Interleaved Training Strategy in Hybrid Massive MIMO

• Interleaved training strategy is an adaptive method that alternates beam training and user feedback to efficiently assess channel quality in hybrid massive MIMO systems.
• The methodology employs closed-form expressions for expected training length and outage probability, significantly lowering training overhead in both single-user and multi-user settings.
• Practical implementation leverages adaptive stopping, immediate feedback, and efficient beam assignment, enhancing throughput and energy efficiency, especially in sparse-channel regimes.

Interleaved training strategy refers to a class of adaptive, dynamically scheduled training mechanisms that alternate between system components, modalities, or tasks, intentionally breaking with traditional fixed-block or non-adaptive training schedules. The following sections synthesize the primary principles, mathematical formulations, implementation details, and real-world consequences of interleaved training as established in the context of hybrid massive MIMO downlink systems, with consideration for both single-user (SU) and multi-user (MU) architectures (Zhang et al., 2017).

1. Adaptive Interleaved Training Design for Massive MIMO

Interleaved training in the hybrid massive antenna downlink context fundamentally departs from static or “full-training” approaches, where a base station (BS) trains all available beams in a predetermined, rigid order before transmission. In interleaved training, training and feedback (pilot transmission and channel feedback) are concatenated in sequence: after each beam’s training, the user estimates and immediately feeds back the effective channel quality to the BS.

This concatenation makes the training length adaptive to the instantaneous channel realization. At each step, the set of beams with non-zero gains is assessed to determine whether they are sufficient to meet a target SNR requirement. If so, data transmission proceeds; if not, the process continues until a satisfactory beam subset is identified or all beams have been trained. This adaptive, realization-dependent process sharply contrasts with non-interleaved strategies that always require a fixed-length training phase, regardless of the underlying channel state.

In summary, the interleaved approach exploits real-time feedback to adaptively terminate training, minimizing unnecessary energy and time expenditures on beams that do not contribute meaningfully to transmission.

2. Analytical Characterization: Training Length and Outage Probability

Explicit closed-form expressions characterize both the expected training length and the system’s outage probability in the interleaved training scheme for SU.

Let $N_t$ denote the number of BS antennas, $L$ the number of channel paths, $N_{RF}$ the number of RF chains, and $\alpha$ the normalized SNR threshold. Let $P_i$ be the probability that training ends at the $i$th beam, with :

$$T_{\textrm{IT-SU}} = N_t - \sum_{i=1}^{N_t-1} (N_t - i)\, P_i$$

where for $i=1$,

$P_1 = \frac{L}{N_t}\, e^{-L\alpha/N_t}$

and $P_i$ for $2 \leq i \leq N_t-1$ involves multi-summations over combinatoric terms of the paths, as detailed in the paper’s Equations (8)-(9).

The outage probability, which measures the likelihood that the system cannot find an adequate set of beams after training, is given in closed form (Equation (14)) using the lower incomplete gamma function:

$$\text{out}(\text{IT-SU}) = \binom{L}{N_{RF}} \left[ \frac{\Upsilon\left(N_{RF},\frac{\alpha L}{N_t}\right)}{(N_{RF}-1)!} + \sum_{l=1}^{L-N_{RF}} (-1)^{N_{RF}+l-1} \frac{(L-N_{RF})!}{(L-N_{RF}-l)!\, l!} \left( \frac{N_{RF}}{l} \right)^{N_{RF}-1} \left( \frac{e^{ -(\cdots) } - 1 }{-1-\frac{l}{N_{RF}} - B(l)} \right) \right]$$

$B(l)$ is defined piecewise for $N_{RF}\ge 2$ and incorporates sums of terms involving the incomplete gamma function.

These formulas allow practitioners to quantitatively predict the impact of system parameters on the primary efficiency metrics.

3. Extension to Multi-User Systems: Joint Training and Beam Assignment

For MU scenarios, interleaved training becomes part of a joint design that additionally must solve a “feasible beam assignment” problem. The BS initially trains a minimal number of beams—at least the number of users, $U$, to ensure each user can estimate some effective channel. As extra beams are trained and user feedback arrives, the BS collects the set of “active” beams.

A beam assignment is feasible if each user is assigned a nonzero beam, and the resulting channel matrix is full-rank (avoiding singularity in zero-forcing precoding). The paper advances two assignment strategies:

• Optimal assignment: Exhaustively searches over all possible assignments from the feedback set $\mathcal{B}$ (complexity: $\mathcal{O}(|\mathcal{B}|^U)$).
• Max-min assignment: Sequentially assigns beams to users by maximizing the minimum effective gain, removing the assigned user and beam from contention (complexity: $\mathcal{O}(U^2|\mathcal{B}|^2)$). Simulations show this strategy yields near-optimal performance at much lower computational cost.

Once a feasible assignment satisfying the SNR requirement is found, data transmission is initiated with hybrid, analog-digital zero-forcing precoding.

4. Comparative Performance and Scaling Behavior

The interleaved training strategy achieves the same outage probability as full-training, non-interleaved approaches, but it does so with substantially lower training overhead—an effect amplified in sparse-channel regimes (smaller $L$).

• In the SU case, for $N_{RF}=1$, the average training length $T_{\textrm{IT-SU}} \approx N_t/(L+1)$ (Lemma 1). For $L=1$, this is roughly half the length of the full-training approach; as $L$ increases, the savings become even more pronounced.
• As $L$ increases proportionally with $N_t$, the training length in the interleaved scheme becomes bounded; in contrast, non-interleaved training always performs $N_t$ beam trainings irrespective of the underlying channel resolvability.
• Simulation studies confirm that for both SU and MU configurations, the interleaved design minimizes training cost without any deterioration in outage reliability, and outperforms partial-training (apriori beam selection) non-interleaved strategies for fixed training symbol budgets.

5. Implementation Considerations and Deployment

Deployment of interleaved training in hybrid massive MIMO systems involves:

• Immediate, recurrent feedback: Real-time reporting of effective channel conditions after each trained beam, instead of batching or deferred summary feedback.
• Adaptive stopping: The need for rapid channel-quality assessment logic at the user terminal and fast control signaling to terminate training early when SNR objectives are met.
• Task-specific controller: In MU settings, efficient, scalable heuristics (as with max-min assignment) for fast beam-user allocation and channel matrix invertibility checking.
• Analog-digital hardware: Support for quick reconfiguration of hybrid analog and digital precoders as the active beam set can change for each realization.

Practical implementation is especially attractive in mmWave or similar sparse-channel regimes, where reducing training symbol requirements frees substantial link resources for data communication and directly improves system throughput and energy efficiency.

6. Broader Implications and Future Directions

The interleaved training paradigm in massive antenna downlink systems underscores the value of adaptive protocol design tied to instantaneous channel conditions. Key implications include:

• The possibility of scaling to very large antenna arrays with bounded overhead.
• Enabling dynamic, resource-efficient scheduling in environments with highly variable or bursty channel conditions.
• Potential for generalized application in other context-adaptive multi-agent and multi-parameter wireless systems, particularly when combined with fast hardware feedback infrastructure.

This approach has already informed subsequent developments in training reduction techniques and is likely to influence future standards in sparse-channel wireless communication.