Linear Mimo Receivers Vs Tree Search Detection

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

LINEAR MIMO RECEIVERS VS. TREE SEARCH DETECTION: A PERFORMANCE COMPARISON OVERVIEW Clemens Michalke, Ernesto Zimmermann and Gerhard Fettweis Vodafone Chair Mobile Communications Systems, TU Dresden, D-01062 Dresden, Germany A BSTRACT Next generation wireless systems will use a combination of large system bandwidths and multiple antennas (MIMO) to deliver very high data rate services. The efficient demodulation of MIMO signals at the receiver can be a challenging task. In this paper, we study the gains achievable by using capacityapproaching tree search MIMO detection algorithms, for differently parameterized OFDM system setups and channel scenarios. Our results indicate that the high amount of diversity typically available in broadband MIMO-OFDM systems together with the use of low rate channel coding allows achieving very good performance using even simple linear MMSE detection. In iterative receiver approaches, the combination of initial linear MMSE detection and subsequent soft interference cancellation performs within 1-2dB of the respective performance bound. The complexity involved in tree search detection techniques provides benefits mainly in very low-diversity environments, or if high rate channel coding is used together with higher order modulation. I.

I NTRODUCTION

As engineers strive to satisfy the demand for ever higher data rates in future wireless systems, they are faced with a serious challenge: regulation and other factors render radio frequency spectrum a scarce and thus valuable resource. Multiple-input multiple-output (MIMO) systems allow using this resource very efficiently by multiplexing several data streams into the same time-frequency bin [1]. If channel state information (CSI) of sufficient quality is available and appropriately exploited at the transmitter side, the MIMO channel can be decoupled into a set of parallel SISO channels (this is referred to as SVDMIMO, or Eigenmode signaling), thereby substantially reducing the complexity of the spatio-temporal processing at the receiver [2]. However, in a number of scenarios “blind” MIMO transmission schemes such as the classical BICM approach [3] have to be used: whenever CSI at the transmitter is either unavailable (due to missing CSI feedback in the FDD mode), or cannot be straightforwardly applied (e.g. due to non-reciprocal RF chains and interference scenarios in the TDD mode [4]). The correct separation of the transmitted signals at the receiver is a significant challenge in such an open-loop MIMO setup. Optimal a posteriori probability (APP) detection of the signals is well known to require an effort growing exponentially in the (raw) spectral efficiency – our figure of merit for using MIMO. Recent years have therefore seen an intense research effort to develop detection algorithms which provide a good performance-complexity trade-off. The plethora of proposals ranges from simple linear receivers over succ 1-4244-0330-8/06/$20.00
2006 IEEE

cessive interference cancellation (and variations) to capacityapproaching tree search techniques (sphere detection, list sequential detection), to name but a few. By using feedback from the outer channel decoder in an iterative “Turbo-MIMO” setup, performance remarkably close to APP detection has been achieved with a number of different detection techniques. The huge amount of available options makes it difficult to determine how much gain is achievable by using more advanced detection strategies, and which algorithm should be chosen for a practical implementation. The answer to this question depends on a large number of parameters, such as the available amount of diversity, the channel coding rate, the size of the modulation alphabet, and last but not least on the question whether single-shot detection-decoding or Turbo-MIMO is employed at the receiver. In this paper we will present results for a number of relevant application scenarios, to determine where it makes sense to invest computational effort in the use of advanced detection techniques, and where simple linear detection still provides a good performance-complexity trade-off. The remainder of this document is structured as follows: Section II. introduces the system model and principles of (iterative) MIMO detection. Section III. presents a selection of application scenarios, in terms of system setups as well as channel models. In Section IV. we discuss the non-iterative case, before we draw attention to the Turbo-MIMO case in Section V.. We finally draw conclusions in Section VI.. II. A.

MIMO D ETECTION

The MIMO Detection Problem

We consider a MIMO-BICM system with MT transmit and NR receive antennas, as depicted in Figure 1: the information bits are encoded, interleaved, partitioned into blocks ci of MT · L bits and mapped onto vector symbols xi whose components are drawn from some complex constellation C of cardinality 2L . Binary Source

u

Outer Encoder

e

Rate R

x ... H ...

