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Layered Processing for MIMO OFDM
January 2004 doc.: IEEE /0016r2 January 2004 Layered Processing for MIMO OFDM Yang-Seok Choi, Siavash M. Alamouti, Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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CSI is available to Rx only
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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January 2004 doc.: IEEE /0016r2 January 2004 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) jointly over all antennas and subcarriers Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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STC STC STC STC encoder generates multiple streams
January 2004 doc.: IEEE /0016r2 January 2004 STC STC STC encoder generates multiple streams Large dimension STC decoding is prohibitively complex in MIMO OFDM STTC - Conventional techniques such as space-time trellis coding are very complex STBC - Simpler techniques such as space-time block codes are limited in dimension (2x2 for Alamouti code) Not only decoding, but also “designing good code” is complex STC Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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January 2004 doc.: IEEE /0016r2 January 2004 Serial Coding 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,…) Serial Coding Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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January 2004 doc.: IEEE /0016r2 January 2004 Question? Is there any efficient way of maximizing both Space- and Frequency-diversity while achieving 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) Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Parallel Coding Parallel coding : Multiple Encoders Parallel Coding
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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System Model where January 2004 doc.: IEEE 802.11-04/0016r2
Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Linear Equalizers (LE)
January 2004 doc.: IEEE /0016r2 January 2004 Linear Equalizers (LE) MF : LS (or ZF) : MMSE : Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Layered Processing (LP)
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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“Instantaneous” Capacity
January 2004 doc.: IEEE /0016r2 January 2004 “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%. Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Mutual Information in LE
January 2004 doc.: IEEE /0016r2 January 2004 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] Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Mutual Information in LE (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 Mutual Information in LE (cont’d) In general equality (A) can be met in most practical systems. In general the equality (B) is not 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Mutual Information in LP
January 2004 doc.: IEEE /0016r2 January 2004 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 !!! Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Mutual Information in LP (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Mutual Information in LP (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Practical Constraints
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Solutions Error propagation problem Layer capacity is not constant
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Spreading Without Spreading With Spreading Received Signal power for :
January 2004 doc.: IEEE /0016r2 January 2004 Spreading Without Spreading Received Signal power for : With Spreading where T is a unitary matrix is carried by which is a linear combination of Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Spreading for Orthogonal channel
January 2004 doc.: IEEE /0016r2 January 2004 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 also constant Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Spreading for Orthogonal channel (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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, Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Spreading for Orthogonal channel (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Spreading for iid MIMO channel
January 2004 doc.: IEEE /0016r2 January 2004 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) Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Spreading for Block Diagonal Channel
January 2004 doc.: IEEE /0016r2 January 2004 Spreading for Block Diagonal Channel MIMO OFDM : Block Diagonal channel matrix Spreading Matrix : Spreading over Space : Spreading over Frequency Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Spreading for Block Diagonal Channel (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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, Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Spreading for Block Diagonal Channel (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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 nT instead of nT K because the channel matrix is a block diagonal matrix and the spreading matrix is unitary Spreading increases interference power since it destroys orthogonality Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Ordered Decoding at RX Corollary 1
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Ordered Decoding at RX (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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) Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Grouping (cont’d) Theorem 3 (GLP)
January 2004 doc.: IEEE /0016r2 January 2004 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] Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Layer Interleaving (LI)
January 2004 doc.: IEEE /0016r2 January 2004 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 especially in diagonal or block diagonal channel matrix Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Numerical Experiments
January 2004 doc.: IEEE /0016r2 January 2004 Numerical Experiments General Tx Structure Simulation Conditions Without Symbol/Layer Interleaver (unless otherwise mentioned) 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Numerical Experiments (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Numerical Experiments (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Numerical Experiments (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Numerical Experiments (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Numerical Experiments (cont’d)
January 2004 doc.: IEEE /0016r2 January 2004 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 dB Gain Ideal N-by-N STC 3.5 dB Gain Ideal 2-by-2 STC w/ SP&GLP Loss due to non-ideal 2-by-2 STC Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Comments on Serial code w/ SP
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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More on Partial Spreading
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Versatilities of Parallel coding
January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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January 2004 doc.: IEEE /0016r2 January 2004 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 Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Thank you for your attention!!
January 2004 doc.: IEEE /0016r2 January 2004 Thank you for your attention!! Questions? Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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Back-up Different Spreading Matrix January 2004
doc.: IEEE /0016r2 January 2004 Back-up Different Spreading Matrix Yang-Seok Choi et al., ViVATO Yang-Seok Choi et al., ViVATO
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