VBLAST require more amount of computations as

compared to linear methods as SIC is done and the ordering and filters need to be

calculated for every transmit stream, but as the iteration progresses the number of

complex operations per iteration decreases, because of the reduced (deflated)

channel matrix as there is a decrease in inter-stream interference. The ZF-

VBLAST requires more complexity than the MMSE-VBLAST for the reason

mentioned earlier (Pseudoinverse requires more complexity than normal

inversion). From Figure-3.6 it can be seen that the low complexity detectors LC-

ZF/LC-MMSE have almost half the complexity reduced because of using

interpolated solutions. The complex operations for finding the interpolated

solutions are also included, however, the complexity is drastically reduced, since

the linear interpolation (or) simple averaging doesn’t increase the computations.

The ML detection requires huge amount of complexity which increases

exponentially with more number of transmit and receive antennas since the search

space increases drastically. Thus, ML is generally not preferred for

implementation as compared to other non linear schemes like ZF/MMSE-

VBLAST.

Table 3.1: Complexity comparison

MIMO detector No. of. Complex operations

Decorrelator ( )2 3 25 22r t t tN N N N N+ +

MMSE ( )3 2 25 t t r tN N N N N+ +

LC-ZF ( )2 3 25 222 r t t t t rN N N N N N N+ + +

LC-MMSE ( )3 2 252 t t r t t rN N N N N N N+ + +

ZF-VBLAST ( )2 3 2

15 22

tN

r ti

N N i i N=

⎛ ⎞+ +⎜ ⎟

⎝ ⎠∑

MMSE-VBLAST ( )3 2 2

1

5tN

r ri

N i N i N i=

⎛ ⎞+ +⎜ ⎟

⎝ ⎠∑

75

3.4.4 Simulation results and discussion

This subsection presents the simulation results for the MIMO detection

algorithms discussed so far and the effect of CE on the system performance. The

system model assumed for the simulation is shown in Figure-3.5. As already

discussed, the MIMO detection schemes discussed in section 3.2 is applicable to

the MIMO-OFDM system at the subcarrier level. The system parameters used are

given as follows; the number of subcarriers, N is 64, the CP 16 samples, the

bandwidth is equal to 20MHz, and QPSK modulation is used. The TGn channel

model D in NLOS condition is considered here. All results are obtained for 10000

independent realizations of channel and AWGN. Ideal synchronization is assumed

between the transmitter and the receiver.

The MSE of the MIMO detection scheme for a 2x2 system is shown in

Figure-3.7 for decorrelator/ZF, MMSE, ML, VBLAST-ZF and VBLAST-MMSE

detection methods. From the figure it can be observed that the MSE performance

2 3 40

2

4

6

8

10

12

14

16

18x 104

No.of. Antennas Nt=Nr

No.

of. C

OM

PLE

X M

UL

and

AD

D

ZFLC-ZFMMSELC-MMSEZF-VBLASTMMSE-VBLAST

Figure 3.6: Comparison of computational complexity for various MIMO detection schemes

76

of the ML detector is better than that of all the other schemes. However, the ML

method is computationally complex. The MSE of the ZF detector is directly

proportional to the noise variance and it decreases linearly as the Eb/No increases.

The MMSE detector has a small value MSE in lower Eb/No region compared to

that of the ZF detector since it does not lead to noise enhancement. However, as

Eb/No increases, the MSE tends to approach the MSE of the ZF detector. This is

because in the higher Eb/No region, the performance degradation is mainly due to

inter stream interference. The VBLAST-ZF/MMSE has better MSE performance

compared to the normal ZF/MMSE method because of the OSIC.

A similar plot for 4x4 system is shown in Figure-3.8. It can be

observed from the figure that VBLAST-ZF & VBLAST-MMSE perform well.

This is because the OSIC for 4 streams cancels the interference in successive

stages to get more diversity advantage as discussed in section 3.3.

