Full-Rate MIMO Techniques for NextGeneration Wireless Networks Onur OGUZ1, Serdar SEZGINER2, Alberto TARABLE3 1 Université catholique de Louvain, Place du Levant, 2, B-1348 Louvain-la-Neuve, Belgium. Tel : +32 10 47 80 71, Email:
[email protected] 2 Sequans Communications, 19, Le Parvis de la Défense, 92073 Paris La Défense Cedex, Tel: +33 1 70721600, Email:
[email protected] 3 Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy Tel: +39 011 0904228, Fax: +39 011 0904099, Email:
[email protected] Abstract: Next-generation wireless network systems are foreseen to provide high peak spectral efficiencies (as much as 15 bps/Hz in the downlink and 6.75 bps/Hz in the uplink under ideal conditions) and high mobility (up to 120km/h). Due to such demanding requirements, the need for efficient MIMO signalling schemes and corresponding efficient receiver architectures becomes mandatory. In this work, we investigate a number of alternative full-rate MIMO transmission schemes with different receiver structures. Beyond a brief description of the proposed schemes, simulation results are presented, where the test parameters and the performance requirements are chosen, whenever possible, in compliance with the IEEE 802.16m Evaluation Methodology Document (EMD). Such simulation results assess the performance of the proposed schemes in a WiMAX scenario and allow comparing the different solutions on a foot of parity. Keywords: MIMO, spatial multiplexing, space-time block codes, WiMAX, LTE.
1. Introduction Next-generation wireless network systems, also known as IMT-Advanced (IMT.ADV), are foreseen to provide high spectral efficiencies and high mobility. Playing the key role for answering such demanding requirements, multi-input multi-output (MIMO) communication schemes provide a rich set of alternatives tailored for different scenarios. In fact, MIMO techniques have already become an essential part of emerging technologies like WiMAX (Worldwide Interoperability for Microwave Access) [1] and LTE (Long Term Evolution) [13]. MIMO schemes can be divided into two categories with respect to their target, i.e., diversity versus multiplexing gain. The first category includes space-time (or frequency) block code (STBC) structures, where multiple copies of the same symbol are transmitted through different antennas to exploit the various received versions of the data. Hence, STBCs improve the reliability of data-transfer by introducing spatial diversity. Among STBCs, Alamouti code (namely, Matrix A of IEEE 802.16e specifications [1]) has been included in most of the standards and already been implemented in various systems. Its popularity comes from the fact that it achieves full transmit diversity with a receiver having linear decoding complexity. However, Alamouti code suffers from the rate loss. In IEEE 802.16e, an alternative STBC, namely Matrix C, has been added. This code is a variant of Golden code [12], which is known to be the best 2×2 STBC achieving the diversitymultiplexing frontier. But the problem of this code is its decoding complexity. Recently, this motivated many researchers to investigate new STBCs having similar performance as Golden code, but with much lower decoding complexity. An example of such STBCs has
been developed in [2] and [4], where it was shown that the proposed STBC achieves essentially the same performance while reducing the hard decoding complexity significantly. The second category consists of Spatial Multiplexing (SM), where the data stream is multiplexed over the transmit antennas. Therefore, the transmission rate is multiplied by the number of transmit antennas, resulting in a transmission without rate loss, whereas no transmit diversity is exploited. Unlike Alamouti code, optimal detection complexity of SM increases exponentially with the number of parallel streams and the modulation size. Therefore, suboptimal receivers including linear detectors, iterative receivers, sphere detectors, etc., are utilized to decode spatially multiplexed signals. In the literature, while analysing their performance, MIMO schemes are usually treated as stand-alone, i.e., without considering the accompanying forward error correcting (FEC) code. However, in practical systems, where FEC cannot be avoided, channel coding is often able to exploit some intrinsic source of diversity available in the environment, e.g., timevariations in the channel, thanks to the memory utilization and added redundancy. The mobility supported in IMT.ADV, combined with the OFDM(A)-based technologies, introduces a bottleneck in detection of STBCs and SM due to the resulting intercarrier interference (ICI). This adds a new level of complexity to the detection of SM. Moreover, the quasi-static channel assumption made for STBCs, which is vital for simple equalization, becomes more arguable in rapidly varying channels. Thus, it is necessary to verify the performance of MIMO schemes for IMT.ADV-compliant scenarios, i.e., with FEC and under high mobility. In this work, based on such scenarios [15], we assess the performance of the considered schemes in IEEE 802.16e specifications as well as the alternative STBCs [2], [4] and compare different techniques on a foot of parity. Rather than advocating one particular scheme, our aim is to provide a general idea on the selection of MIMO schemes with respect to the objectives (e.g., data rate) and parameters (e.g., mobility) of the considered communication scenario. In order to limit the wide range of alternatives at the receiver side, we limit our work to consider only receivers that do not deal with ICI mitigation. The rest of the paper is organized as follows; in Section 2, we summarize full-rate MIMO transmission schemes. We discuss SM in a generalized form and briefly explain the alternative full-rate STBCs. Then, in Section 3, we describe the considered suboptimal receiver structures. Section 4 is devoted to simulation results. Finally, the paper is concluded in Section 5.
2. Full-Rate MIMO Transmission 2.1 Multilayer SM In multilayer SM ([2], [8]), whose block diagram for NT transmit antennas is shown in Figure 1, the data stream is split into K sub-streams, where K is the number of layers. In the k-th layer, the k-th sub-stream is FEC-encoded with rate r, and modulated using a 22L-QAM constellation. Then, each symbol stream is again de-multiplexed into NT sub-streams so that, for the j-th transmit antenna, K modulated symbols are linearly combined resulting in an effective constellation of size M = 22LK. At each transmit antenna, the symbol stream is then OFDM modulated and transmitted. Note that, for K=1, multilayer SM is in fact equal to the classical SM or “Matrix-B”, as defined in the IEEE 802.16e standard [1], with arbitrary number of transmit antennas. An imminent advantage of SM schemes is the flexibility of spectral efficiency given by, EffSpectral = 2rLKN T bps/subcarrier.
(1)
Enc 1
Binary Data
MOD
DeMUX
K NT
DeMUX
Enc K
MOD
DeMUX
K
Figure 1: Transmitter structure for multilayer SM
The use of SM in MIMO transmission significantly simplifies the optimization problem both at the transmitter and the receiver by allowing unified analysis of the receiver structures independent of specific space-time/frequency block code constructions. Therefore, SM is easily adaptable to the divergent needs of different applications in terms of spectral efficiency, number of transmit and receive antenna configurations, as well as different permutations. In addition to these general advantages of SM, multilayer SM provides very good performance, when a careful optimisation of the combination coefficients is performed and iterative decoding is used at the receiver. The receiver has an affordable complexity, polynomial in NT (instead of exponential), thanks to the suboptimal front-end [7]. In addition, considering the whole system, the multilayer SM technique, by improving the performance, boosts the power efficiency, increases the battery life, and reduces the related costs. 2.2 Full-Rate Full-Diversity Space-Time Block Codes During the last decade, STBC design has taken a remarkable attention and different criteria has been considered in order to find the best STBC. Among the proposed criteria, maximization of the diversity and coding gains have been considered in the majority of the attempts (see, e.g., [4], and references therein). Based on these criteria, many interesting STBCs have been proposed and, among them, the Golden code [12] appears to have the best performance. In particular, the Golden code provides full-rate and full-diversity with the highest known nonvanishing coding gain. Because of these attractive features, a variant of Golden code, namely, Matrix C, has already been included in IEEE 802.16e specification [1]. For a group of 4 symbols (s1 , s2 , s3 , s4 ) , Matrix C is given by XC =
1 α(s1 + θs2 ) α(s 3 + θs4 ) , 5 iα (s 3 + θ s4 ) α (s1 + θ s2 )
(2)