Interleaver

AWGN Hard Decision Binary Sink

Constellation Mapper

c

n y

SISO Decoder

LA,Dec

LE,Dec

-1

LE,Det

MIMO Detector

LA,Det

Figure 1: Transmission model with BICM-MIMO transmitter and (iterative) MIMO receiver. We focus on the case of broadband MIMO-OFDM systems

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

(examples will be given in the following section). Transmission hence takes place over flat fading subcarriers. In the equivalent base-band model, the signal yi received on time-frequency resource i is given by: yi = Hi xi + ni ,

(1)

where Hi ∈ CNR ×MT is the channel matrix whose entries are normalized such that E{|hk,l |2 } = 1 – each subchannel is passive. ni ∈ CNR ×1 is receiver noise whose components are zero mean i.i.d. complex Gaussian random variables with variance N0 . The transmit energy is distributed equally over the antennas (which is the optimal power allocation strategy in the absence of CSI at the transmitter). The signal-to-noise ratio (SNR) at each receive antenna is given by SNR = Es /N0 . The task of the MIMO detector is to generate reliability information on the code bits cl of each received vector symbol y (we drop the index i for ease of notation), given the channel state information and optional a priori knowledge from the decoder. This soft output is typically produced in the form of so called log-likelihood ratios (LLRs):
p (y|x(c)) · P [c] x(c)∈Xl+1 P [cl = +1|y]
= ln L(cl |y) := ln P [cl = −1|y] p (y|x(c)) · P [c] 

x(c)∈Xl−1

 2  − y − Hx ≈ max + ln P [cl ] (2) N0 x(c)∈Xl+1 l   2  − y − Hx − max + ln P [cl ] , N0 x(c)∈Xl−1 l

where Xl±1 denotes the set of 2M ·L−1 symbols x(c) for which cl = ±1 and the second line follows from the application of the so called “maxLog approximation”. Evaluating the two maxoperations in (2) by brute-force maximum a posteriori probability detection (max-APP, or MAP) evidently requires an effort growing linear with the cardinality of Xl±1 and thus exponentially in the number of transmitted bits per vector symbol. This is clearly infeasible for higher spectral efficiencies. However, there exist low complexity algorithms that show very good performance in a number of relevant scenarios, at only a small fraction of the full MAP complexity. We will discuss some examples in the following. B.

Detection Algorithms – A Short Overview

Linear equalization is the most simple technique – it suppresses the interference among layers, thereby turning the MIMO detection problem into a set of MT parallel SISO detection problems and hence substantially reducing the complexity of demodulation. There are several drawbacks to this approach: the first is the potentially severe noise enhancement, together with a reduction of the spatial diversity order to 1. The second is that, due to the full decoupling of the layers, we can no longer achieve MAP, but only ML performance. The advantage is that the noise enhancement can be precisely characterized, which

helps a lot whenever there is enough frequency (or time) diversity available to code over the “bad” channel realizations with strong noise enhancement. If close-to-optimal detection performance is the target, tree search based techniques should be employed. Based on the recognition that only a few hypotheses in Xl±1 maximize each of the respective terms in (2), these back-substitution based algorithms construct a subset list L ⊂ X to determine the LLRs. This subset list should on the one hand include only a fraction of the elements from X – to minimize complexity, but on the other hand be large enough to allow approaching the true detector L-values as closely as possible – to maximize performance. Examples of such schemes are list sphere [5, 6] (LSD), list sequential [7] (LISS) and iterative tree search [8] (ITS) detection. The performance-complexity trade-off can be tuned by choosing the number of entries in the list L. List sphere and list sequential detection require a certain number of full length candidates to be found – the detection complexity is therefore variable. The M-algorithm based ITS [8] fixes the number of paths which are retained in each layer. The advantage is a fixed detection complexity, but the algorithm will no longer find the global optimum and is prone to error propagation, especially for low values of M . A special case of the M-Algorithm with M = 1 is widely known as successive interference cancellation (SIC) – in each layer, only the best path for this depth is retained. In our BICM setup, such detectors generally suffer from error propagation effects, as the coding gain cannot be used to decrease the number of decision errors in the cancellation step. This problem can be somewhat reduced by using soft cancellation (SoftSIC) – subtracting not hard decided symbols, but soft symbols based on the reliability of detection. The variance of these soft estimates can be used to determine the residual noise after the cancellation step [9]. However, the error propagation can only be treated statistically, so the produced LLRs are of relatively low quality, especially for higher order modulation. As a prerequisite for all tree search based methods, the channel matrix has to be decomposed to obtain a matrix of upper triangular structure – either via a Cholesky factorization, or a QR decomposition. As detecting reliably received signals first decreases complexity for list sphere and sequential detection [6, 10] and increases performance for iterative tree search and SoftSIC, a sorted QR decomposition [11] should be used. This approach also facilitates the extension of tree search based detection methods to the MMSE case [12]. The importance of MMSE preprocessing for solving the MIMO detection problem efficiently has been stressed in [6]. C.