0 5 10 15 20 25 30 3510-6

10-5

10-4

10-3

10-2

10-1

100

101

102

Eb/N0 in dB

MS

E

ZFMMSEVBLAST-ZFVBLAST-MMSEML

Figure 3.7: MSE performance of various MIMO detection schemes for 2x2 system in channel D, NLOS

77

0 5 10 15 20 25 30 3510-4

10-3

10-2

10-1

100

101

102

Eb/N0 in dB

MS

E

ZFMMSEVBLAST-ZFVBLAST-MMSE

Figure 3.8: MSE performance of various MIMO detection schemes for 4x4 uncoded system in channel D, NLOS

Figure 3.9: MSE performance of various low complexity MIMO detection schemes for 2x2 uncoded system in channel D, NLOS

0 5 10 15 20 25 30 3510-3

10-2

10-1

100

101

102

Eb/N0 in dB

MS

E

LC-ZFLC-MMSEZFMMSE

78

The MSE performance of the low complexity MMSE and decorrelator

is plotted in Figure-3.9. The figure shows that the low complexity

MMSE/decorrelator method performs very close to normal MMSE/decorrelator

method till a point in SNR of 10 dB and has an error floor thereafter and it is

because of using the interpolated solutions on alternate subcarrier positions as

explained in section 3.4.

The BER performance of the MIMO detection schemes is plotted in

Figure-3.10. We can observe that the performance of the MIMO detection

schemes in BER terms is in accordance with their MSE performance i.e., the order

in which the schemes perform is same both in terms of the BER and the MSE. The

LC-ZF/LC-MMSE detector performs close to ZF/MMSE till about 15dB of Eb/N0

and has an error floor of 10-2 in BER, which is quite high. Thus, the LC-ZF/LC-

MMSE are not suitable for uncoded systems, however, it performs well in IEEE

802.11n systems which will be discussed in later sections.

0 5 10 15 20 25 30 3510-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N0 in dB

BE

R

ZFMMSEVBLAST-ZFVBLAST-MMSEMLLC-ZFLC-MMSE

Figure 3.10: BER performance of various MIMO detection schemes for 2x2 uncoded system in channel D, NLOS

79

The performance of the system is affected by the errors in CEs. The

following simulation results show the effect of different CE schemes on the

system performance in terms of BER. The preamble used here is of the TO type

which is discussed in chapter 2. The estimation schemes used are LS, LMMSE,

TMMSE with complex weights, and LCCE. The MMSE MIMO detector is used.

The BER plot for 2x2 system for the different CE schemes is shown in Figure-

3.11. The BER performance of the system with LMMSE CE scheme is very close

to that of the system with ideal estimation and TMMSE3 with complex weights

and LCCE schemes have almost similar effect on the BER performance which is

quite closer to that of the LMMSE CE. The LS CE results in 3 dB loss in system

performance compared to that of the ideal estimation.

3.5 TGn SYNC SYSTEM

This section discusses the TGn sync proposal for 802.11n (TGn sync

proposal, 2004). We study the effect of CE on the system performance using the

LC-ZF/LC-MMSE MIMO detection methods.

0 5 10 15 20 25 30 35 40 4510-5

10-4

10-3

10-2

10-1

100

SNR per Rx.antenna in dB

BE

R

IdealLSLCCELMMSETMMSE

Figure 3.11: BER performance of MMSE detection with different CE schemes for 2x2 system in channel D, NLOS

80

3.5.1 System model

The system model of the TGn sync proposal is shown in the Figure-

3.12. The mandatory mode requires the use of 2x2 antennas in a 20 MHz

bandwidth.

The transmitter architecture with 2 spatial streams in the basic MIMO

mode is shown in Figure-3.12.1. In the basic MIMO mode the number of spatial

streams is equal to the number of transmit antennas. The scrambled information

bits are first passed through a convolutional encoder from which the other rates

are derived by puncturing. The output of the puncturing block feeds the coded bits

into the spatial parser (SP), which creates several spatial streams in a round robin

fashion. The frequency interleaver interleaves the bits to be loaded in one OFDM

symbol for subcarriers and constellation positions as given in the standards. The

interleaved bits are then mapped to constellation points. The resulting QAM

symbols are fed as a block of data to the IFFT to create the time domain signal.

