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**CHANNEL ESTIMATION AND LOW COMPLEXITY DETECTION FOR HIGH SPEED WLANs**

A THESIS Submitted by MUTHURAJA N In partial fulfillment for the award of the degree of MASTER OF SCIENCE (BY RESEARCH) FACULTY OF INFORMATION AND COMMUNICATION ENGINEERING ANNA UNIVERSITY : CHENNAI APRIL 2006

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**Outline Introduction Channel estimation for MIMO-OFDM systems**

MIMO Detection methods Summary

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**Effective data throughput (in Mbps)**

IEEE evolution Wi-Fi Performance Summary The performance of the various PHY extensions of can be analyzed according various criterion. RF Band: , b, and g are strictly operationally confined to the 2.4 GHz band while a is operational in the 5 GHz band. The n standard is relevant to both bands since there is a clear agreement that the 2.4 GHz band cannot meet the capacity requirements presumed for this market. Hence, products that can intelligently switch between the bands will likely be the norm in the near future. Regulation in some countries are still needed to harmonize the 5 GHz band operation. Data Rate: The family of standards supports peak data rates ranging from 1 to 600 Mbps in discrete steps. There has been a constant upgrade of the peak data rates based on popularity and demand. Moreover, new methods and techniques developed primarily by academics are being incorporated into the family to meet the perceived demands. Transmission Technique: While spread spectrum techniques are used in b, a/g/n use OFDM. Also, n combines Multiple Input Multiple Output (MIMO) and OFDM to achieve the 600 Mbps targets. The MIMO technique is an elaborate trick with multiple antennas that has some stunning effects on data rates. Range: The effective distance over which an off-the-shelf network will work is about 100 meters, which is about as far as healthy people can hear when yelling out to each other. Range is managed with techniques like rate adaptation, which is used in all the extensions to keep the connections alive and working as the distance between the transmitter and receiver increases. Higher power products for niche applications can achieve higher ranges, and these have been used for outdoor and niche applications. Directive antennas can also increase the radio range, but these might be more relevant to point-to-point or backhaul applications. 802.11 802.11b 802.11a 802.11g 802.11n Frequency 2.4 GHz 5.X GHz 2.4/5.x GHz Data rate (in Mbps) 1,2 Min-1Mbps 6,9,12,18,24,36,48,54 1,2,5.5,11,6,9,12,18,24,36,48,54 Up to 600 Mbps Modulation FHSS, DSSS DSSS OFDM DSSS / OFDM MIMO-OFDM Maximum Range 300 ft Effective data throughput (in Mbps) 0.5,1 5 32 >100 Channel BW 22 MHz 20 MHz 20/40 MHz 3-26

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Evolution of IEEE The effective application rate offered by the existing WLANs was still far lesser than the LAN (by 2004) WLAN standard has evolved from the basic IEEE (which supports to 1Mbps) to 54 Mbps by modifying PHY and MAC layer. IEEE a/g was the standard widely used for WLANs (by 2004) IEEE n taskgroup (TGn) was formed with the goal of increasing the application throughput to atleast 100Mbps by making changes in the PHY and MAC layer Support to Legacy stations

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**IEEE 802.11n – Main Features 802.11n WLAN Efficient OFDM**

Multiple antennas MAC Two elements in the advanced n PHY dramatically increase data rates. One of these elements is a collection of mechanisms that increases the efficiency of the OFDM signal. One of these tightens interference control as it reduces the number of subcarriers for guard bands. Guard bands are reserved parts of the channel’s spectrum, at the extreme upper and lower edges, which are left unoccupied as a countermeasure against interference with services in neighboring channels in the spectrum. Another is some coding details that have been called on to further enhance the efficiency of the OFDM signal. These are mandatory changes that ensure an upper limit of 65 Mbps for data rates. The 40 MHz-wide channel option will probably be used in the 5 GHz band to further increase data rates. The second element of change is the use of multiple antennas. The most popular use of multiple antennas is Multiple Input Multiple Output (MIMO), which is also called Spatial Multiplexing. The use of multiple antennas can lead to rather stunning increases in the channel data rates. Currently, two antennas are mandatory at the AP side and one antenna is sufficient for the client or user side. Most traditional WLAN devices, like laptops, will have multiple antennas but some low-cost clients like handsets might have only one antenna. Aggregation Block Ack Advanced Power save MIMO 2 Antennas at AP and 1 antenna at the user Reduced guard interval Reduced guard band Modulation and Coding