Tree Search Detection vs. Linear MMSE – Expected Gains

To obtain a first “educated guess” on the potential gains from using tree search detection, we take a look at the MIMO capacity for the high and low diversity case. Figure 2 shows results (ergodic and 1% outage capacity, respectively) for a spatially uncorrelated 4x4 MIMO system. Depicted are the capacities of a system using CSI at the transmitter (SVD-MIMO, Waterfilling), and a system without CSI at the transmitter (MIMOBICM) using optimal vs. simple linear MMSE detection.

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

Spectral Efficiency [bit / channel use]

30 ∆ >> 1000 (ergodic capacity)

20

MIMO Configuration System bandwidth [MHz] FFT Bandwidth[MHz] FFT size Used subcarriers Subcarrier spacing [kHz] Useful OFDM symb. [µs] Cyclic prefix [µs] Total OFDM symb. [µs]

Capacity w/ CSI@Tx Capacity w/o CSI@Tx

∆=3 (1% outage capacity)

10 Linear MMSE

∆ ... diversity order

0 0

10

SNR [dB]

20

30

Figure 2: Ergodic and outage capacities for an uncorrelated 4x4 MIMO system using different receiver strategies. The gains from exploiting CSI at the transmitter are quite low in the high diversity environment (ergodic capacity results), at the SNR values typically considered for MIMO transmission (10 dB and beyond) – another motivation for considering a simple BICM transmitter architecture. The offset between linear MMSE and optimal detection is no larger than 5dB in this scenario, even for very high spectral efficiencies. For a spectral efficiency of 4 bit/channel use (rate 1/2 coded 4-QAM transmission) it is only 2dB – linear detection can hence be expected to yield very good results for lower spectral efficiencies and high diversity environments. For the low diversity case (diversity order ∆ = 3), the offset between linear and near-optimal tree search detection can be expected to be significantly higher, as is evident from the results in Figure 2 – the loss in spatial diversity then leads to a strong performance penalty for linear detection techniques. Note, however, that for spectral efficiencies of 8 bits per channel use (rate 1/2 coding, 16-QAM) and below, the loss is again only in the order of 3-4dB. III. A.

A PPLICATION S CENARIOS

Broadband MIMO-OFDM Systems

Next generation wireless systems will not only use MIMO to increase spectral efficiency, they will also use large bandwidths to further boost data rates. In order to efficiently equalize frequency selective broadband channels, OFDM is typically used. Examples for MIMO-OFDM systems in the short range wireless LAN area are IEEE 802.11n, and the physical layer proposals for the WIGWAM [13] and the WINNER project [14], which aim at achieving data rates of up to 1 GBit/s in 100 MHz bandwidth. For the wide area cellular case, MIMO-OFDM has been proposed at least as a downlink solution in 3GPP long term evolution (LTE). In the remainder of this paper, we study the performance of different MIMO detection algorithms using a WIGWAM system, a 802.11n based system, and a “LTE-like” system as examples for a high, medium and low diversity environment, respectively. The system parameters are summarized in Table 1.

