January 2004 doc IEEE 802 11 040016 r

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Layered Processing for MIMO OFDM Yang-Seok Choi, yschoi@vivato. net Siavash M. Alamouti, siavash@vivato. net Submission 1 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 2 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Motivations … § To fully exploit Space- and Frequency-diversity in MIMO OFDM – Each information bit should undergo all possible space- and frequencyselectivity – 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 Submission STC 3 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Motivations (cont’d)… § Serial coding : Use Single stream code and apply Turbocode 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, …) Serial Coding § 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) Submission 4 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 5 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 System Model § where Submission 6 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Linear Equalizers (LE) § § MF : § LS (or ZF) : § MMSE : Submission 7 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 8 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 “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%. Submission 9 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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] Submission 10 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 11 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 !!! Submission 12 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 13 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 14 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 15 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 16 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 : Submission 17 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 18 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Spreading for Orthogonal channel (cont’d) § : SINR of Spreading matrix after MMSE equalizer with § 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, Submission 19 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 20 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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) Submission 21 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Spreading for Block Diagonal Channel § MIMO OFDM : Block Diagonal channel matrix § Spreading Matrix – – Submission : Spreading over Space : Spreading over Frequency 22 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Spreading for Block Diagonal Channel (cont’d) § New channel matrix where § Assume Then SINR at k-th subcarrier and n-th antenna where over frequency) – Again, Submission is the SINR when 23 (No spreading Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 instead of n K because the channel matrix is a block diagonal matrix and the spreading matrix is unitary T T § Spreading increases interference power since it destroys orthogonality Submission 24 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 25 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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) – – Submission 26 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 27 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 28 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Grouping (cont’d) § Theorem 3 (GLP) GLP does not lose information rate when full rank and MMSE equalizer is applied is Proof : See [1] § At each layer, MMSE equalized vector instead of for the decoding § Under certain conditions [1] Submission 29 is used Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 30 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 31 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 32 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 33 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 34 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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) Serial STC w/o Spreading Parallel STC Submission 35 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Numerical Experiments (cont’d) § GLP of Parallel STC w/ SP has the best performance § Serial STC has less frequency diversity gain Ideal 2 -by-2 STC w/ GLP & w/o SP 2. 1 d. B Gain Ideal N-by-N STC 3. 5 d. B Gain Ideal 2 -by-2 STC w/ SP&GLP Submission Loss due to non-ideal 2 -by-2 STC 36 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 37 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 38 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 39 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 40 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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 Submission 41 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 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. 126133, Dec. 1997 Submission 42 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Thank you for your attention!! Questions? Submission 43 Yang-Seok Choi et al. , Vi. VATO

January 2004 doc. : IEEE 802. 11 -04/0016 r 0 Back-up § Different Spreading Matrix Submission 44 Yang-Seok Choi et al. , Vi. VATO