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IEEE n standard The basic technology for increasing the rate is the use of multiple antennas for spatial multiplexing (SM). However, transmit diversity with space time coding, beamforming, and SVD based schemes are also proposed as optional features. The standard proposes the use of upto 4 antennas The number of useful subcarriers is increased to 52 There is an optional mode with 40MHz BW, wherever the regulatory body allows it Shortened GI, code rate upto 7/8, advanced FEC coding are other optional features. Rates supported vary from 6.5Mbps to 500 Mbps.

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**Reduced guard interval**

802.11n PHY layer Efficient OFDM Multiple antennas Channel Bandwidth STBC Reduced guard band Spatial multiplexing Reduced guard interval Modulation and Coding Tx. Beam forming

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MIMO-OFDM systems The orthogonal frequency division multiplexing (OFDM) transmission scheme is an efficient technique to combat ISI and simplify the equalization problem The use of multiple antennas at transmitter and/or at the receiver helps in many ways such as diversity gain, spatial multiplexing and beamforming The MIMO signaling can easily be overlayed on an OFDM based system. The MIMO signaling treats each subcarrier in OFDM as an independent narrowband frequency flat channel. It can be viewed as N parallel MIMO systems operating with flat fading channel coefficients. MIMO-OFDM system offers an increase in rate by employing SM at the same time as we combat the ISI problem in an elegant way

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**important parameter in**

Spatial Multiplexing General MIMO example Data stream 1 (OFDM symbols) ... Uncorrelated channels AP Tx1 Tx2 Rx1 Rx2 h11 h12 h21 h22 Data stream 2 (OFDM symbols) ... Received signal at the antennas is the combination of the spatially multiplexed data from the different transmit antennas. Matrix channel is an important parameter in analysis and design

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**MIMO-OFDM systems Challenges in MIMO-OFDM systems:**

Channel estimation (CE) Synchronization MIMO detection Channel estimation – to estimate the channel coefficients corresponding to all transmit receive antenna pair and on all subcarrier positions. MIMO detection also becomes computationally intensive as it has be applied on all the subcarriers.

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**Contribution of the thesis**

The main focus is towards analysing the various PHY layers proposed for n The thesis covers two portion Channel estimation for n MIMO detection schemes The performance of several preambles used for MIMO channel estimation and different schemes are analysed Low complexity way of implementing the CE schemes are also discussed by exploiting the SFCF. System performance of various MIMO detection schemes is presented.

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**Section2: Channel estimation for 802.11n systems**

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**Outline Channel estimation in MIMO-OFDM systems**

Different kind of preambles TM method SM method and its variation TO method SO method Preambles in IEEE n TGn sync: SM (twice) WWise: SO EWC: TO

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**Outline IEEE 802.11n channel model Different MIMO preambles**

Preambles in IEEE n proposal Channel estimation schemes LS LMMSE Interpolation based estimation (LCCE) TMMSE ML method Complexity of CE schemes Performance for various CE schemes Mean square error System performance in terms of BER MSE results for TGn channels for TGn sync, WWise and EWC proposals

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**TGn channel model IEEE 802.11n TGn channel model**

MIMO channel model for indoor and typical office environment in LOS and NLOS conditions Cluster based channel model

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**Cluster based channel model**

Modification of Saleh Valenzula model - By adding of arrival statistics The complete impulse response with respect to both time and angle The time of arrival of the ith cluster is Ti τj,i is the time of arrival of the ijth path. The clusters and the rays within the cluster decay in amplitude and time The decay rate of cluster and the rays are Λ, λ,

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**Cluster based channel model**