WIGWAM 4x4 100 160 1024 596 156.25 6.4 0.8 7.2

802.11n 4x4 20 20 64 48 312.50 3.2 0.8 4.0

LTE 2x2 5 5 512 450 9.77 102.4 10.0 112.4

Table 1: Physical layer parameters of the MIMO-OFDM systems used for the performance evaluation. For channel coding, we use a Turbo Code with (13R , 15) constituent convolutional codes, 8 internal iterations of maxLogMAP decoding, and scaling of the extrinsic messages (0.5 in the 1st , 1.0 in the 8th and 0.75 in all other iterations). The code is punctured to rate 1/2 (by puncturing each other parity bit), and to rate 3/4 using the pattern from [15]. We use Gray mapped 4-/16- and 64-QAM transmission. B. Propagation Scenarios In broadband MIMO-OFDM systems, all three degrees of freedom in electromagnetic wave propagation – space, frequency and time – become available. The amount of fading and hence the level of exploitable diversity, however, is influenced by the propagation environment and transmission system parameters. The level of frequency diversity gained from multipath fading depends on the ratio of the system bandwidth BS to the channel’s characteristic coherence bandwidth BC . As a rule of thumb, the coherence bandwidth can be estimated from the delay τmax of the latest significant arriving multipath component: BC ≈ 1/τmax . Equivalently, the amount of temporal diversity can be estimated by relating the symbol period TS to the channel coherence time TC , which is proportional to the inverse of the maximum occurring Doppler frequency. However, in order to avoid inter-carrier-interference due to Doppler spread, the subcarrier spacing – which is the inverse of the symbol period TS – is typically much larger than the maximum Doppler frequency. Hence, the channel remains almost unchanged over several OFDM symbols (TS  TC ) and the amount of temporal diversity is very limited. Multiple antennas offer usage of the directional properties of the channel, i.e., spatial diversity. When using spatial multiplexing, the number of non-zero singular values (or Eigenmodes) of the channel matrix Hi defines the number of streams that can be simultaneously supported by the channel. In the absence of any correlation, the average unordered singular values exhibit the same value and the maximum number of parallel signals can be transmitted. The ratio between the largest and the smallest singular value – the Eigenvalue spread σEV – can thus serve as measure for the capability of the channel to support spatial multiplexing. High Eigenvalue spread corresponds to high antenna correlation at either the transmitter, the receiver or both. In such cases, beamforming instead of

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

spatial multiplexing should be applied, or the number of data streams/antennas has to be adapted to the channel conditions.

LTE WIGWAM SCM 1 SCM 2 LTE Winner C1 LTE WIGWAM Winner D1 802.11n B 802.11n 802.11n B WIGWAM 802.11n 802.11n E 802.11n D

IV.

S INGLE S HOT D ETECTION -D ECODING

A. Sphere Detection vs. Iterative Tree Search We first study the performance of Sphere detection and ITS, in order to obtain reasonable configurations for the following evaluations in which they will serve as upper performance bounds (ML and MAP bound in the non-iterative and iterative case, respectively). Figure 4 shows results for different numbers of paths retained in the tree search, using a WIGWAM OFDM system and rate 1/2 and 3/4 coded 16-QAM modulation in the 802.11n E channel scenario. Results for linear MMSE detection are plotted as reference. Iterative Tree Search vs. Sphere Detection

0

10

16−QAM, R = 3/4

Figure 3: Classification of system-channel combinations in the Eigenvalue spread - frequency diversity pane In Figure 3 combinations of the system approaches from the previous section and different channel models are evaluated regarding the available frequency diversity and capability of transmitting parallel data in spatial multiplexing. Systemchannel combinations in the lower right region are well suited for MIMO-OFDM transmission, whereas points in the upper left part represent the low diversity case. The models C1 and D1 from the European IST WINNER project [16] represent further developments of the SCM channels [17] (spatial extensions of the ITU channel models Pedestrian A – SCM 1, Vehicular A – SCM 2 and Pedestrian B – SCM 3). They provide moderate frequency diversity with respect to the applied system and have moderate to high Eigenvalue spread. The channel models from the IEEE 802.11 TGn [18] are designed for indoor as well as outdoor transmission and are spatial extensions of the HiperLAN channels. As can be seen from Figure 3 their Eigenvalue spread is very small. Hence spatial multiplexing is a reasonable MIMO strategy. The highest amount of frequency diversity is available when using the WIGWAM system design in combination with the IEEE 802.11n E channel model.

802.11n D 802.11n E WINNER C1 WINNER D1

τmax 390ns 730ns 410ns 170ns

BC 2.5MHz 1.25MHz 2.5MHz 6MHz

σEV 3 2.7 41 6.2

Note Hiperlan A Hiperlan B suburban rural

Table 2: Characteristic parameters for the investigated channel models Table 2 lists the characteristics of the channels used for performance evaluation in the next section, such as the maximum excess delay, the coherence bandwidth and the Eigenvalue spread. A remark to environment or channel model precursor is also given. The channels are marked in Figure 3 with a filled red circle.

