Navneet Garg

Precoder quantization for interference alignment with limited feedback

Interference Alignment is a promising technique for achieving higher rates by aligning interference at the receiver. To design such a system, the global channel state information at the transmitter (CSIT) as well as at the receiver is necessary. But in practice, it is hard to obtain this information, therefore, limited feedback is used to provide CSIT or the precoder design information to the transmitter. Conventionally, precoders are quantized at receiver by finding its best match in the codebook using chordal distance and its index is fedback to the transmitter. In this paper, instead of minimizing chordal distance, we propose algorithms with objectives that are derived from subspace alignment method, SINR maximization, or minimization of leakage interference power to measure the “goodness” of quantized vector. These algorithms achieve higher rates for small size codebooks. The rate loss has been analyzed for precoder quantization. We also find less computational intensive solution to find the desired vectors in the codebook. The simulation results show that for small codebooks, significant sumrate gains can be achieved for (2 × 2,1)3 for 2-6 bits of feedback per user, compared to quantization based on chordal distance, while for large codebooks, the chordal distance based quantization performs better.

Genetic max-SINR algorithm for interference alignment

In this paper, we propose interference alignment (IA) algorithms inspired by Genetic Algorithm (GA). By simulations for (2 × 2, 1)3 system, we observe that the existing max-SINR (MS) algorithm converges to different sumrates for different initializations of precoders. And the initializations for which sumrate is good, cannot be found trivially using channel state information. Also, in the case of limited feedback (LFB) of precoders, the sumrates can be achieved greater than that can be achieved using conventional chordal distance, if the precoder is selected properly along with receiver combining matrix. Therefore, in this paper, two algorithms are proposed inspired by GA: first, to make the max-SINR robust to initializations: MS-GA, and second, to achieve better sumrates in case of limited feedback: MS-GA-LFB. These optimal sumrates are obtained at the cost of increased computation complexity which is proportional to the population size chosen in the Genetic Algorithm. The simulation results show that the sum rates of the proposed algorithms match with that obtained using brute force approach to find the good initialization.

A quantization method for precoder feedback in interference channel

In this paper, we modeled the precoder feedback for interference channel as a combinatorial optimization problem. Conventionally, in limited feedback, chordal distance has been used to find the best precoder index from the codebook. But, the brute force approach on the problem shows that higher sumrates can be achieved with the same sized codebook, i.e, the same feedback bits. Thus, in this paper, we propose a method to get better sum rates in limited feedback. The simulation results show that the proposed approach perform close to brute force approach and gives better sum rates than the approaches like chordal distance, maximizing SINR, etc.

Interference alignment in cellular system with multiple D2D networks

In this paper, we have modeled underlaying multiple D2D networks into interference channel and used interference alignment (IA) in two different ways. In the first IA design, all the cell and D2D users (CUs & eNB and DUs & DRs) are considered in mitigating the interference, while in the second design, the group of CUs and eNB is omitted in IA design to reduce the overhead of channel state information (CSI). To show the distance or location dependence, the cross channel variance (τ) between DUs-eNB group and the CUs-DR groups has been varied. The rate loss upper bound between the two IA schemes is calculated that shows, the rate difference increases with increase in SNR and is proportional to cross channel variance. The simulation results show that for small values of τ, the second IA scheme gives almost similar sum rates. For large values of τ, the DU sum rates are low and show a constant rate loss. Thus, second IA technique can be utilized to reduce overhead in D2D communication.

Rate loss analysis for precoder feedback in interference channel with imperfect CSI

In this paper, we derive the rate loss upper bound for precoder feedback when imperfect channel state information (CSI) is available in interference channel. The upper bound shows that the loss caused due to uncertainty in the channel is proportional to the SNR. The quantization with chordal distance shows that rate loss due to quantization reduces with the increase in the level of uncertainty. And so, the less feedback bits are needed for higher uncertainty in the channel. The simulation results show that the imperfect CSI limits the sum rates achievable which can be obtained with less feedback bits with the increase in uncertainty variance.

Reduced dimension superimposed precoder feedback for interference alignment

In this paper, analog feedback of precoder is proposed for K-user interference channel with equal number of antennas at transmitters and receivers. We also consider the superimposed pilot based training scheme where training pilots and feedback data are sent simultaneously. This scheme requires the same number of time slots as non-superimposed one. In addition to this framework, we propose reduced dimension precoder feedback by utilizing the unit norm of the precoder. This reduced dimension feedback with multiple antennas improves the precoder estimation at transmitters, which improves the sumrates of the system. The simulation results verify that this reduced dimension precoder feedback schemes decrease the rate loss, and improve the sumrate.

Partially Loaded Superimposed Training Scheme for Large MIMO Uplink Systems

This paper proposes a new superimposed training (ST) scheme for uplink multi-user multi-cell system, where each base station, equipped with a large number of antennas (M), communicates to single antenna users. In uplink training phase, large number of users within limited coherence time introduces the pilot contamination, which causes two types of interferences in data estimation. The first type, which is referred as self interference, arises due to the dependence between channel estimate and estimation error of the same user, while the second type, known as cross interference, occurs because of the correlation between ST vectors of different users. In this paper, an ST scheme with variable data length is proposed for Rician fading channels. For simplicity of analysis, a single cell model is considered first to derive mean squared error and signal to interference plus noise ratio. The analysis is further extended to multi-cell system. Various limiting cases are investigated, and the design parameters viz., power allocation factor and length of data vector, are optimized. Simulation results verify that the proposed ST scheme reduces self interference, and yields sum rate improvement over conventional ST scheme.

Precoder Quantization vs Channel Quantization in Interference Channel with Limited Feedback

In this paper, we compare the precoder and channel feedback in interference channel (IC) when interference alignment (IA) is used. In literature, the channel direction has been quantized and fed back in IC. Here, we consider the precoder quantization and feedback (PQFB) in IC, and seek its benefits over channel feedback. The involvement of IA (where the alignment is sensitive to channel changes) and comparison of required time slots, codebook size and feedback bit rate, show that PQFB is a better choice. The theoretical rate loss for both schemes show that precoder feedback gives less loss in sum rate as compared to channel direction feedback. These results are verified with simulations.

Sum rate of K-user MIMO interference channel for finite constellation inputs with interference alignment

In this paper, we discuss the information rate with finite constellation inputs for interference channels. In literature, the information rate related analysis for finite constellations has been presented in Ganesan et al. and Wu et al. By using this analysis, they have provided an algorithm to maximize the sum rates but the interference effect has not been considered. In this paper, we derive the same sumrate expressions in a simpler manner for finite constellations, and apply three popular interference alignment (IA) algorithms to compare the sumrates and symbol error rate (SER) performances. The simulation results show that for (2 × 2, 1)3 system with BPSK and QPSK constellations, the max-SINR algorithm performs better in terms of sumrate and SER for finite constellation systems.