doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 1 Layered Processing for MIMO OFDM Yang-Seok Choi, Siavash M. Alamouti,

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 2 Assumptions  Block Fading Channel –Channel is invariant over a frame –Channel is independent from frame to frame  CSI is available to Rx only –Perfect CSI at RX –No feedback channel  Gaussian codebook

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 3 Motivations …  To fully exploit Space- and Frequency-diversity in MIMO OFDM –Each information bit should undergo all possible space- and frequency- selectivity –Subcarriers should be considered as antennas (Space and frequency should be treated equally) –Apply Space-Time code (STC) over all antennas and subcarriers  STC –STC encoder generates multiple streams –Large dimension STC decoding is prohibitively complex in MIMO OFDM –Not only decoding, but also “designing good code” is complex STC

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 4 Motivations (cont’d)…  Serial coding : Use Single stream code and apply Turbo- code style detection/decoding –Serial code generates single stream (convolutional code, LDPC, Turbo-code,..) –MAP, ML or simplified ML with iterative decoding is complicated in MIMO OFDM (calculating LLR, large interleaver size,…)  Is there any efficient way of maximizing both Space- and Frequency-diversity while achieving the capacity? –Use existing code (No need of finding new large dimension STC) –Reduce decoding complexity of ML or MAP (linearly increase in the number of subcarriers and antennas) Serial Coding

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 5 Parallel Coding  Parallel coding : Multiple Encoders –Encoder generates single stream –Each layer carries independent information bit stream –In order to reduce decoding complexity, equalizer can be adopted Parallel Coding

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 6 System Model  where

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 7 Linear Equalizers (LE)   MF :  LS (or ZF) :  MMSE :

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 8 Layered Processing (LP)  LP –Loop –Choose a layer whose SINR (post MMSE) is highest among undecoded layers –Apply MMSE equalizer –Decode the layer –Re-encode and subtract its contribution from received vector –Go to Loop until all layers are processed

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 9 “Instantaneous” Capacity  Capacity under given realization of channel matrix with perfect knowledge of channel at Rx from this point on for convenience the conditioning on H will be omitted  If transmitted frames have spectral efficiency less than above capacity, with arbitrarily large codeword, FER will be arbitrarily small  If transmitted frames have spectral efficiency greater than above capacity, with arbitrarily large codeword, FER will approach 100%.

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 10 Mutual Information in LE  Theorem 1 (LE) For any linear equalizer –Equality (A) holds where A is a non-singular matrix –Equality (B) holds iff and are diagonal Proof : See [1]

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 11 Mutual Information in LE (cont’d)  In general equality (A) can be met in most practical systems.  In general the equality (B) is hard to be met.  In most cases, the sum of mutual information in LE is strictly less than the capacity  There is a loss of information when is used as the decision statistics for  This means that only is not sufficient for detecting since the information about is smeared to as a form of interference.  Hence, we need joint detection/decoding such as MLSE across not only time but all layers as well. –However, MLSE can be applied prior to equalization  No need for an equalizer

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 12 Mutual Information in LP  Theorem 2 (LP) In LP (use MMSE at each layer) where is the SINR (post MMSE) at k -th layer Proof : See [1] LP is an optimum equalizer !!!

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 13 Mutual Information in LP (cont’d)  Chain rule says :  Note where is the modified received vector at k -th stage in LP  –Decoder complexity can be reduced in LP –In LP, according to Theorem 2, MMSE equalizer output scalar is enough for decoding while the chain rule shows that vector is required

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 14 Mutual Information in LP (cont’d)  There is no loss of information in LP  Perfect Equalizer  is a perfect decision statistic for  The received vector y is ideally equalized through LP  Hence, through “parallel ideal code”, k -th layer can transfer without error  In LP it is natural that the coding should be done not across layers but across time (parallel coding)  Don’t need to design large dimension Space-Time code

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 15 Practical Constraints  Error propagation problem –No ideal code yet  Layer capacity is not constant –Even if the sum of layer capacity is equal to the channel capacity, individual layer capacity is variant over layers –Unless CSI is available to Tx and adaptive modulation is employed, we cannot achieve the capacity  Optimum decoding order –SINR calculations: determinant calculations –One of bottlenecks in LP