BLER

c

16−QAM, R = 1/2 c −1

10

−2

10

MMSE−LD ITS (M−Algorithm), M=32 ITS (M−Algorithm), M=8 Sphere Detection, 16 candidates Sphere Detection, 2 candidates

10

12

14

16

SNR [dB]

18

20

Figure 4: Comparison of the performance of Sphere Detection and ITS for rate 1/2 and 3/4 coded 16-QAM transmission, using the WIGWAM OFDM system parameters, 4x4 MIMO, and the IEEE 802.11n E channel model. While the hard output from tree search techniques is always of higher quality than that of the linear detector, the quality of the soft output depends crucially on the number of candidates found. This issue is illustrated by the results in Figure 4. For a low number of retained paths, counter-hypotheses will be missing for some bits (Xl±1 ∩ L = ∅), leading to a low quality of the soft output for those bits (LLR clipping [5, 8] is typically used to address this issue). The results in Figure 4 show that setting M = 32 for ITS and finding the 16 best candidates using the Sphere detector already provides good results, and the performance does not improve significantly if we increase complexity any further (gains are substantially below 0.5dB). Regarding the relative complexity of Sphere detection and ITS, the former has a lower average, but a much higher maximum complexity. Taking the case of rate 1/2 coded transmission from Figure 4 as an example, the number of extended nodes for ITS (using the multi-level-property of Gray mapping, for details refer to [8]) is P = 197 for M = 32. Four branch metrics are calculated for each extended node, resulting in a total of around 800 branch metric computations. For the case of Sphere detection, an average of only P = 70 node extensions are required in the waterfall region around SNR=12dB. The average number of tree branches is only around 140, as the search radius strongly limits the search tree. However, the worst case

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

number of branch metric computations lies in the order of 3000 – almost 4 times the figure for ITS. In the following, ITS with M = 32 will serve as our performance bound. B.

The Medium Diversity Case

Figure 5 shows the performance of a linear MMSE detector for a 802.11n system on the 802.11n D channel. For all cases of rate 1/2 coded transmission, the offset to the ITS bound is in the order of 1dB, confirming our expectation from Section II.C.. The results for higher spectral efficiencies show an offset of 3-5dB. Comparing the linear detection results for rate 1/2 coded 64-QAM transmission and rate 3/4 coded 16-QAM transmission (which achieve the same spectral efficiency) show that in the case of linear detection, it is advantageous to use low rate channel coding together with higher order modulation.

C.

Results for the low diversity case are presented in Figure 6. There is almost no frequency diversity available (cf. the 16-QAM rate 3/4 results) and the Eigenmode spread is quite high. Therefore, only a 2x2 MIMO setup is used – for which the linear detector still shows reasonable performance. For 4-QAM transmission, the reduced noise enhancement (due to MMSE filtering) is enough to bring the linear detector within only 1-2dB of the ML bound. However, the reduction of the diversity order to 1 will evidently cause the offset between ML and linear detection to grow substantially for low target block error rates. The use of advanced detection strategies is hence very attractive for modulation orders of 16-QAM and beyond, where the achievable gains increase to over 5dB, for a block error rate of 1%.

Single Shot Linear Detection in High Diversity Scenario

0

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The Low Diversity Case

Single Shot Linear Detection in Low Diversity Channel

0

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16−QAM, R = 1/2 c

−1

4−QAM, R = 1/2 c

−2

Linear Detection ML Bound (ITS, M=32)

10

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BLER

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16−QAM, R = 3/4 c

64−QAM, R = 1/2 c

15

SNR [dB]

20

−2

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Figure 5: Performance of MMSE linear detection vs. ITS (M=32) as ML bound for a 4x4 MIMO 802.11n system on the IEEE 802.11n D channel and spectral efficiencies from 4 bit/s/Hz (QPSK, rate 1/2) up to 18 bit/s/Hz (64-QAM, rate 3/4). For tree search detection, the picture looks quite different. As the modulation order increases, there is an increased loss in (extrinsic) information if no a priori knowledge on the information bits is available (cf. equation (2)) and the offset between ML and MAP bound increases. Moreover, the offset between MIMO (outage) capacity (which is defined by the spectral efficiency only) and the MAP bound also grows, as there is an increased mismatch between a powerful outer code and the MAP detector [19]. It is hence preferable to use high rate channel coding in conjunction with lower order modulation. The detection strategy employed at the receiver should hence be taken into account when choosing the modulation-coding scheme at the transmitter. Comparing the gain of ITS over linear MMSE detection in Figure 4 and Figure 5 illustrates that even the 20MHz mode of the 802.11n system in combination with the slightly less frequency-selective 802.11n D channel still exhibits sufficient diversity in order for the linear MMSE receiver to achieve quite decent performance. The offset to the ML bound increases only slightly (by ≈ 1dB for code rate 3/4).

