Interferenceaware receiver structure for multiuser MIMO and LTE
 Rizwan Ghaffar^{1}Email author and
 Raymond Knopp^{1}
https://doi.org/10.1186/16871499201140
© Ghaffar and Knopp; licensee Springer. 2011
Received: 1 December 2010
Accepted: 14 July 2011
Published: 14 July 2011
Abstract
In this paper, we propose a novel lowcomplexity interferenceaware receiver structure for multiuser MIMO that is based on the exploitation of the structure of residual interference. We show that multiuser MIMO can deliver its promised gains in modern wireless systems in spite of the limited channel state information at the transmitter (CSIT) only if users resort to intelligent interferenceaware detection rather than the conventional singleuser detection. As an example, we focus on the long term evolution (LTE) system and look at the two important characteristics of the LTE precoders, i.e., their low resolution and their applying equal gain transmission (EGT). We show that EGT is characterized by full diversity in the singleuser MIMO transmission but it loses diversity in the case of multiuser MIMO transmission. Reflecting on these results, we propose a LTE codebook design based on two additional feedback bits of CSIT and show that this new codebook significantly outperforms the currently standardized LTE codebooks for multiuser MIMO transmission.
1. Introduction
The spatial dimension surfacing from the usage of multiple antennas promises improved reliability, higher spectral efficiency [1], and the spatial separation of users [2]. This spatial dimension (MIMO) is particularly beneficial for precoding in the downlink of multiuser cellular systems (broadcast channel), where these spatial degrees of freedom at the transmitter can be used to transmit data to multiple users simultaneously. This is achieved by creating independent parallel channels to the users (canceling multiuser interference) and the users subsequently employ simplified singleuser receiver structures. However, the transformation of crosscoupled channels into parallel noninteracting channels necessitates perfect channel state information at the transmitter (CSIT) whose acquisition in a practical system, in particular frequency division duplex (FDD) system, is far from realizable. This leads to the precoding strategies based on the partial or quantized CSIT [3], which limit the gains of multiuser MIMO.
Ongoing standardizations of modern cellular systems are investigating different precoding strategies based on lowlevel quantized CSIT to transmit spatial streams to multiple users sharing the same timefrequency resources. In thirdgeneration partnership project longterm evolution (3GPP LTE) system [4], the CSIT acquisition is based on the precoder codebook approach. These LTE precoders are characterized by low resolution and are further based on the principle of equal gain transmission (EGT). These precoders when employed for the multiuser MIMO mode of transmission are unable to cancel the multiuser interference thereby increasing the suboptimality of conventional singleuser detection. This has led to the common perception that multiuser MIMO mode is not workable in LTE [[5], p. 244].
Considering multiuser detection, we propose in this paper a lowcomplexity interferenceaware receiver [6] for the multiuser MIMO in LTE. Though multiuser detection has been extensively investigated in the literature for the uplink (multiple access channel), its related complexity has so far prohibited its employment in the downlink (broadcast channel). For the multiple access channel, several multiuser detection techniques exist in the literature starting from the optimal multiuser receivers [7] to their nearoptimal reduced complexity counterparts (sphere decoders [8]). The complexity associated with these techniques led to the investigation of lowcomplexity solutions as suboptimal linear multiuser receivers [9], iterative multiuser receivers [10, 11], and decisionfeedback receivers [12, 13]. Since in practice, most wireless systems employ error control coding combined with the interleaving, recent work in this area has addressed multiuser detection for coded systems based on soft decisions [14, 15].