Frequency interleaver across 48 data tones

Frequency interleaver across 48 data tones

Modulation

mapper

Modulation

mapper

S / P

Channel encoder

+ puncturring

IFFT (20MHz) 48 – data 4 - pilots

IFFT (20MHz) 48 – data 4 - pilots

Insert

GI

Insert

GI

RF BW

~17MHz

RF BW

~17MHz

Figure 3.12.1: TGn sync transmitter – 2 Tx., 20 MHz BW

Remove GI

FFT

(20MHz)

FFT

(20MHz)

MIMO Detector

Modulation De-mapper

Deinterleave S C

Depuncture +

Viterbi decoder

Remove GI

Modulation De-mapper

Deinterleave

Figure 3.12.2: A typical receiver for TGn sync – 2x2, 20 MHz BW

81

The pilot tones are also inserted in the frequency domain. The cyclic prefix (CP) is

inserted in the time domain and the windowing of the OFDM symbols is also

performed in the time domain.

A typical receiver for a 2x2 system is shown in the Figure-3.12.2. The

CP is removed from the received signal on the two antennas, which are then

passed through the FFT block to create a frequency domain signal. The received

signal on each subcarrier from the two antennas is passed through the MIMO

detector, which separates out the transmitted streams. Demodulation is done on

each stream, followed by the deinterleaving operation. The spatial combiner (SC)

multiplexes the two streams in a round robin fashion and the bits or the soft values

are passed through the viterbi decoder after suitable depuncturing, which is then

passed through the descrambler to obtain the information bits.

3.5.2 Effect of CE on system performance

In the previous section, we have discussed the effect of CE on the

uncoded MIMO-OFDM systems and the performance of the low complexity

MIMO detection schemes. It is very important to know the amount of

performance degradation due to the CE in terms of BER and PER for IEEE

802.11n. The TGn sync proposal is taken as reference. The CE schemes

considered here are the LS, LMMSE, LCCE and TMMSE. The performance

measure of the system is presented in terms of both BER and PER. The PER is

defined as the ratio between the number of packets received with alteast one bit

error to the total number of packets transmitted. The CEs are obtained from

HTLTF symbols as outlined in the earlier chapter.

3.5.3 Simulation results and discussion

The simulation model used is given in Figure-3.13. and the simulation

parameters are summarized in Table 3.2. The IEEE 802.11n TGn sync channel

model is used and ideal synchronization is assumed.

82

Table 3.2: Simulation parameters

Parameter Value

CR ½

Modulation QPSK

Nt x Nr 2x2

Payload 1000 bytes

The BER and PER performance of all the MIMO detection scheme is

plotted in Figure-3.14 and 3.15. From Figure-3.14 it can be seen that the order in

which the schemes perform better is the VBLAST-MMSE, MMSE, VBLAST-ZF

and the ZF detector. The MMSE detector performs better than the VBLAST-ZF in

coded system, whereas in uncoded system VBLAST-ZF performs slightly better

than the MMSE detector The same trend is observed in the PER plot shown in

Figure-3.15. Of all the schemes discussed here, the MMSE detector has a

reasonable performance both in terms of BER and PER with less computational

complexity compared to other non-linear schemes and it is used in most practical

system implementations. In practice a PER of 10-2 is considered to be a good

operational point. It can be seen that all the schemes except ZF offers 10-2 within

20dB of Eb/N0.

TGn sync Tx

TGn sync Rx.

Channel Estimation using

preambles

Info bits

Est bits

Figure 3.13: Simulation model

Channel

83

5 10 15 20 25 3010-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N0 in dB

BE

R

ZFMMSEZF-VBLASTMMSE-VBLAST

Figure 3.14: BER performance of various MIMO detection schemes for 2x2 TGn sync system in channel D, NLOS

0 5 10 15 20 25 3010-4

10-3

10-2

10-1

100

Eb/N0 in dB

PE

R

ZFMMSEZF-VBLASTMMSE-VBLAST

Figure 3.15: PER performance of various MIMO detection schemes for 2x2 TGn sync system in channel D, NLOS

84

The BER and PER performance of the LC MMSE/ZF scheme with

BPSK modulation for 2x2 case is shown in the Figure-3.16 and 3.17. From the

BER, PER performance plots it can be observed that the LC MMSE/ZF perform

very close to ZF/MMSE schemes. An error floor less than 10-5 and 10-2 in BER

and PER, respectively, is observed for the LC MMSE/ZF schemes. Thus, the LC

MMSE/ZF does not have performance loss in the useful Eb/N0 region but has a

50% reduction in complexity. The results follow similar trend for 3x3 and 4x4.