16−QAM, R = 1/2 c

4−QAM, R = 1/2 c

−1

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Linear Detection ML Bound (ITS, M=16)

0

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SNR [dB]

20

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Figure 6: Performance of the MMSE linear detection vs. ITS (M=16) as ML bound for the LTE-like system using 2x2 MIMO on the WINNER D1 channel, for spectral efficiencies from 2 bit/s/Hz up to 6 bit/s/Hz.

V. A.

I TERATIVE D ETECTION -D ECODING

Linear Detection with SoftSIC “Post-Processing”

There is only little gain if linear receivers are used in an iterative detection-decoding setup. In order to improve performance, the detector must use the information provided by the decoder to suppress interference. The combination of linear detection in the first iteration and SoftSIC (cf. Section II.B.) in the following iterations is very attractive, especially in combination with the complexity reduction methods proposed for the SoftSIC in [20]. The SoftSIC can then be seen as a kind of “post-processing” using the decoder to improve the soft output of the linear detector. When doing iterative detection-decoding, it is important to match the EXIT chart transfer characteristic of the inner MIMO detector and the outer channel decoder. Since the transfer characteristic of the MIMO detector has a significant positive slope even for Gray mapped transmission, it is preferable to use a (slightly) weaker channel code. We therefore used memory 2

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

(7R , 5) constituent convolutional codes for the rate 1/2 Turbo Code. The reduction in the code memory from 3 to 2 allows doubling the number of internal decoder iterations to 16 without increasing the total decoding complexity. This approach fits very well with our idea of post-processing for the linear detector: applying the proposals from [19], we use a total of 3 detector-decoder iterations and allow the decoder to distribute the 16 internal decoder iterations as needed, based on the a priori knowledge at its input. The only complexity increase in our iterative setup now stems from the two applications of the SoftSIC detector, which is quite small, compared to the effort required for a tree search based detector. The High Diversity Case

Results for a scenario with a high amount of frequency and spatial diversity are presented in Figure 7. For the case of rate 1/2 coded 4/16-QAM transmission, the proposed linear detection with post-processing performs within 1dB of the MAP bound. Note that the decoding effort invested is only half that for the MAP setup (where a total of 32 internal decoder iterations are used), and the detection complexity is negligible compared to that of the ITS detector used as performance bound. 0

BLER

c

−1

−2

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Linear Detection ML Bound (ITS, M=32) 1xMMSE−LD + 2xSoftSIC MAP Bound (4xITS, M =32)

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VI. 16−QAM, R = 1/2 c

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SNR [dB]

A. 15

ML Bound (ITS, M = 16) Linear detection MAP Bound (4xITS, M = 16) 1xMMSE−LD + 2xSoftSIC

5

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SNR [dB]

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Figure 8: Performance of MMSE linear detection with SoftSIC post-processing vs. 4xITS (M=16) as MAP bound for the LTE-like system (2x2 MIMO, WINNER C1 channel model) and spectral efficiencies of 2 bit/s/Hz (QPSK, rate 1/2) and 4 bit/s/Hz (16-QAM, rate 1/2).

16−QAM, R = 3/4

4−QAM, R = 1/2 c

4−QAM, R = 1/2 c

10

10

10

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16−QAM, R = 1/2

Iterative Detection Methods in High Diversity Channel

10

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Figure 7: Performance of MMSE linear detection with SoftSIC post-processing vs. 4xITS (M=32) as MAP bound, for a 4x4 MIMO WIGWAM system on the IEEE 802.11n E channel and for spectral efficiencies from 4 bit/s/Hz up to 12 bit/s/Hz. For the case of higher rate channel coding, the offset between the proposed scheme and the ITS/MAP bound is around 2-3dB – falling short of achieving even ML performance. However, the offset to the ML bound is only 1dB, so this approach might be a valid alternative to single-shot detection-decoding using a more powerful detection strategy. C.