Our proposed lowcomplexity interferenceaware receiver structure not only reduces one complex dimension of the system but is also characterized by exploiting the interference structure in the detection process. Considering this receiver structure, we investigate the effectiveness of the lowresolution LTE precoders for the multiuser MIMO mode and show that multiuser MIMO can bring significant gains in future wireless systems if the users resort to intelligent interferenceaware detection as compared to the suboptimal singleuser detection. We further look at the second characteristic of the LTE precoders, i.e., EGT both for the singleuser and multiuser MIMO modes. We show that the EGT has full diversity in the singleuser MIMO mode (a result earlier derived for equal gain combining for BPSK in [16] and for EGT in MIMO systems in [17]); however, it suffers from a loss of diversity in multiuser MIMO mode [18]. Based on this analysis, we propose a design criteria for the precoder codebooks and show that the additional feedback of two bits for CSIT can lead to significant improvement in the performance of the multiuser MIMO.
Regarding notations, we will use lowercase or uppercase letters for scalars, lowercase boldface letters for vectors and uppercase boldface letters for matrices. The matrix I_{ n } is the n × n identity matrix. . and . indicate norm of scalar and vector while (.) ^{ T } , (.)*, and (.)^{†} indicate transpose, conjugate, and conjugate transpose, respectively. (.) _{ R } indicates the real part and (.) _{ I } indicates the imaginary part of a complex number. The notation E (.) denotes the mathematical expectation while denotes the Gaussian Qfunction. All logarithms are to the base 2.
The paper is divided into eight sections. In Sec. II, we give a brief overview of LTE and define the system model. In Sec. III, we consider a geometric scheduling strategy for the multiuser MIMO mode in LTE and propose a lowcomplexity interferenceaware receiver structure. In Sec. IV, we look at the information theoretic perspective of the proposed receiver structure. Sec. V is dedicated to the performance analysis of the EGT that is followed by the simulation results. Before concluding the paper, we propose a design criteria for the precoder codebooks of the forthcoming standardizations of LTE. The proof details in the paper have been relegated to appendices to keep the subject material simple and clear.
2. LTE system model
A. LTEA brief overview
In 3GPP LTE, a 2 × 2 configuration for MIMO is assumed as the baseline configuration; however, configurations with four transmit or receive antennas are also foreseen and reflected in the specifications [19]. LTE restricts the transmission of maximum of two codewords in the downlink that can be mapped onto different layers where one codeword represents an output from the channel encoder. Number of layers available for the transmission is equal to the rank of the channel matrix (maximum 4). In this paper, we restrict ourselves to the baseline configuration with the eNodeB (LTE notation for the base station) equipped with two antennas while we consider single and dualantenna user equipments (UEs). Physical layer technology employed for the downlink in LTE is OFDMA combined with bit interleaved coded modulation (BICM) [20]. Several different transmission bandwidths are possible, ranging from 1.08 to 19.8 MHz with the constraint of being a multiple of 180 kHz. Resource blocks (RBs) are defined as groups of 12 consecutive resource elements (REs  LTE notation for the subcarriers) with a bandwidth of 180 kHz thereby leading to the constant RE spacing of 15 kHz. Approximately, 4 RBs form a subband and the feedback is generally done on subband basis. Seven operation modes are specified in the downlink of LTE; however, we shall focus on the following four modes:

Transmission mode 2. Fallback transmit diversity. Transmission rank is 1, i.e., one codeword is transmitted by the eNodeB. Employs Alamouti spacetime or spacefrequency codes [21].

Transmission mode 4. Closedloop spatial multiplexing. Transmission rank is 2, i.e., two codewords are transmitted by the eNodeB to the UE in the singleuser MIMO mode. UEs need to have minimum of two antennas.

Transmission mode 5. Multiuser MIMO mode. Supports only rank1 transmission, i.e., one codeword for each UE.

Transmission mode 6. Closedloop precoding for rank1 transmission, i.e., one codeword for the UE in the singleuser MIMO mode.
In the case of transmit diversity and closedloop precoding, one codeword (data stream) is transmitted to each UE using Alamouti code in the former case and LTE precoders in the latter case. Timefrequency resources are orthogonal to the different UEs in these modes thereby avoiding interference in the system. However, in the multiuser MIMO mode, parallel codewords are transmitted simultaneously, one for each UE, sharing the same timefrequency resources. Note that LTE restricts the transmission of one codeword to each UE in the multiuser MIMO mode.