where θ = (1 + 5 ) / 2 , θ = (1 − 5 ) / 2 , α = 1 + i − iθ , α = 1 + i − iθ , and i = − 1 . This STBC leads to a spatial diversity of order 4 for 2 receiver antennas in the absence of channel coding, and it achieves substantially better performance than the SM whose spatial diversity is limited to the number of receive antennas (in this case 2). However, as explained above, the problem of this STBC is its inherent detection complexity. Therefore, other full-rate full-diversity STBCs are being introduced as alternatives to Golden code, characterized by having lower optimum decoding complexity. This is crucial especially for the current mobile wireless applications. Indeed, for a signal constellation with M points, the optimum hard-decoding receiver for Matrix C involves the computation of M4 Euclidean distances and selects the symbol quadruplet achieving the minimum distance. This is prohibitive in practical applications for the current technology and this requires the use of new STBCs having close performance to that of XC with lower detection complexity. Recently, decoding complexity has been taken into account in the design of STBCs [2] and the attention has been turned to STBCs with low decoder complexity. They attempt to
maximize both the diversity gain and the coding gain, while leading to an optimum detection of reduced complexity (subject to quasi-static channel assumption). In this context, a full-rate full-diversity 2×2 STBC has been presented in [2] and [4] namely, Matrix D, as an alternative to Matrix C. Motivated by the orthogonality of Alamouti STBC, Matrix D achieves the diversitymultiplexing frontier with optimum detection complexity O(M2). Matrix D is expressed in its general form as:
as + bs3 XD = 1 as2 + bs4
− cs 2* − ds4* . cs1* + ds3*
(3)
where, a, b, c, d are design parameters to be optimized to achieve full diversity with the highest possible coding gain. For detailed derivations and demonstrations one can refer to [5], where different criteria have been considered for comparison in the absence of channel coding. In this paper, we consider Matrix C and Matrix D and compare them with SM, in the presence of channel coding. It is also worth mentioning that the STBCs having similar properties as (2) and (3) yield very close performances and, therefore, will not be presented for the sake of clarity.
3. Receivers for MIMO transmission In this section, we briefly present two approaches commonly adopted in the receiver design i.e., iterative receiver and sequential receiver, as depicted in Figure 2 and Figure 3, respectively.
Figure 2: Iterative receiver
Figure 3: Sequential receiver
3.1 Iterative receiver The iterative receiver is in fact an approximate solution to a MAP detection, i.e., joint equalization-detection problem [6]. As depicted in Figure 2, it consists of two blocks exchanging information with each other. The first (inner) block (called suboptimal front-end, SOFE) in general sense, is an approximated MAP demodulator, whose purpose is to deliver posterior information (in the form of log-likelihood ratios, LLRs) on coded bits (for each layer), using the observation from the channel and current a-priori information. The second (outer) block consists of a bank of soft-input soft-output channel decoders (one for each layer), working in parallel. In principle each channel decoder updates information (again in the form of LLRs) about both the data bits and the coded bits for the corresponding layer. To lower the complexity, a stopping rule is usually set for the iterations between SOFE and channel decoders, and excess iterations without changes on LLRs can be avoided. In addition, the number of these iterations is also usually limited to avoid the receiver lingering when the observation is severely corrupted. Obviously, the performance of the iterative receiver is directly related with the utilized SOFE. Thus, it is necessary to remind the operations performed in SOFE block in a given iteration [7]:
Input LLRs (for all layers) produced by the channel decoders, are translated into symbol distributions (initially equiprobable). 1. Soft ISI cancellation is performed, in order to obtain channel output concerning only a single transmit antenna at a time. 2. For each transmit antenna, equalization for all the transmitted symbols is performed using a linear equalization filter. The filter coefficients may be updated for each symbol depending on the utilized equalization method. This method usually determines the distinction between different suboptimum receivers. 3. Symbol distributions are updated using a Gaussian approximation of the residual ISI after filtering, and from these distributions output LLRs are computed. According to the linear equalization filter chosen in step2, several types of suboptimum receivers can be distinguished: •
Linear MMSE (L-MMSE) SOFE receiver [2]: the filter is a linear MMSE filter that depends on input LLRs and changes from iteration to iteration. It lays in the Wang-Poor family of solutions [9].