Iterative Detection in Low Diversity Scenario

0

10

BLER

B.

is also very low, around 2 (cf. the results for the linear detector and 16-QAM transmission). Again, using a simple linear MMSE detection works very well for the case of 4-QAM transmission: linear detection with post-processing achieves ML performance and comes within 1dB of the MAP bound, as shown in figure 8. For the case of higher order modulation, more advanced detection strategies should be used, as only these are able to extract the (limited) spatial diversity from the channel and thus show high gains over linear detection for low target block error rates.

The Low Diversity Case

For this scenario, we simulated the performance of the LTElike 2x2 MIMO system in a suburban channel scenario with very high correlation at the BS side (WINNER channel model C1, angular spread of only 5◦ ). The frequency diversity order

C OMPLEXITY E VALUATION AND C ONCLUSIONS

Performance-Complexity Analysis

To set the SNR gains achievable by using advanced detection techniques in relation to the increase in required effort, we analyzed the complexity required for ITS, linear and SoftSIC detection. Figure 9 summarizes the performance-complexity trade-offs achievable by ITS and linear MMSE detection (with and without SoftSIC post-processing), for rate 1/2 and 3/4 coded 16-QAM transmission in the high and low diversity environment, and for both the single-shot and the iterative detection-decoding case. Points towards the lower left indicate a better performance-complexity trade-off. For the sake of simplicity, we neglected the complexity of preprocessing (which depends on the channel coherence time and the burst length) and decoding. We also normalized the complexity figures to those of single-shot linear detection. The presented results illustrate that even in the case of high rate coding and low diversity, linear MMSE detection achieves reasonable performance at very low cost – if better performance is the target, the detection effort has to be increased substantially (around a 10-fold increase). For tree search based detection, it appears to be more attractive to use single-shot

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

detection-decoding with a higher number of retained paths, as opposed to running the detector multiple times with lower complexity (even when neglecting the complexity of decoding). The complexity invested in SoftSIC post-processing for linear detection is quite high, but it can be substantially reduced by applying the ideas from [20] to improve the performancecomplexity trade-off for this approach. Alternatively, one may consider post-processing based on tree search techniques. High diversity case, 16−QAM Relative Complexity

100

10

x ... ITS, M = 32 * ... ITS, M = 8 o ... MMSE−LD / MMSE−LD + SoftSIC

Iterative detection Single−shot detection

Blue: Rc = 1/2

1 Green: Rc = 3/4 9 11

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Relative Complexity

100

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SNR for BLER 5% [dB]

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Low diversity case, 16−QAM + ... ITS, M = 16 > ... ITS, M = 4 o ... MMSE−LD / MMSE−LD + SoftSIC

Iterative detection Single−shot detection

Blue: Rc = 1/2

1 Green: Rc = 3/4 16 18

20

22

24

SNR for BLER 5% [dB]

28

Figure 9: Performance-complexity trade-off for the high diversity case (WIWGAM, 802.11n E channel) and the low diversity case (LTE, WINNER D1 channel), for rate 1/2 and 3/4 coded 16-QAM transmission. B.

Conclusions

We evaluated the performance of linear MMSE detection for a number of relevant application scenarios, ranging from a broadband MIMO-OFDM system experiencing rich scattering and highly frequency selective fading in a hot spot environment to a wideband MIMO-OFDM based cellular system operating in an environment with very limited spatial and frequency diversity. By also simulating the performance of capacityapproaching tree search based detection techniques, we were able to give an overview of the gains achievable in both a noniterative and iterative MIMO detection-decoding setup. The presented results show that for lower channel coding rates and/or lower order modulation (4-QAM), simple linear detection (with and without SoftSIC post-processing) performs within only 1-2dB of the respective performance bounds, independent of the available amount of diversity, making it very attractive from the complexity point-of-view. The use of advanced detection strategies is therefore mainly attractive for cases where high rate channel coding is used and/or transmission takes place with higher order modulation over a channel with very low diversity order (substantially below 10). ACKNOWLEDGMENT This work was supported by the German ministry of research and education within the project Wireless Gigabit with advanced multimedia support (WIGWAM) under grant 01 BU 370.

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