The angle of arrival statistics Angular domain Impulse response Θi ~ uniform [0,2π] - mean angle of arrival in ith cluster. ωij - correspond to the jth ray angle in ith cluster, modeled as Laplacian distributed random variable. Each cluster has the following angular statistics Mean angle of arrival (AoA) Mean angle of departure (AoD) Azhimuth angluar spread (AS) Elevation angular spread

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**Power Angular spectrum**

The angle of arrival statistics within a cluster - Laplacian distribution Figure 2.2: Laplacian PAS σ - Angular spread

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**Cluster based channel model**

The complex correlation coefficients – PAS, AS, AoA and Individual tap powers RXX – crosscorrelation function between the real/imag parts RXYcross correlation between the real part and imaginary part To calculate the numerical values of correlation matrices we use a Matlab program developed and distributed by L. Schumacher

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**TGn channel model - Channel parameters**

Models Max. delay spread (in ns) RMS delay spread NLOS (ns) K factor (in dB) No.of. Clusters LOS NLOS A -∞ 1 B 80 15 2 C 200 30 D 390 50 3 E 730 100 6 4 F 1050 150 For each cluster in a channel model, AStx ASrx AoA AoD are specified

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Power delay profile Cluster 2 Cluster 1 150ns rms delay spread

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**Channel generation steps**

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**Spaced frequency correlation**

TGn channel models – B toF, NLOS conditions

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**MIMO-OFDM system Subcarrier domain view IFFT S/P P/S CP**

Multipath channel h11(n) h22(n) h21(n) h12(n) FFT X1(k) X2(k) Y1(k) Y2(k) X1(k) X2(k) H11(k) H22(k) H21(k) H12(k) Flat fading channel Subcarrier domain view Y1(k) Y2(k)

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**ESTIMATE THE CHANNEL COEFFICIENTS AT ALL SUBCARRIER POSITIONS**

MIMO OFDM system Received signals at kth subcarrier in a simple 2x2 system Rx. Ant 1: Rx. Ant 2: In matrix representation ESTIMATE THE CHANNEL COEFFICIENTS AT ALL SUBCARRIER POSITIONS

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**Time Multiplexed method**

S0 S1 …….. SN-2 SN-1 Ant 1 S0 S1 …….. SN-2 SN-1 Ant 2 MLTF1 MLTF2 Time Multiplexed (TM) method In each MLTF – Transmission from one antenna Simple channel estimation – LS estimate

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**Time Multiplexed method**

Training symbol at ‘k’ the subcarrier from the two antennas Ant 1 Ant 2 MLTF1 MLTF2 The received signal at kth subcarrier

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**Time Multiplexed method**

The channel estimates at Kth subcarrier is given by Mean square error : MSE in dB SNR in dB Average transmit power Total Energy required MSE is inversely proportional to SNR

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**Subcarrier Multiplexed method**

S2 S1 S3 ………. SN-2 ……….. SN-1 Ant1 Ant 2 MLTF1 Subcarrier multiplexed method Odd subcarriers – Transmitted from Antenna 1 Even subcarriers – Transmitted from Antenna 2 Interpolation needs to be done to estimate channel on all subcarriers

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**Subcarrier Multiplexed method**

Training symbol at the kth subcarrier from the two antennas Ant 1 Ant 1 Ant 2 Ant 2 MLTF1 MLTF1 The received signal at kth subcarrier

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**Subcarrier Multiplexed method**

In all odd subcarrier positions In all even subcarrier positions Even subcarriers of channel coefficients corresponding to TX.ant 1 are obtained by Interpolation. Odd subcarriers of channel coefficients corresponding to TX.ant 2 are obtained by Interpolation.