•
Fixed MMSE (F-MMSE) SOFE receiver: the filter is a standard linear MMSE filter, which does not depend on input LLRs and is kept fixed. Hence, equalization is performed once and used for each outer iteration.
•
Switched (SW) SOFE receiver [14]: In switched SOFE, a MRC precedes the linear MMSE filter. The signal-to-interference-plus-noise ratio (SINR) at the filter output is compared to the SINR at the filter input (which is MRC output). Whenever the latter becomes larger than the former, LLRs will be computed directly from MRC output, for all subsequent iterations.
If the ICI is neglected, the complexity introduced by these receivers can be roughly quantified as a function of the MIMO configuration. Let NR be the number of receive antennas. For the L-MMSE turbo receiver, the computation of the filter coefficients involves one matrix inversion (of size-NR) per symbol per iteration, apart for the first iteration. The F-MMSE SOFE receiver requires only one matrix inversion (of size-NR) per channel coherence time, to initialize the iterations. The MRC SOFE receiver does not require any matrix inversion. The Switched SOFE receiver, like the F-MMSE receiver, requires only one size-NR matrix inversion per channel coherence time. Note that, the lowered complexity associated with the MAP approximation, makes the iterative receiver an attractive option for detection of SM transmission, e.g., [2]. 3.2 Sequential receiver Instead of MAP detection, sequential receivers attack the ML detection of data. In this way demodulation and data detection steps can be performed separately in two distinct blocks, i.e., (approximate) ML front-end and channel decoder, as depicted in Figure 3. Note that, ML detection/demodulation is usually exponential in the number of possible constellation points, making it unsuitable for practical purposes. Numerous approximations have been devised for ML demodulation according to the MIMO scheme utilized but all suffer from rather limited performance [10]. The most commonly considered techniques are linear receivers and successive interference (ISI due to multiple transmit antenna) cancellation, whose performance is limited by the quality of the strongest detected signal. As an alternative, the concept of sphere detection (SD) is introduced in [11] where ML search is restricted to include only vector constellation points that fall within a certain
search sphere. For sufficiently high SNR range this approach allows for finding the ML solution with only polynomial complexity [10]. While, SD is an attractive option, when ICI is neglected ML demodulation of STBCs can be simplified thanks to their (quasi)orthogonal structures.
4. Performance of the MIMO schemes for IMT.ADV In the previous sections, we have identified and briefly described two different categories of MIMO techniques; generalized SM in Section 2.1, coupled with an iterative suboptimum receiver described in Section 3.1, and two full-rate full-diversity STBCs in Section 2.2. In this section, we provide simulation results for the performance evaluation of these schemes. We focus on scenarios that basically emphasize the impact of such techniques while embodying the main characteristics of IMT.ADV systems. Simulations have been conducted for an OFDMA system with an FFT size of 1024, operating at 2.5 GHz with a bandwidth of 10 MHz. To mimic the time variations of a pedestrian channel and a vehicular channel, two ITU channel models, namely, ITU Ped-B and ITU Veh-A, with 6 paths each, have been utilized. A 2×2 MIMO configuration has been considered with uncorrelated antennas both at transmitter and receiver sides. For the FEC, a convolutional turbo code (CTC) is utilized with code rates equal to 1/2 and 5/6, and sufficiently long code blocks (containing 400 to 500 information bits). Accompanied with 64QAM (4QAM for 3-layer SM) modulation, considered schemes support spectral efficiencies equal to 6 and 10 bps/Hz for the given code rates. Note that, at the receiver, we utilized quasi-static channel assumption with channel state at the middle of each OFDM symbol is assumed valid