For closedloop transmission modes (mode 4, 5 and 6), precoding mechanisms are employed at the transmit side with the objective of maximizing throughput. The precoding is selected and applied by the eNodeB to the data transmission to a target UE based on the channel feedback received from that UE. This feedback includes a precoding matrix indicator (PMI), a channel rank indicator (RI), and a channel quality indicator (CQI). PMI is an index in the codebook for the preferred precoder to be used by the eNodeB. The granularity for the computation and signaling of the precoding index can range from a couple of RBs to the full bandwidth. For transmission mode 5, the eNodeB selects the precoding matrix to induce high orthogonality between the codewords so that the interference between UEs is minimized. In transmission modes 4 and 6, the eNodeB selects the precoding vector/matrix such that codewords are transmitted to the corresponding UEs with maximum throughput.
Note that there is a possibility of swapping the columns in P but the swap must occur over the entire band.
B. System model
where y_{1,k}, z_{1,k}∈ ℂ^{2 × 1} are the vectors of the received symbols and circularly symmetric complex white Gaussian noise of doublesided power spectral density N_{0}/2 at the 2 receive antennas of UE1, respectively. H_{1,k}∈ℂ^{2 × 2} is the channel matrix from eNodeB to UE1.
3. Multiuser MIMO mode
We now look at the effectiveness of the lowresolution LTE precoders for the multiuser MIMO mode. We first consider a geometric scheduling strategy [22] based on the selection of UEs with orthogonal precoders.
A. Scheduling strategy
The scheduling strategy is based on the principle of maximizing the desired signal strength while minimizing the interference strength. As the decision to schedule a UE in the singleuser MIMO, multiuser MIMO or transmit diversity mode will be made by the eNodeB, each UE would feedback the precoder that maximizes its received signal strength. So this selected precoder by the UE would be the one closest to its matched filter (MF) precoder in terms of the Euclidean distance.
For the multiuser MIMO mode, the eNodeB needs to ensure good channel separation between the coscheduled UEs. Therefore, the eNodeB schedules two UEs on the same RBs that have requested opposite (orthogonal) precoders, i.e., the eNodeB selects as the second UE to be served in each group of allocatable RBs, one of the UEs whose requested precoder p_{2} is 180° out of phase from the precoder p_{1} of the first UE to be served on the same RBs. So if UE1 has requested , q ∈ {±1, ±j}, then eNodeB selects the second UE that has requested . This transmission strategy also remains valid also for the case of dualantenna UEs where the UEs feedback the indices of the precoding vectors that maximize the strength of their desired signals, i.e., Hp^{2}. For the multiuser MIMO mode, the eNodeB schedules two UEs on the same RE, which have requested 180° out of phase precoders. The details of this geometric scheduling strategy can be found in [22].
Though this precoding and scheduling strategy would ensure minimization of the interference under the constraint of lowresolution LTE precoders, the residual interference would still be significant. Singleuser detection, i.e., Gaussian assumption of the residual interference and its subsequent absorption in noise, would lead to significant degradation in the performance. On the other hand, this residual interference is actually discrete belonging to a finite alphabet and its structure can be exploited in the detection process. However, intelligent detection based on its exploitation comes at the cost of enhanced complexity. Here, we propose a lowcomplexity interferenceaware receiver structure that on one hand reduces one complex dimension of the system while on the other hand, it exploits the interference structure in the detection process.
B. Lowcomplexity interferenceaware receiver
where indicates the crosscorrelation between the two effective channels. Here, we have used the relation a  b^{2} = a^{2} + b^{2}  2 (a*b) _{ R } where the subscript (.) _{ R } indicates the real part. Note that the complexity of the calculation of bit metric (10) is .