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**Subcarrier Multiplexed method**

Average transmit power Total Energy required

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**Subcarrier Multiplexed method - twice**

Training symbol at ‘k’ the subcarrier from the two antennas Ant 1 Ant 1 Ant 2 Ant 2 MLTF1 MLTF2 MLTF1 MLTF2 The received signal at kth subcarrier

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**Time orthogonal method**

S0 S1 …………. SN-2 SN-1 S0 S1 …………. SN-2 SN-1 Ant 1 S0 S1 ………… SN-2 SN-1 -S0 -S1 ……….. -SN-2 -SN-1 Ant 2 MLTF1 MLTF2

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**Time Orthogonal method**

Training symbol at ‘k’ the subcarrier from the two antennas Ant 1 Ant 2 MLTF1 MLTF2 The received signal at kth subcarrier

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**Time Orthogonal method**

The channel estimates at Kth subcarrier is given by Mean square error : MSE in dB SNR in dB Average transmit power Total Energy required MSE is inversely proportional to SNR

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**Subcarrier orthogonal method**

…………. SN-2 SN-1 Ant 1 S0 -S1 S2 ………… SN-2 -SN-1 Ant 2 MLTF1

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**Subcarrier Orthogonal method**

Training symbol at ‘k’ the subcarrier from the two antennas Ant 1 Ant 1 Ant 2 Ant 2 MLTF1 MLTF1 The received signal at kth subcarrier

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**Subcarrier Orthogonal method**

The channel estimates can be obtained by

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**Preambles used in IEEE 802.11n proposals**

Preambles used for channel estimation TGn sync – SM (twice) WWise – SO method EWC – TO method

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TGn sync proposal

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**Packet structure Ant 1 Ant 2 LSTF LLTF LSIG HT-SIG HT STF HTLTF1**

DATA 8μs 8μs 4μs 8μs 2.4μs 7.2μs 7.2μs Ant 2 LSTF LLTF LSIG HT-SIG HT STF HTLTF1 HTLTF2 DATA 8μs 8μs 4μs 8μs 2.4μs 7.2μs 7.2μs MIMO Channel estimation Is done during this part CDD Simplified PPDU format in 2x2 system-TGn sync proposal for IEEE n

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**Long preamble structure in TGn sync**

Time domain view GI Set 1 Set 1 GI Set 2 Set 2 Ant 1 GI Set 2 Set 2 SI Set 1 Set 1 Ant 2 HTLTF1 (7.2μs) HTLTF2 (7.2μs) Subcarrier domain view K=0 Set 1 S-26 S-24 ….. S-2 S2 ….. S24 S26 Set 2 S-25 S-23 ….. S-1 S1 ….. S23 S25

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**Least squares channel estimation**

Linear relationship between the channel and the received signal Solving the linear equations leads to Least squares (LS) channel estimates Mean square error (MSE) is directly proportional to the noise variance

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WWise proposal

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**WWise preamble – Mixed mode**

Ant 1 SS20 LS20 SIG-MM LS20 SIG-N DATA Ant 2 SS20 LS20 SIG-MM LS20 SIG-N DATA 8μs 8μs 4μs 8μs 4μs Cyclic delay of 400ns Cyclic delay of 1600ns Cyclic delay of 3100ns

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**WWise preamble – Green field mode**

Ant 1 SS20 LS20 SIG-N DATA Ant 2 SS20 LS20 SIG-N DATA 8μs 8μs 4μs Cyclic delay of 400ns Cyclic delay of 1600ns

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**Training symbol at ‘k’ the subcarrier from the two antennas**

WWISE method Training symbol at ‘k’ the subcarrier from the two antennas Ant 1 Ant 1 Ant 2 Ant 2 MLTF1 MLTF1 The received signal at kth subcarrier during first repetition

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CE method for WWISE The channel estimates are obtained by

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MSE closed form The spaced frequency correlation is obtained from F.T of PDP

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EWC proposal

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**EWC preamble – Mixed mode**

Ant 1 L-STF L-LTF LSIG HTSIG HT STF HT LTF1 HT LTF2 DATA Ant 2 L-STF L-LTF LSIG HTSIG HT STF HT LTF1 HT LTF2 DATA 8μs 8μs 4μs 8μs 4μs 4μs 4μs Cyclic delay of 200ns Cyclic delay of 400ns

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**EWC preamble – Green field mode**

Ant 1 L-STF HTLTF 1 HTSIG HT LTF2 DATA Ant 2 L-STF HTLTF 1 HTSIG HT LTF2 DATA 8μs 8μs 8μs 4μs Cyclic delay of 200ns Cyclic delay of 400ns