for entire OFDM symbol; hence the ICI occurring due to the mobility is not mitigated. In Figure 4, block error rate (BLER) performance with a pedestrian speed of 3 km/h is shown for the described MIMO schemes. The performance of STBCs, which are decoded with approximate ML decoding as described previously, is represented by dotted curves and markers “*” for Matrix C and “+” for Matrix D. The BLER performance of single-layer SM is represented by solid curves, concerning both sequential receiver together with sphere decoder “♦” with radius equal to infinity, and iterative receivers utilizing the described SOFEs, i.e., L-MMSE “▲”, F-MMSE “■” and Switched (SW SOFE) “●” front-ends. The performance of three-layer SM (dashed curves) is analysed only for iterative receivers utilizing L-MMSE, F-MMSE and SW SOFEs. From Figure 4, it can be seen that, for 6 bps/Hz, the best performing schemes are the single-layer SM with iterative receiver and L-MMSE or SW SOFE, but with the three-layer (again with the iterative receiver and L-MMSE or SW front-end) essentially at a tie (less than 1dB of loss for BLER = 10-2), while the single-layer SM with sequential receiver and the STBCs lose about 2 dB from the best scheme. For the 10 bps/Hz case obtained by a weaker FEC (5/6 instead of 1/2), ordering is reverted and sequential receivers perform superior to iterative ones. This is mainly due to the inability of the sub-optimal front ends to supply adequately good initial estimates on data to start the iterations. A strong FEC can compensate for this flaw and improve error performance in later iterations (i.e., as in 6 bps/Hz) while a weaker FEC fails to do so and the initial SOFE estimates become dominant. Hence for the 10 bps/Hz scenario, schemes are ordered with respect to their initial equalization performance, i.e., SD, simplified ML (conditioned on certain channel conditions such as quasi-static channel) and SOFE. Figure 5 shows the BLER performance of the MIMO schemes for a vehicular speed of 60 km/h and a spectral efficiency of 6 bps/Hz. Similar to the pedestrian setting for this efficiency; iterative receivers benefit from the strong FEC and perform better than the
sequential receivers. The increased mobility only results in almost uniform performance degradation due to the increased ICI which is not mitigated. 1e+0
10 bps/Hz
Block Error Rate
1e-1
6 bps/Hz
PED-B Channel
1e-2
Mat-D Mat-C 1-Layer SM 3-Layers SM F-MMSE SW SOFE L-MMSE Sphere Decoder 1e-3 10
15
20
25
30
SNR [dB] per receive antenna
Figure 4: Error performance of 2×2 MIMO schemes over ITU Ped-B channel, at 3 km/h 1e+0
Block Error Rate
1e-1
6 bps/Hz
VEH-A Channel
1e-2
Mat-D Mat-C 1-Layer SM 3-Layers SM F-MMSE SW SOFE L-MMSE Sphere Decoder 1e-3 10
15
20
25
SNR [dB] per receive antenna
Figure 5: Error performance of 2×2 MIMO schemes over ITU Veh-A channel at 60 km/h
30
5. Conclusions In this paper, full-rate MIMO schemes, together with both iterative and sequential receivers, have been compared in several IMT.ADV-compliant scenarios. The results show that, a suitable MIMO scheme should be selected depending on the objectives (e.g., data rate), parameters (e.g., mobility) and constraints (e.g., FEC, complexity) of the considered scenario. For the low complexity case, where ICI is not mitigated, performance results show that, if a strong FEC is available, iterative receivers are favourable to the sequential receivers, whereas for the low FEC case sequential receivers have to be preferred. Initial results show that the ICI due to the mobility influences the performance of all the receiver structures rather uniformly. However, further work has to be done in order to give a complete understanding of the relationship between the context (e.g., channel conditions, mobility, and target spectral efficiency) and the MIMO scheme that fits the best to such context.
Acknowledgement The authors would like to acknowledge the support of the European Commission through the FP7 projects WiMAGIC (see www.wimagic.eu) and NEWCOM++ (see http://www.newcom-project.eu/).
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