Note that the subscript (.) _{ I } indicates the imaginary part.
where → indicates the discretization process in which among the finite available points of x_{2,R}and x_{2,I}, the point closest to the calculated continuous value is selected. So if x_{2} belongs to QAM256, then instead of searching 256 constellation points for the minimization of (14), the metric (15) reduces it to merely two operations thereby trimming down one complex dimension in the detection, i.e., the detection complexity is independent of χ_{2} and reduces to .
The receiver structure would remain same with being replaced by H_{1}, i.e., the channel from eNodeB to the two antennas of UE1. Subsequently and are the MF outputs while ρ_{12} = (H_{1}p_{1})^{†}H_{1}p_{2} is the crosscorrelation between two effective channels.
Comparison of receivers complexity
Receiver  Real multiplications  Real additions 

Interferenceaware receiver (equal energy alphabets)  8n_{ r } + 10M + log(M)  4  
Interferenceaware receiver (non equal energy alphabets)  12n_{ r } + 18M + log(M)  6  
Maxlog MAP receiver  2M^{2}n_{ r } + 8Mn_{ r }  6M^{2}n_{ r } + 4Mn_{ r }+ log(M)  M^{2} 
Singleuser receiver (equal energy alphabets)  10n_{ r } + 6  10n_{ r }  3 
Singleuser receiver (non equal energy alphabets)  10n_{ r } + 3M + log(M)  3 
The interferenceaware receiver is therefore not only characterized by low complexity but also resorts to intelligent detection by exploiting the structure of residual interference. Moreover, this receiver structure being based on the MF outputs and devoid of any division operation can be easily implemented in the existing hardware. However, the proposed receiver needs both the channel knowledge and the constellation of interference (coscheduled UE). As the UE already knows its own channel from the eNodeB and the requested precoder, it can determine the effective channel of the interference based on the geometric scheduling algorithm, i.e., the precoder of the coscheduled UE is 180° out of phase of its own precoder. Consequently there is no additional complexity in utilizing this receiver structure as compared to using singleuser receivers except that the UE needs to know the constellation of interference.
4. Information theoretic perspective
where P = [p_{1}p_{2}] is the precoder matrix, is the mutual information of UE1 once it sees interference from UE2 and is the mutual information of UE2 once it sees interference from UE1. Y_{1} is the received symbol at UE1 while X_{1} is the symbol transmitted by the eNodeB to UE1. Note that interference is present in the statistics of Y_{1} and Y_{2}. No sophisticated power allocation is employed to the two streams as the downlink control information (DCI) in the multiuser mode in LTE includes only 1bit power offset information, indicating whether a 3 dB transmit power reduction should be assumed or not. We therefore consider equalpower distribution between the two streams. For the calculation of mutual information, we deviate from the unrealistic Gaussian assumption for the alphabets and consider them from discrete constellations. The derivations of the mutual information expressions for the case of finite alphabets have been relegated to Appendix A for simplicity and lucidity.
The geometric scheduling algorithm ensures that the eNodeB chooses the second UE to be served on the same RE as the first UE such that their channels and lie in the opposite quadrants.
Another interesting result is the effect of the two characteristics of LTE precoders, i.e., low resolution and EGT. There is a slight improvement in the sum rate at medium SNR when the restriction of low resolution (LTE quantized precoders) is relaxed, i.e., eNodeB employs MF EGT precoders; however, there is a significant improvement in the sum rate when the restriction of EGT is eliminated, i.e the eNodeB employs MF precoders. This shows that the loss in spectral efficiency due to the employment of LTE precoders is mainly attributed to the EGT rather than their low resolution (quantization).
5. Performance analysis
where is the normalized minimum distance of the constellation χ_{1}, d_{free} is the free distance (minimum Hamming distance) of the code. Note that c_{1} and are the correct and error codewords, respectively. Eq. 25 clearly shows full diversity of the EGT for singleuser MIMO. Note that this result was earlier derived in [16] but was restricted to the case of BPSK. The same result was derived in [17] for EGT in MIMO systems using the approach of metrics of diversity order. Here, we have generalized this result and have adopted the natural approach of pairwise error probability to show the diversity order. Analysis of the EGT for multiuser MIMO system seemingly does not have closed form solution so we shall resort to the simulations for its analysis in Sec. 6.