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**EWC Time domain view GI Set 1 Set 1 GI -Set 1 Ant 1 GI Set 2 Set 2 GI**

HTLTF1 (7.2μs) HTLTF2 (4μs) Set 2 is Cyclic shifted by 400ns of Set 1 Subcarrier domain view Set 1 -Set 1 S1-26 S1-25 S1-24 ……... S124 S125 S126 -S1-26 -S1-25 -S1-24 ……... -S124 -S125 -S126 Set 2 Set 2 S2-26 S2-25 S2-24 …….. S224 S225 S226 S2-26 S2-25 S2-24 …….. S224 S225 S226 HTLTF 1 HTLTF 2

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**Mixed mode – Least squares**

Ant 1 Ant 2 HTLTF1 HTLTF2 Received signal at Kth subcarrier is given by The channel estimates at Kth subcarrier is given by

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**Green field mode – Least squares**

Received signal at Kth subcarrier is given by The channel estimates at Kth subcarrier is given by

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**Enhanced CE schemes LMMSE Interpolation based estimation (LCCE) TMMSE**

ML method

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**LMMSE channel estimation**

The spaced frequency correlation in the channel is used to get better estimate compared to LS estimate. Bx1 vector Autocorrelation, ‘R’ matrix captures the frequency domain correlation in the channel LMMSE estimate :

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**LMMSE channel estimation**

LMMSE filter requires the autocorrelation matrix and the noise variance Imperfect estimation of R and the noise variance leads to the irreducible error floor in the MSE Computational complexity of the LMMSE scheme is very high as it requires B 2 multiplications and a matrix inversion A block wise LMMSE - Reduce the complexity at the expense of performance degradation

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**LMMSE channel estimation**

The spaced frequency correlation in the channel is used to get better estimate compared to LS estimate. Bx1 vector Autocorrelation, ‘R’ matrix captures the frequency domain correlation in the channel LMMSE estimate :

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**Blockwise LMMSE BL – Reduced block length B – Original Block length**

NB – Number of BL blokcs in B The autocorrelation matrix block of length BL LMMSE estimate for p th block

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**Interpolation based Low complexity channel estimation (LCCE)**

Interpolation based channel estimation Correlation among the adjacent subcarriers are used without the need for the autocorrelation matrix, R and huge computations. Channel estimates are got by weighted average of LS estimates and the interpolation estimates

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**Block diagram HTLTF 1 HTLTF 2 RX. 1 RX. 2 LS est RX. 1 LS est RX. 2**

Int Int 1-W W 1-W W

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**Low complexity channel estimation**

The final channel estimates is the weighted average of direct LS estimate and the interpolated estimate Simple linear interpolation filter – Low computational overhead Linear interpolation : Weights of the linear interpolation are chosen to be powers of 2 to use shifting instead of multiplication Other Interpolations like cubic, spline can be done – Complexity increases

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**Low complexity channel estimation**

Weight value Low SNR region High SNR region W = 0.5 3.5 dB improvement over LS estimation Error floor depends upon RMS delay spread W>0.5 <3.5 dB improvement over LS estimation Error floor is less compared to W=0.5 W<0.5 >3.5dB improvement over LS estimation. (But not more that 4.25dB) Error floor is high compared to W=0.5 Error floor is directly proportional to the RMS delay spread

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**MSE closed form for linear interpolation method**

The spaced frequency correlation is obtained from F.T of PDP

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**Truncated MMSE (TMMSE) - CE**

Smoothing LS estimates by weight values obtained from MMSE solution The MMSE solution matrix Vp of a truncated R matrix is obtained as follows Rp is the correlation matrix of dimension PxP The middle row of Vp matrix is used as weight vector

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TMMSE - CE Filter the LS CEs using these weight values as filter coefficients There is a loss in performance compared to LMMSE, due to truncation and smoothing with less number of weights To reduce complexity the modulus of the complex weights is considered and quantized to the nearest power of 2 LCCE method is a special case of TMMSE method when the weights are real