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 16 Solutions  Error propagation problem –Iterative Interference cancellation Ordered Serial Iterative Interference Cancellation/Decoding (OSI-ICD) Minimize error propagation and the number of iterations  Layer capacity is not constant –Spreading at Tx : Spread each layer’s data over all layers  Regulate Received Signal power –Ordered detection/decoding at Rx : Serial Detection/Decoding  No loss of information rate –Grouping Increase Layer size –Layer Interleaver –Minimize variance of SINR over layers  Maximize Diversity Gain  Decoding Order –Layer Interleaver and Spreading :  Less sensitive to decoding order

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 17 Spreading  Without Spreading –Received Signal power for :  With Spreading where T is a unitary matrix – is carried by which is a linear combination of –Received Signal power for :

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 18 Spreading for Orthogonal channel  Assume that channel vectors are orthogonal each other –Example : Single antenna OFDM under time-invariant multipath -- The channel matrix is diagonal (OFDM w/ Spreading called MC-CDMA[2]) –Assume –Then, the received signal power is constant –SINR after MMSE is constant as well

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 19 Spreading for Orthogonal channel (cont’d)  : SINR of after MMSE equalizer with Spreading matrix  Constant SINR over k regardless of choice of T  Constant Received Signal Power, SINR and Layer Capacity  Maximum diversity gain  Note is a harmonic mean of  Hence,

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 20 Spreading for Orthogonal channel (cont’d)  Although constant layer capacity is achieved, layer capacity is less than the mean layer capacity from Jensen’s inequality or Theorem 1  Spreading destroys orthogonality of the channel matrix  Inter-layer interference

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 21 Spreading for iid MIMO channel  There is no benefit when spreading is applied to iid MIMO channel –Since the spreading matrix is a unitary matrix, the channel matrix elements after the spreading are iid Gaussian –Spreading may provide some gain in Correlated MIMO channel (when the layer size is smaller than number of Tx antennas)

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 22 Spreading for Block Diagonal Channel  MIMO OFDM : Block Diagonal channel matrix  Spreading Matrix – : Spreading over Space – : Spreading over Frequency

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 23 Spreading for Block Diagonal Channel (cont’d)  New channel matrix where  Assume Then SINR at k -th subcarrier and n -th antenna where is the SINR when (No spreading over frequency) –Again,

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 24 Spreading for Block Diagonal Channel (cont’d)  Spreading regulates received signal power and SINR at the output of the MMSE equalizer, and hence maximizes diversity  Inverse matrix size for MMSE is n T instead of n T K because the channel matrix is a block diagonal matrix and the spreading matrix is unitary  Spreading increases interference power since it destroys orthogonality

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 25 Ordered Decoding at RX  Corollary 1 In LP, different ordering does not change the sum of layer capacity which is equal to channel capacity. Proof : Clear from the proof of Theorem 2  Thus, even random ordering does not reduce the information rate. –However, different ordering changes individual layer capacity and yields different variance.  Hence, optimum ordering is required to maximize minimum layer capacity

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 26 Ordered Decoding at RX (cont’d)  Assume that channel vectors are orthogonal  Without Spreading the layer capacity is where the decoding order is assumed to be k  With Spreading (see [1] for proof) –

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 27 Grouping  A simple way of reducing layer capacity variance is to reduce the number of layers by grouping (i.e. increasing layer dimension) –Namely, coding over several antennas or subcarriers  N element data vector d is decomposed to subgroups (or layers)  In general, each layer may have a different size

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 28 Grouping (cont’d)  Is there an equalizer which reduces decoder complexity without losing information rate?  Generalized Layered Processing (GLP) –Assuming a decoding order to be k, at the k -th layer, the received vector can be written as where –MMSE Equalizer ( L is the layer size) –Let MMSE equalizer output

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 29 Grouping (cont’d)  Theorem 3 (GLP) GLP does not lose information rate when is full rank and MMSE equalizer is applied Proof : See [1]  At each layer, MMSE equalized vector is used instead of for the decoding  Under certain conditions [1]

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 30 Layer Interleaving (LI)  Layer Interleaving provide Layer diversity –Doesn’t require memory and doesn’t introduce any delay –Doesn’t require synchronization –Diversity gain is less significant than spreading L=1 case