6. Simulation results
Simulations are divided into three parts. In the first part, we look at the performance of the proposed interferenceaware receiver structure for the multiuser MIMO mode in LTE while second part is dedicated to the sensitivity analysis of this receiver structure to the knowledge of the constellation of interference. This sensitivity analysis is motivated by the fact that the DCI formats in the transmission mode 5 (multiuser MIMO) do not include the information of the constellation of the coscheduled UE. Third part looks at the diversity order of the EGT in both singleuser and multiuser MIMO modes in LTE.
7. Design of LTE precoder codebook with additional feedback
It was shown in the information theoretic analysis and was subsequently confirmed in the simulations that the loss in spectral efficiency due to the lowlevel quantized CSIT (LTE precoders) in the multiuser MIMO mode is more attributed to the EGT of the LTE codebook rather than its low resolution. It was also shown that EGT loses diversity in the multiuser MIMO mode. Focusing on these fundamental results, we now look at the design of the precoder codebook for future standardizations of LTE. Feedback of CSIT is expected to increase in these forthcoming wireless systems. However, the complexity associated with the feedback overhead combined with the low rate feedback channels would allow only a limited increase in the feedback. We therefore consider the case of two additional feedback bits for the quantized CSIT (precoder codebook) and look how these additional bits can be efficiently employed.
With this new precoding codebook design, the earlier described scheduling strategy remains same, i.e., for a UE to be scheduled in the multiuser MIMO mode, the eNodeB selects the second UE to be served on the same timefrequency resources (coscheduled UE) such that the desired signal strength is maximized while interference strength is minimized for both the UEs. So if UE1 has requested the precoder p_{1}, the eNodeB finds the precoding vector p_{2} in the codebook, which minimizes their crosscorrelation and then schedules the second UE with UE1, which has requested p_{2} as its desired precoding vector. The receiver structure being independent of the codebook design also remains same for these new precoding codebooks.
8. Conclusions
In this paper, we have looked at the feasibility of the multiuser MIMO for future wireless systems that are characterized by lowlevel quantization of CSIT. We have shown that multiuser MIMO can deliver its promised gains if the UEs resort to intelligent detection rather than the suboptimal singleuser detection. To this end, we have proposed a lowcomplexity interferenceaware receiver structure that is characterized by the exploitation of the structure of residual interference. We have analyzed two important characteristics of the LTE precoders, i.e., low resolution and EGT. We have shown that the performance loss of the LTE precoders in the multiuser MIMO mode is attributed to their characteristic of EGT rather than their low resolution. We have further shown that the EGT is characterized by full diversity in the singleuser MIMO mode but it loses diversity in the multiuser MIMO. Based on these fundamental results, we have proposed a design of the precoder codebook for forthcoming standardizations of LTE incorporating more levels of transmission.
Appendix A
Mutual information for finite alphabets
The above quantities can be easily approximated using sampling (MonteCarlo) methods with N_{ z } realizations of noise and realizations of the channel where the precoding matrix depends on the channel. So we can rewrite (29) as (30).
where are the number of channel realizations of the channel . Note that the precoding vector p_{1} is dependent on the channel .
Appendix B
Diversity analysis of EGT in singleuser MIMO
At high SNR, second term converges to while the third term converges to . So
Declarations
Acknowledgements
Eurecom's research is partially supported by its industrial partners: BMW, Bouygues Telecom, Cisco Systems, France Télécom, Hitachi Europe, SFR, Sharp, ST Microelectronics, Swisscom, Thales. The research work leading to this paper has also been partially supported by the European Commission under SAMURAI and IST FP7 research network of excellence NEWCOM++.
Authors’ Affiliations
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