The following simulation results show the effect of different CE

schemes on the system performance in terms of BER and PER. We use LS,

LCCE, TMMSE, and LMMSE CE schemes for the TGn sync preamble with

MMSE MIMO detector. The BER and PER performance for 2x2 system for the

different CE schemes in channel D, NLOS are plotted in Figure-3.18 and Figure-

3.19. From Figure-3.18 it can be observed that the LMMSE CE scheme has the

performance very close to that of the ideal CE. The TMMSE with complex

0 5 10 15 20 25 3010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N0 in dB

BE

R

ZFMMSELC-ZFLC-MMSE

Figure 3.16: PER performance of LC-MIMO detection schemes for 2x2 TGn sync system in channel D, NLOS

85

weights and the LCCE schemes have almost similar effect on the BER

performance which is quite close to that of the LMMSE CE. The LS CE results in

a 2.75 dB loss in performance compared to that of the ideal CE.

From Figure-3.19 it can be seen that at 10-1 PER the LC CE leads to a

performance loss of about 2.5 dB, the LCCE and RMMSE schemes perform

almost same having a loss less than 1 dB, and the performance of LMMSE

scheme is almost close to that of the ideal CE.

0 5 10 15 20 25 3010-4

10-3

10-2

10-1

100

Eb/N0 in dB

PE

R

ZFMMSELC-ZFLC-MMSE

Figure 3.17: BER performance for various CE schemes with MMSE detection for 2x2 TGn sync system in channel D, NLOS

86

Figure 3.19: PER performance of LC MIMO detection schemes for 2x2 TGn sync system in channel D, NLOS.

5 10 15 20 25 3010-4

10-3

10-2

10-1

100

Eb/N0 in dB

PE

R

LSLCCELMMSETMMSEIdeal

0 5 10 15 20 25 3010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N0 in dB

BE

R

LSLCCELMMSETMMSEIdeal

Figure 3.18: PER performance for various CE schemes with MMSE detection for 2x2 TGn sync system in channel D, NLOS

87

The performance gap (Gp) in dB between the ideal CE and the other CE

schemes at 10-5 BER point is plotted in Figure-3.20 for B to F channel models in

NLOS condition. As we move from channel B to F, the Gp increases for the CE

schemes which use the frequency correlation. i.e., the Gp corresponding to channel

B is lesser than that of channel F, since the correlation across the frequency

response of the channel is more for channel B, which could be used to get better

estimates.

3.6 SUMMARY

In this chapter various MIMO detectors are discussed and their

performance in uncoded system in terms of MSE and BER is presented based on

simulation. The effect of CE on the performance of uncoded MIMO system is also

presented. A low complexity solution for MIMO-OFDM detection is proposed

and it reduces the computational complexity by 50%. The performance of the TGn

sync system is presented for various MIMO detection methods in terms of BER

B C D E F0

0.5

1

1.5

2

2.5

3

3.5

Channel models

Per

form

ance

Los

s, G

p

LMMSETMMSELCCELS

Figure 3.20: Gp Loss in performance of 10-5 BER for different CE method on all channel models

88

and PER. It is shown by simulations that the LC MIMO detectors result in very

less performance degradation for practical channel conditions. Thus, the LC

MIMO detectors can be used for IEEE 802.11n proposals as they reduce the

computational complexity load at the receiver.

The effect of various CE schemes on the performance of IEEE 802.11n

TGn sync proposal is presented in terms of BER and PER. The results indicate

that the LS scheme results in about 3 dB loss in performance at 10-5 BER point,

while the low complexity CE schemes such as LCCE, TMMSE have less

performance degradation. Thus, the TMMSE and LCCE CE schemes can be used

for IEEE 802.11n proposals leading to fewer computations and less performance

degradation.