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 31 Numerical Experiments  General Tx Structure  Simulation Conditions –Without Interleaver –2-by-2 MIMO OFDM, K=32 subcarriers  N=64 –iid MIMO channel –Maximum delay spread is ¼ of symbol duration –rms delay spread is ¼ of Maximum delay spread –Exponential delay profile –Decoding order is based on maximum layer capacity –32-by-32 Walsh-Hadamard code for frequency spreading –No spreading over space

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 32 Numerical Experiments (cont’d)  CDF of normalized layer capacity in MIMO OFDM, L=1 –Spreading yields steeper curve  Diversity –LP improves Outage Capacity –Recall by Theorem 1&2

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 33 Numerical Experiments (cont’d)  CDF in MIMO OFDM, L=2(Grouped over antennas, ) –Grouping can significantly improve outage capacity –Unless Best grouping is employed, GLP has less outage capacity than LP –Spreading is still useful in reducing the variance of the layer capacity –Recall

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 34 Numerical Experiments (cont’d)  Effect of Layer size and Spreading in LP and GLP –w/o Spreading : distance of grouped subcarriers is maximized –w/ Spreading : neighboring subcarriers are grouped SP is effective when layer size is small Ideal “single stream code” is better than Ideal “4-by-4 code” !!! We don’t know optimum spreading matrix structure

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 35 Numerical Experiments (cont’d)  GLP performance with 2-by-2 STC –16 state 2 bps/Hz QPSK STTC (1 bps/Hz/antenna) –L=2, 128 symbols per layer –Two iterations (hard decision) Parallel STC Serial STC w/o Spreading

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 36 Numerical Experiments (cont’d)  GLP of Parallel STC w/ SP has the best performance  Serial STC has less frequency diversity gain 3.5 dB Gain Loss due to non-ideal 2-by-2 STC Ideal N-by-N STC Ideal 2-by-2 STC w/ SP&GLP Ideal 2-by-2 STC w/ GLP & w/o SP 2.1 dB Gain

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 37 Comments on Serial code w/ SP  Spreading provides diversity gain (steeper curves) but increases interference  Unless ML or Turbo type decoding over antennas and subcarriers is applied, capacity cannot be achieved –Complexity grows exponentially with the number of subcarriers and antennas  Partial spreading –The spreading matrix T is unitary but some of elements are zero –Reduces interference –Reduces ML decoder complexity –Reduces diversity

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 38 More on Partial Spreading  Partial Spreading in MIMO OFDM –K : number of subcarriers –SF : Spreading factor, number of subcarriers spread over –SF> Max delay in samples  Negligible frequency diversity loss –Partial spreading over subcarriers –The partial spreading matrix is useful when K is not a multiple of 4

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 39 Versatilities of Parallel coding  Allows LDMA (Layer Division Multiple Access) –Parallel coding can send multiple frames by nature –Different frames can be assigned to different users (Different spreading code are assigned to different users) –A convenient form of multiplexing for different users –Control or broadcasting channel can be established  Adaptive modulation –By changing not only modulation order but also the number of frames

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 40 MMSE or MF instead of LP  MMSE can be used instead of LP at first iteration in order to reduce latency or complexity –Then, it requires more iteration than LP because LP provides better SINR.  MF can also be used to reduce complexity. –But it will require more iterations and error propagation is more severe.  LP requires less number of iterations

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 41 Conclusions  Large dimension STC design/decoding is prohibitively complex  Serial code can have limited diversity gain or the complexity grows at least cubically with the number of subcarriers and antennas  Use parallel coding, apply SP at Tx and LP at Rx  Spreading increases diversity gain when layer size is small  LP does not lose the information rate while LE does  SP and Layer interleaver can reduce the sensitivity to decoding order in LP or GLP  Complexity of LP : Linearly increase in the number of subcarriers and antennas  LP needs less number of iterations  LP w/ SP is an efficient way of increasing diversity gain with reduced code design effort and decoding complexity

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 42 References  [1] Yang-Seok Choi, “Optimum Layered Processing”, Submitted to IEEE Transactions on Information Theory, 2003  [2] Hara et al., “Overview of Multicarrier CDMA”, IEEE Transactions on Commun. Mag., pp , Dec. 1997

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 43 Thank you for your attention!! Questions?

doc.: IEEE /0016r0 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 44 Back-up  Different Spreading Matrix