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ML method ML channel estimation – with assumption that the maximum length of the channel impulse response is not greater than the guard time. Step 1: Step 2: Step 3: Step 4: Where, F is the Fourier matrix and Fred is the reduced Fourier matrix whose dimension is L x L Suitable only for symbol spaced channel

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**Computational complexity**

Method Comlex multiplications Complex additions Other LS B - LMMSE-52 B2 + B (B-1)B Finding common LMMSE filter O(B3) complex multiplications LMMSE-13 NBBL2 + B NB(BL-1)BL O(BL3) complex multiplications LCCE (Linear intp) 2B 2B shifting operation. TMMSE-P B(P+1) B(P-1) Finding the P filter coefficients B is the number of subcarrier; For TGnSycn B=52, WWISE & EWC B = 56

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**Results for all the methods**

Performance of various preambles Performance - TGn sync preamble Performance - EWC preamble Performance - WWISE preamble Effect of various channel estimation schemes on system performance interms of BER & PER – Section3

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**per receive antenna per subcarrier**

Simulation model , The SNR used here refers to signal to noise ratio per receive antenna per subcarrier The performance measure is the MSE of the channel estimate are the ideal and estimated CEs on the kth subcarrier

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**Performance of various preambles**

Noise Power in dB MSE performance of different preambles in channel D, NLOS conditions MSE

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TGn sync

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**Performance of LCCE method**

MSE performance of LCCE for TGn sync preamble, Channel D NLOS.

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**MSE performance of LMMSE for TGn sync preamble, Channel D NLOS.**

LMMSE method MSE performance of LMMSE for TGn sync preamble, Channel D NLOS.

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**LMMSE method – Mismatch Correlation matrix**

MSE performance of LMMSE for TGn sync preamble, Channel D NLOS Autocorrelation matrix mismatch

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**Figure 2.22: MSE performance of LMMSE method for TGn sync preamble in channel D, NLOS**

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TMMSE method, P=3 Figure 2.24: MSE performance of TMMSE scheme with P=3 for TGn sync preamble, Channel D NLOS

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TMMSE method, P=5 Figure 2.25: MSE performance of TMMSE scheme with P=5 for TGn sync preamble, Channel D NLOS

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**Performance of various CE methods**

MSE performance of various CE scheme

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**Gain at 0 dB for all CE schemes**

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**Cutoff point of all schemes**

Cutoff point of all CE scheme

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WWISE

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**Performance of smoothing window method for all channel models**

MSE performance of 2x2 WWISE preambles for all channel models – SW method

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**WWISE – MSE Performance for different schemes**

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**Performance of ML based method**

MSE performance of ML method

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**Enhanced Wireless Consortium**

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**LCCE scheme MSE performance of LCCE with linear interpolation for**

EWC Greenfield mode in Channel D NLOS.

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**EWC - Performance for various CE schemes**

MSE performance of CE schemes for 2x2 of EWC

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**Figure 2.35: MSE performance of LMMSE, LCCE scheme for GF and MM in Channel D NLOS**

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**Effect of CE errors on BER and PER**

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**BER performance – Uncoded system**

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

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**BER performance – TGn sync system QPSK – ½ rate**

BER performance of LC MIMO detection schemes for 2x2 TGn sync system in channel D, NLOS.

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**PER performance – TGn sync system QPSK – ½ rate**

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

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**Complexity of CE schemes**

Method Comlex multiplications Complex additions Other LS B - LMMSE-52 B2 + B (B-1)B Finding common LMMSE filter O(B3) complex multiplications LMMSE-13 NBBL2 + B NB(BL-1)BL O(BL3) complex multiplications LCCE (Linear intp) 2B 2B shifting operation. TMMSE-P B(P+1) B(P-1) Finding PxP LMMSE filter O(P3) complex multiplications

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**Section2 : MIMO Detection methods for 802.11n**

>> A simple uncoded system >> TGn Sync system

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**MIMO Detection schemes**

Decorrelator / ZF MMSE Successive Interference Cancellation (SIC) ZF/MMSE VBLAST (Ordered SIC) Maximum Likelihood (ML) Explain in detail about each of these schemes.

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**MIMO Detection schemes**

Maximum Likelihood (ML) Optimum and most complex detection method Zero-Forcing (ZF) Pseudo inverse of the channel, simplest detection method Minimum mean-squared error (MMSE) : Intermediate complexity and performance

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**MIMO Detection schemes**

V-BLAST Ordered successive interference cancellation (SIC) detector Finding Nulling Solution (Zero Forcing ) (MMSE filter ) Ordering Choosing the best channel is the jth row of G Nulling Nullifying the effect of the channel faced by kth stream

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**Non-feedback MIMO Receivers (contd..)**

Slicing Quantizing the nullified symbol with appropriate constellation Canceling Cancel the effect of detected stream from the received signal Finding new channel matrix Find new channel matrix by replacing the columns corresponding to the detected streams with zeros Iteration Repeat from step 1 with new channel matrix until all the streams are detected

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**V-BLAST – 2 x 2 Example Let the received signal be where**

Finding Nulling Solution Using zero forcing or MMSE solution Ordering Find the energy of all the rows of G Choosing the best channel Nulling Assume k=2, then the nulling vector

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V-BLAST – 2 x 2 Example Nullifying the effect of the channel faced by 2th stream Slicing Quantizing the nullified symbol with appropriate constellation Canceling Cancel the effect of detected stream from the received signal Finding new channel matrix Iteration Repeat from step 1 another time to get the 1st stream.

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**Mean square error in 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 MSE easy to derive for MIMO detection. From simulation, the reduction in MSE leads to BER reduction.

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**Low complexity MIMO detection**

We need to employ N independent MIMO detectors in a MIMO system with N subcarrier. The frequency correlation among the subcarriers can be used to reduce the complexity of the MIMO-OFDM system Instead of independently employing MIMO detector in all subcarriers, only the solution for the MIMO detector on alternate subcarrier positions are found The solution for the other subcarriers is found by interpolating the solutions obtained for the neighboring subcarriers.

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**Low complexity MIMO detection**

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 let k be the subcarrier position in which the solution is obtained by linear interpolation Where Vk is the matrix solution for MIMO detection 50% reduction in the complexity when compared to the normal MIMO-OFDM detection methods 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.

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**Complexity comparison**

Number of complex multiplication is considered

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**Complexity comparison**

Comparison of computational complexity for various MIMO detection schemes

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**A simple MIMO-OFDM system**

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**Simulation results and discussion**

Uncoded system Simulation results for MIMO detection algorithms Effect of CE on the system performance Simulation parameters Number of Subcarriers, N =64 Cyclic prefix = 16 samples BW = 20MHz QPSK modulation TGn channel D – NLOS Results presented in terms of MSE performance, BER and PER.

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**MIMO detection schemes for 2x2 and 4x4**

Figure:MSE performance of various MIMO detection schemes for 2x2 system in channel D, NLOS Figure: MSE performance of various MIMO detection schemes for 4x4 uncoded system in channel D, NLOS

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**Low complexity MIMO detection scheme**

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

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**BER performance with different CE**

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

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**TGn Sync system – System model**

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**TGn Sync - Simulation results**

Info bits TGn sync Tx TGn sync Rx. Channel Channel Estimation using preambles Figure : Simulation model Parameter Value CR Modulation QPSK Nt x Nr 2x2 Payload 1000 bytes Results presented in terms of BER and PER

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**MIMO detection schemes – BER & PER**

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

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**LC-MIMO detection schemes – BER & PER**

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

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**Effect of CE schemes on system performance**

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

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**Effect of CE schemes on system performance for all channel models**

Figure : Gp Loss in performance of 10-5 BER for different CE method on all channel models Gp is defined as the Loss in performance in terms of SNR at a cut off point of 10-5 BER

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Thank You

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Summary 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 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 n proposals as they reduce the computational complexity load at the receiver. The effect of various CE schemes on the performance of IEEE n 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 n proposals leading to fewer computations and less performance degradation.

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